%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO905^6 : 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 : n025.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 09:55:11 AM UTC 2026
% Result : Theorem 89.60s 14.05s
% Output : Refutation 89.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 158
% Number of leaves : 26
% Syntax : Number of formulae : 1052 ( 690 unt; 0 typ; 11 def)
% Number of atoms : 34652 (1040 equ; 0 cnn)
% Maximal formula atoms : 159 ( 32 avg)
% Number of connectives : 90325 (2234 ~;1576 |;5290 &;58028 @)
% ( 11 <=>;10221 =>; 0 <=; 0 <~>)
% Maximal formula depth : 85 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 403 ( 403 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 76 usr; 17 con; 0-3 aty)
% (9675 !!;3290 ??; 0 @@+; 0 @@-)
% Number of variables : 14108 (12795 ^;1311 !; 2 ?;14108 :)
% 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(f3742,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2141,f2415,f2680,f2964,f2967,f2968,f2969,f3305,f3354,f3476,f3550,f3570,f3741]) ).
thf(f3741,plain,
( ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f3740]) ).
thf(f3740,plain,
( $false
| ~ spl0_17
| ~ spl0_22 ),
inference(trivial_inequality_removal,[status(thm)],[f3739]) ).
thf(f3739,plain,
( ( $false = $true )
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3738,f3612]) ).
thf(f3612,plain,
( ! [X26: mworld] :
( $false
= ( v3 @ X26 ) )
| ~ spl0_17 ),
inference(not_proxy_clausification,[status(thm)],[f3605]) ).
thf(f3605,plain,
( ! [X26: mworld] :
( ( ~ ( v3 @ X26 ) )
= $true )
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f3604]) ).
thf(f3604,plain,
( ! [X26: mworld] :
( $true
= ( $true
=> ~ ( v3 @ X26 ) ) )
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f3603,f358]) ).
thf(f358,plain,
! [X2: mworld,X1: mworld] :
( ( mrel @ X1 @ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f357]) ).
thf(f357,plain,
! [X1: mworld] :
( ( !! @ mworld @ ( mrel @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f356]) ).
thf(f356,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] : ( !! @ mworld @ ( mrel @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f349]) ).
thf(f349,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] : ( !! @ mworld @ ( mrel @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f211]) ).
thf(f211,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] : ( mrel @ Y0 @ Y1 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f101]) ).
thf(f101,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] : ( mrel @ Y0 @ Y1 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f100]) ).
thf(f100,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X1 @ X0 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X4: mworld,X2: mworld] : ( mrel @ X2 @ X4 ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mrel_universal) ).
thf(f3603,plain,
( ! [X26: mworld,X25: mworld] :
( $true
= ( ( mrel @ X25 @ X26 )
=> ~ ( v3 @ X26 ) ) )
| ~ spl0_17 ),
inference(beta_eta_normalization,[status(thm)],[f3602]) ).
thf(f3602,plain,
( ! [X26: mworld,X25: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X25 @ Y0 )
=> ~ ( v3 @ Y0 ) )
@ X26 ) )
| ~ spl0_17 ),
inference(pi_clausification,[status(thm)],[f3601]) ).
thf(f3601,plain,
( ! [X25: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X25 @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f3600]) ).
thf(f3600,plain,
( ! [X25: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X25 @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
= $true )
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f3599,f358]) ).
thf(f3599,plain,
( ! [X24: mworld,X25: mworld] :
( ( ( mrel @ X24 @ X25 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X25 @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
= $true )
| ~ spl0_17 ),
inference(beta_eta_normalization,[status(thm)],[f3598]) ).
thf(f3598,plain,
( ! [X24: mworld,X25: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) )
@ X25 )
= $true )
| ~ spl0_17 ),
inference(pi_clausification,[status(thm)],[f2963]) ).
thf(f2963,plain,
( ! [X24: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f2962]) ).
thf(f2962,definition,
( spl0_17
<=> ! [X24: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f3738,plain,
( ! [X10: mworld] :
( ( v3 @ X10 )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3737]) ).
thf(f3737,plain,
( ! [X10: mworld] :
( ( $true
=> ( v3 @ X10 ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3736,f358]) ).
thf(f3736,plain,
( ! [X10: mworld,X9: mworld] :
( ( ( mrel @ X9 @ X10 )
=> ( v3 @ X10 ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3735]) ).
thf(f3735,plain,
( ! [X10: mworld,X9: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( v3 @ Y0 ) )
@ X10 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3734]) ).
thf(f3734,plain,
( ! [X9: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( v3 @ Y0 ) ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3733]) ).
thf(f3733,plain,
( ! [X9: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3732,f358]) ).
thf(f3732,plain,
( ! [X8: mworld,X9: mworld] :
( ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( v3 @ Y0 ) ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3731]) ).
thf(f3731,plain,
( ! [X8: mworld,X9: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) )
@ X9 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3730]) ).
thf(f3730,plain,
( ! [X8: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3729]) ).
thf(f3729,plain,
( ! [X8: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3728,f358]) ).
thf(f3728,plain,
( ! [X8: mworld,X7: mworld] :
( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3727]) ).
thf(f3727,plain,
( ! [X8: mworld,X7: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v3 @ Y2 ) ) ) ) ) )
@ X8 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3726]) ).
thf(f3726,plain,
( ! [X7: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v3 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3725]) ).
thf(f3725,plain,
( ! [X7: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v3 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3724,f358]) ).
thf(f3724,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 )
=> ( v3 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3723]) ).
thf(f3723,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 )
=> ( v3 @ Y3 ) ) ) ) ) ) ) )
@ X7 )
= $true )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3722]) ).
thf(f3722,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 )
=> ( v3 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3721]) ).
thf(f3721,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 )
=> ( v3 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3720,f358]) ).
thf(f3720,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 )
=> ( v3 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3719]) ).
thf(f3719,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 )
=> ( v3 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3718]) ).
thf(f3718,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 )
=> ( v3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3717]) ).
thf(f3717,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 )
=> ( v3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3716,f358]) ).
thf(f3716,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 )
=> ( v3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3715]) ).
thf(f3715,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 )
=> ( v3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3714]) ).
thf(f3714,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 )
=> ( v3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3713]) ).
thf(f3713,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 )
=> ( v3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3712,f358]) ).
thf(f3712,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 )
=> ( v3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3711]) ).
thf(f3711,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 )
=> ( v3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3710]) ).
thf(f3710,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 )
=> ( v3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(trivial_inequality_removal,[status(thm)],[f3706]) ).
thf(f3706,plain,
( ! [X3: mworld] :
( ( $false = $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 )
=> ( v3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(backward_demodulation,[status(thm)],[f2754,f3704]) ).
thf(f3704,plain,
( ! [X5: mworld] :
( $false
= ( v10 @ X5 ) )
| ~ spl0_22 ),
inference(not_proxy_clausification,[status(thm)],[f3703]) ).
thf(f3703,plain,
( ! [X5: mworld] :
( ( ~ ( v10 @ X5 ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3702]) ).
thf(f3702,plain,
( ! [X5: mworld] :
( $true
= ( $true
=> ~ ( v10 @ X5 ) ) )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3701,f358]) ).
thf(f3701,plain,
( ! [X4: mworld,X5: mworld] :
( ( ( mrel @ X4 @ X5 )
=> ~ ( v10 @ X5 ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3700]) ).
thf(f3700,plain,
( ! [X4: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ~ ( v10 @ Y0 ) )
@ X5 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3699]) ).
thf(f3699,plain,
( ! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ~ ( v10 @ Y0 ) ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3698]) ).
thf(f3698,plain,
( ! [X4: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ~ ( v10 @ Y0 ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3697,f358]) ).
thf(f3697,plain,
( ! [X3: mworld,X4: mworld] :
( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ~ ( v10 @ Y0 ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3696]) ).
thf(f3696,plain,
( ! [X3: mworld,X4: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) )
@ X4 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3695]) ).
thf(f3695,plain,
( ! [X3: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3694]) ).
thf(f3694,plain,
( ! [X3: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3693,f358]) ).
thf(f3693,plain,
( ! [X2: mworld,X3: mworld] :
( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3692]) ).
thf(f3692,plain,
( ! [X2: mworld,X3: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) )
@ X3 )
= $true )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3691]) ).
thf(f3691,plain,
( ! [X2: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3690]) ).
thf(f3690,plain,
( ! [X2: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3689,f358]) ).
thf(f3689,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 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3688]) ).
thf(f3688,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 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) )
@ X2 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3687]) ).
thf(f3687,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 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3686]) ).
thf(f3686,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 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3685,f358]) ).
thf(f3685,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( mrel @ ( sK15 @ 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 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3682]) ).
thf(f3682,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK15 @ 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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X1 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3675]) ).
thf(f3675,plain,
( ! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK15 @ 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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3674]) ).
thf(f3674,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK15 @ 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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| $false )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3673]) ).
thf(f3673,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK15 @ 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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ~ $true )
= $true )
| ~ spl0_22 ),
inference(superposition,[status(thm)],[f3670,f2336]) ).
thf(f2336,plain,
! [X13: mworld] :
( ( v15 @ ( sK15 @ X13 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2335]) ).
thf(f2335,plain,
! [X13: mworld] :
( ( ( v15 @ ( sK15 @ X13 ) )
& $true )
= $true ),
inference(forward_demodulation,[status(thm)],[f2334,f358]) ).
thf(f2334,plain,
! [X13: mworld] :
( ( ( v15 @ ( sK15 @ X13 ) )
& ( mrel @ X13 @ ( sK15 @ X13 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2333]) ).
thf(f2333,plain,
! [X13: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) )
@ ( sK15 @ X13 ) ) ),
inference(sigma_clausification,[status(thm)],[f2316]) ).
thf(f2316,plain,
! [X13: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2314]) ).
thf(f2314,plain,
! [X13: mworld] :
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2313]) ).
thf(f2313,plain,
! [X13: mworld] :
( ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f2306,f2312]) ).
thf(f2312,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(binary_proxy_clausification,[status(thm)],[f2306]) ).
thf(f2306,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)],[f2305]) ).
thf(f2305,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 )
=> ( ( !! @ 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(forward_demodulation,[status(thm)],[f2304,f358]) ).
thf(f2304,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 )
=> ( ( !! @ 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(beta_eta_normalization,[status(thm)],[f2303]) ).
thf(f2303,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 )
=> ( ( !! @ 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 )
= $true ),
inference(pi_clausification,[status(thm)],[f2102]) ).
thf(f2102,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(binary_proxy_clausification,[status(thm)],[f2096]) ).
thf(f2096,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 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2095]) ).
thf(f2095,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)],[f2094,f358]) ).
thf(f2094,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)],[f2093]) ).
thf(f2093,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 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [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 ) ),
inference(pi_clausification,[status(thm)],[f2088]) ).
thf(f2088,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 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2087]) ).
thf(f2087,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)],[f2086,f1785]) ).
thf(f1785,plain,
! [X1: mworld] :
( ( ?? @ mworld @ ( mrel @ X1 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1784]) ).
thf(f1784,plain,
! [X1: mworld] :
( $true
= ( $true
& ( ?? @ mworld @ ( mrel @ X1 ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1778,f1781]) ).
thf(f1781,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 )
=> ( ( !! @ 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(binary_proxy_clausification,[status(thm)],[f1778]) ).
thf(f1778,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)],[f1777]) ).
thf(f1777,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)],[f1776,f358]) ).
thf(f1776,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 )
=> ( ( !! @ 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(beta_eta_normalization,[status(thm)],[f1775]) ).
thf(f1775,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)],[f1774]) ).
thf(f1774,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)],[f1773]) ).
thf(f1773,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)],[f339,f1771]) ).
thf(f1771,plain,
( ( ?? @ mworld @ ( mrel @ mactual ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f339]) ).
thf(f339,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 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ mactual ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f338]) ).
thf(f338,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] : ( 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 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f337]) ).
thf(f337,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 @ ( mrel @ mactual ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f336]) ).
thf(f336,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)],[f335]) ).
thf(f335,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)],[f251]) ).
thf(f251,plain,
( $true
= ( ^ [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 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f191,f226,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f188,f188,f188,f188,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f188,f188,f188,f188,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f188,f188,f188,f188,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f188,f188,f188,f188]) ).
thf(f213,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
thf(f71,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f70]) ).
thf(f70,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.aSc01fn5sj/DTF2THF_26726.p',mnot_def) ).
thf(f188,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
thf(f157,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f156]) ).
thf(f156,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) )
= mdia ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
? [X4: mworld] :
( ( mrel @ X2 @ X4 )
& ( X0 @ X4 ) ) )
= mdia ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mdia_def) ).
thf(f239,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
thf(f135,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f134]) ).
thf(f134,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mbox_def) ).
thf(f227,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
thf(f77,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mand_def) ).
thf(f226,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
thf(f158,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.aSc01fn5sj/DTF2THF_26726.p',mlocal_def) ).
thf(f191,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)],[f73]) ).
thf(f73,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)],[f72]) ).
thf(f72,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.aSc01fn5sj/DTF2THF_26726.p',alt1) ).
thf(f2086,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)],[f2085]) ).
thf(f2085,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 ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2084,f358]) ).
thf(f2084,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)],[f2083]) ).
thf(f2083,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)],[f2078]) ).
thf(f2078,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)],[f2077]) ).
thf(f2077,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)],[f2076,f1785]) ).
thf(f2076,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)],[f2075]) ).
thf(f2075,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 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X10 ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2074,f358]) ).
thf(f2074,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)],[f2073]) ).
thf(f2073,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 )
=> ( ( !! @ mworld
@ ^ [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 ) ),
inference(pi_clausification,[status(thm)],[f2066]) ).
thf(f2066,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 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2065]) ).
thf(f2065,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)],[f2064,f1785]) ).
thf(f2064,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)],[f2063]) ).
thf(f2063,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)],[f2062,f358]) ).
thf(f2062,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 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [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(beta_eta_normalization,[status(thm)],[f2061]) ).
thf(f2061,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)],[f2055]) ).
thf(f2055,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)],[f2054]) ).
thf(f2054,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)],[f2053,f1785]) ).
thf(f2053,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 )
=> ( ( !! @ 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(boolean_simplification,[status(thm)],[f2052]) ).
thf(f2052,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)],[f2051,f358]) ).
thf(f2051,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 )
=> ( ( !! @ mworld
@ ^ [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(beta_eta_normalization,[status(thm)],[f2050]) ).
thf(f2050,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)],[f1892]) ).
thf(f1892,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)],[f1878]) ).
thf(f1878,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 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1877]) ).
thf(f1877,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)],[f1876,f358]) ).
thf(f1876,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 )
=> ( ( !! @ 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(beta_eta_normalization,[status(thm)],[f1875]) ).
thf(f1875,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 )
=> ( ( !! @ 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 ) ),
inference(pi_clausification,[status(thm)],[f1863]) ).
thf(f1863,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 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1862]) ).
thf(f1862,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)],[f1855,f1860]) ).
thf(f1860,plain,
! [X6: mworld] :
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1855]) ).
thf(f1855,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)],[f1854]) ).
thf(f1854,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 )
=> ( ( !! @ 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(forward_demodulation,[status(thm)],[f1853,f358]) ).
thf(f1853,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 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ 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(beta_eta_normalization,[status(thm)],[f1852]) ).
thf(f1852,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 )
=> ( ( !! @ 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 ) ),
inference(pi_clausification,[status(thm)],[f1818]) ).
thf(f1818,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 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1817]) ).
thf(f1817,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 ) ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f1810,f1815]) ).
thf(f1815,plain,
! [X5: mworld] :
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1810]) ).
thf(f1810,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)],[f1809]) ).
thf(f1809,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)],[f1808,f358]) ).
thf(f1808,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 )
=> ( ( !! @ 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(beta_eta_normalization,[status(thm)],[f1807]) ).
thf(f1807,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 )
=> ( ( !! @ 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 ) ),
inference(pi_clausification,[status(thm)],[f1806]) ).
thf(f1806,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(boolean_simplification,[status(thm)],[f1805]) ).
thf(f1805,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 ) ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f1802,f1803]) ).
thf(f1803,plain,
! [X4: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f1802]) ).
thf(f1802,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 )
=> ( ( !! @ 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(boolean_simplification,[status(thm)],[f1801]) ).
thf(f1801,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 )
=> ( ( !! @ 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(forward_demodulation,[status(thm)],[f1800,f358]) ).
thf(f1800,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)],[f1799]) ).
thf(f1799,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 )
=> ( ( !! @ 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 ) ),
inference(pi_clausification,[status(thm)],[f1798]) ).
thf(f1798,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)],[f1797]) ).
thf(f1797,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)],[f1796,f1785]) ).
thf(f1796,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 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X3 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1795]) ).
thf(f1795,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)],[f1794,f358]) ).
thf(f1794,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 )
=> ( ( !! @ 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(beta_eta_normalization,[status(thm)],[f1793]) ).
thf(f1793,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 )
=> ( ( !! @ 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 )
= $true ),
inference(pi_clausification,[status(thm)],[f1792]) ).
thf(f1792,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)],[f1791]) ).
thf(f1791,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)],[f1790,f1785]) ).
thf(f1790,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)],[f1789]) ).
thf(f1789,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)],[f1788,f358]) ).
thf(f1788,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)],[f1787]) ).
thf(f1787,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)],[f1781]) ).
thf(f3670,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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ X6 ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3669]) ).
thf(f3669,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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ X6 ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3668,f358]) ).
thf(f3668,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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ X6 ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3667]) ).
thf(f3667,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 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y0 ) ) )
@ X6 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3666]) ).
thf(f3666,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 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y0 ) ) ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3665]) ).
thf(f3665,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 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y0 ) ) ) ) ) )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3664,f358]) ).
thf(f3664,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 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3663]) ).
thf(f3663,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 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) )
@ X5 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3662]) ).
thf(f3662,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 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3661]) ).
thf(f3661,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 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3660,f358]) ).
thf(f3660,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 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3659]) ).
thf(f3659,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 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) )
@ X4 )
= $true )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3658]) ).
thf(f3658,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 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3657]) ).
thf(f3657,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 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3656,f358]) ).
thf(f3656,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 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3655]) ).
thf(f3655,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 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) )
@ X3 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3301]) ).
thf(f3301,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 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(avatar_component_clause,[status(thm)],[f3300]) ).
thf(f3300,definition,
( spl0_22
<=> ! [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 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition]) ).
thf(f2754,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 )
=> ( v3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( v10 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f2753]) ).
thf(f2753,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 )
=> ( v3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ X3 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2752]) ).
thf(f2752,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 )
=> ( v3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ X3 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2751,f358]) ).
thf(f2751,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 )
=> ( v3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ X3 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2750]) ).
thf(f2750,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 )
=> ( v3 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y0 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f2742]) ).
thf(f2742,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 )
=> ( v3 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2741]) ).
thf(f2741,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 )
=> ( v3 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2740,f358]) ).
thf(f2740,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 )
=> ( v3 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2739]) ).
thf(f2739,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 )
=> ( v3 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f2733]) ).
thf(f2733,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 )
=> ( v3 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2732]) ).
thf(f2732,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 )
=> ( v3 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2730,f358]) ).
thf(f2730,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ( mrel @ ( sK18 @ 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 )
=> ( v3 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2728]) ).
thf(f2728,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK18 @ 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 )
=> ( v3 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f2722]) ).
thf(f2722,plain,
! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK18 @ 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 )
=> ( v3 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2721]) ).
thf(f2721,plain,
! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK18 @ 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 )
=> ( v3 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) )
| $false )
= $true ),
inference(boolean_simplification,[status(thm)],[f2717]) ).
thf(f2717,plain,
! [X0: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK18 @ 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 )
=> ( v3 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) )
| ~ $true ) ),
inference(superposition,[status(thm)],[f2234,f2657]) ).
thf(f2657,plain,
! [X15: mworld] :
( $true
= ( v13 @ ( sK18 @ X15 ) ) ),
inference(boolean_simplification,[status(thm)],[f2656]) ).
thf(f2656,plain,
! [X15: mworld] :
( $true
= ( ( v13 @ ( sK18 @ X15 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2646,f358]) ).
thf(f2646,plain,
! [X15: mworld] :
( $true
= ( ( v13 @ ( sK18 @ X15 ) )
& ( mrel @ X15 @ ( sK18 @ X15 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2645]) ).
thf(f2645,plain,
! [X15: mworld] :
( ( ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) )
@ ( sK18 @ X15 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f2644]) ).
thf(f2644,plain,
! [X15: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2643]) ).
thf(f2643,plain,
! [X15: mworld] :
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f2640,f2641]) ).
thf(f2641,plain,
! [X15: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2640]) ).
thf(f2640,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)],[f2639]) ).
thf(f2639,plain,
! [X15: mworld] :
( $true
= ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f2636,f2638]) ).
thf(f2638,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)],[f2636]) ).
thf(f2636,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)],[f2635]) ).
thf(f2635,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)],[f2634,f358]) ).
thf(f2634,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)],[f2633]) ).
thf(f2633,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)],[f2541]) ).
thf(f2541,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 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2533]) ).
thf(f2533,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)],[f2532]) ).
thf(f2532,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)],[f2531,f358]) ).
thf(f2531,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)],[f2530]) ).
thf(f2530,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)],[f2312]) ).
thf(f2234,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 )
=> ( v3 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) )
| ~ ( v13 @ X10 ) ) ),
inference(boolean_simplification,[status(thm)],[f2233]) ).
thf(f2233,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 )
=> ( v3 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) )
| ~ ( v13 @ X10 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2232,f358]) ).
thf(f2232,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 )
=> ( v3 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) )
| ~ ( v13 @ X10 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2231]) ).
thf(f2231,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 )
=> ( v3 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y0 ) ) )
@ X10 )
= $true ),
inference(pi_clausification,[status(thm)],[f2230]) ).
thf(f2230,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 )
=> ( v3 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2229]) ).
thf(f2229,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 )
=> ( v3 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2228,f358]) ).
thf(f2228,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 )
=> ( v3 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2227]) ).
thf(f2227,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 )
=> ( v3 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y1 ) ) ) ) )
@ X9 ) ),
inference(pi_clausification,[status(thm)],[f2226]) ).
thf(f2226,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 )
=> ( v3 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2225]) ).
thf(f2225,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 )
=> ( v3 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y1 ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2224,f358]) ).
thf(f2224,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 )
=> ( v3 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2223]) ).
thf(f2223,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 )
=> ( v3 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y2 ) ) ) ) ) ) )
@ X8 )
= $true ),
inference(pi_clausification,[status(thm)],[f2222]) ).
thf(f2222,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 )
=> ( v3 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2221]) ).
thf(f2221,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 )
=> ( v3 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2220,f358]) ).
thf(f2220,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 )
=> ( v3 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2219]) ).
thf(f2219,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 )
=> ( v3 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y3 ) ) ) ) ) ) ) ) )
@ X7 ) ),
inference(pi_clausification,[status(thm)],[f2218]) ).
thf(f2218,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 )
=> ( v3 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2217]) ).
thf(f2217,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 )
=> ( v3 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2216,f358]) ).
thf(f2216,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 )
=> ( v3 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2215]) ).
thf(f2215,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 )
=> ( v3 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ),
inference(pi_clausification,[status(thm)],[f2213]) ).
thf(f2213,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 )
=> ( v3 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2212]) ).
thf(f2212,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 )
=> ( v3 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2211,f358]) ).
thf(f2211,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 )
=> ( v3 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2210]) ).
thf(f2210,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 )
=> ( v3 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f2205]) ).
thf(f2205,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 )
=> ( v3 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2204]) ).
thf(f2204,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 )
=> ( v3 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2203,f358]) ).
thf(f2203,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 )
=> ( v3 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2202]) ).
thf(f2202,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 )
=> ( v3 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f2197]) ).
thf(f2197,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 )
=> ( v3 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2196]) ).
thf(f2196,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 )
=> ( v3 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2195,f358]) ).
thf(f2195,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 )
=> ( v3 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2194]) ).
thf(f2194,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 )
=> ( v3 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f2189]) ).
thf(f2189,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 )
=> ( v3 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2188]) ).
thf(f2188,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 )
=> ( v3 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2187,f358]) ).
thf(f2187,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 )
=> ( v3 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2186]) ).
thf(f2186,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 )
=> ( v3 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f2181]) ).
thf(f2181,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 )
=> ( v3 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2180]) ).
thf(f2180,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 )
=> ( v3 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2178,f358]) ).
thf(f2178,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v3 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2176]) ).
thf(f2176,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v3 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1975]) ).
thf(f1975,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v3 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1973]) ).
thf(f1973,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v3 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| $false )
= $true ),
inference(superposition,[status(thm)],[f989,f1964]) ).
thf(f1964,plain,
! [X5: mworld] :
( ( v23 @ ( sK9 @ X5 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f1953]) ).
thf(f1953,plain,
! [X5: mworld] :
( $true
= ( ~ ( v23 @ ( sK9 @ X5 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1952]) ).
thf(f1952,plain,
! [X5: mworld] :
( ( ~ ( v23 @ ( sK9 @ X5 ) )
& $true )
= $true ),
inference(forward_demodulation,[status(thm)],[f1951,f358]) ).
thf(f1951,plain,
! [X5: mworld] :
( ( ~ ( v23 @ ( sK9 @ X5 ) )
& ( mrel @ X5 @ ( sK9 @ X5 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1950]) ).
thf(f1950,plain,
! [X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ~ ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) )
@ ( sK9 @ X5 ) ) ),
inference(sigma_clausification,[status(thm)],[f1938]) ).
thf(f1938,plain,
! [X5: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1937]) ).
thf(f1937,plain,
! [X5: mworld] :
( $true
= ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1815,f1936]) ).
thf(f1936,plain,
! [X5: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1815]) ).
thf(f989,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 )
=> ( v3 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ X6 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f988]) ).
thf(f988,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 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v3 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ X6 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f987,f358]) ).
thf(f987,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 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v3 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ X6 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f986]) ).
thf(f986,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 )
=> ( v3 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y0 ) ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f985]) ).
thf(f985,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 )
=> ( v3 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f984]) ).
thf(f984,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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ 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 )
=> ( v3 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f983,f358]) ).
thf(f983,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 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v3 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f982]) ).
thf(f982,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 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v3 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y1 ) ) ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f981]) ).
thf(f981,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 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v3 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f980]) ).
thf(f980,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 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v3 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y1 ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f979,f358]) ).
thf(f979,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 )
=> ( v3 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f978]) ).
thf(f978,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 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v3 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y2 ) ) ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f977]) ).
thf(f977,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 )
=> ( v3 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f976]) ).
thf(f976,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 )
=> ( v3 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f975,f358]) ).
thf(f975,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 )
=> ( v3 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f974]) ).
thf(f974,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 )
=> ( v3 @ Y23 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y3 ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f973]) ).
thf(f973,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 )
=> ( v3 @ Y23 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f972]) ).
thf(f972,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 )
=> ( v3 @ Y23 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f971,f358]) ).
thf(f971,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 )
=> ( v3 @ Y23 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f970]) ).
thf(f970,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 )
=> ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( v3 @ Y24 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f969]) ).
thf(f969,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 )
=> ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( v3 @ Y24 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f968]) ).
thf(f968,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 )
=> ( v3 @ Y24 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f967,f358]) ).
thf(f967,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 )
=> ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( v3 @ Y24 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f966]) ).
thf(f966,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 )
=> ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( v3 @ Y25 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y18 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f344]) ).
thf(f344,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 )
=> ( v3 @ Y25 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y18 ) ) ) ) ) ) ) )
| ~ ( v13 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v23 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f294]) ).
thf(f294,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 > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v23
@ ( ^ [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 )
@ v13 )
@ ( ^ [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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f242,f226,f239,f239,f239,f239,f239,f239,f201,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f201,f213,f239,f239,f239,f201,f239,f239,f239,f239,f239,f239,f239]) ).
thf(f201,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
thf(f117,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f116]) ).
thf(f116,plain,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( mor
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mor_def) ).
thf(f242,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f91]) ).
thf(f91,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f90]) ).
thf(f90,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod33) ).
thf(f3570,plain,
~ spl0_16,
inference(avatar_contradiction_clause,[status(thm)],[f3569]) ).
thf(f3569,plain,
( $false
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f3565]) ).
thf(f3565,plain,
( ( $false = $true )
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f2960,f2929]) ).
thf(f2929,plain,
! [X22: mworld] :
( ( v6 @ ( sK25 @ X22 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f2922]) ).
thf(f2922,plain,
! [X22: mworld] :
( $true
= ( ~ ( v6 @ ( sK25 @ X22 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2921]) ).
thf(f2921,plain,
! [X22: mworld] :
( $true
= ( ~ ( v6 @ ( sK25 @ X22 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2920,f358]) ).
thf(f2920,plain,
! [X22: mworld] :
( ( ~ ( v6 @ ( sK25 @ X22 ) )
& ( mrel @ X22 @ ( sK25 @ X22 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2919]) ).
thf(f2919,plain,
! [X22: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ~ ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) )
@ ( sK25 @ X22 ) ) ),
inference(sigma_clausification,[status(thm)],[f2898]) ).
thf(f2898,plain,
! [X22: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2897]) ).
thf(f2897,plain,
! [X22: mworld] :
( ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f2891,f2896]) ).
thf(f2896,plain,
! [X22: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2891]) ).
thf(f2891,plain,
! [X22: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2886]) ).
thf(f2886,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 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2885]) ).
thf(f2885,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)],[f2884,f358]) ).
thf(f2884,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)],[f2883]) ).
thf(f2883,plain,
! [X21: mworld,X22: mworld] :
( $true
= ( ^ [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 ) ),
inference(pi_clausification,[status(thm)],[f2840]) ).
thf(f2840,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(binary_proxy_clausification,[status(thm)],[f2834]) ).
thf(f2834,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)],[f2833]) ).
thf(f2833,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)],[f2832,f358]) ).
thf(f2832,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)],[f2831]) ).
thf(f2831,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)],[f2826]) ).
thf(f2826,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 ),
inference(boolean_simplification,[status(thm)],[f2825]) ).
thf(f2825,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)],[f2821,f2823]) ).
thf(f2823,plain,
! [X20: mworld] :
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2821]) ).
thf(f2821,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)],[f2820]) ).
thf(f2820,plain,
! [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 )
=> ( ( !! @ 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(forward_demodulation,[status(thm)],[f2819,f358]) ).
thf(f2819,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)],[f2818]) ).
thf(f2818,plain,
! [X19: mworld,X20: mworld] :
( $true
= ( ^ [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 ) ),
inference(pi_clausification,[status(thm)],[f2813]) ).
thf(f2813,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 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2812]) ).
thf(f2812,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 ) ) ) ) ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2811,f1785]) ).
thf(f2811,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)],[f2810]) ).
thf(f2810,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 )
=> ( ( !! @ 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(forward_demodulation,[status(thm)],[f2809,f358]) ).
thf(f2809,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)],[f2808]) ).
thf(f2808,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)],[f2803]) ).
thf(f2803,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)],[f2802]) ).
thf(f2802,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)],[f2801,f1785]) ).
thf(f2801,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)],[f2800]) ).
thf(f2800,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)],[f2799,f358]) ).
thf(f2799,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)],[f2798]) ).
thf(f2798,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)],[f2793]) ).
thf(f2793,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 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2792]) ).
thf(f2792,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)],[f2791,f1785]) ).
thf(f2791,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 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X17 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2790]) ).
thf(f2790,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)],[f2789,f358]) ).
thf(f2789,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)],[f2788]) ).
thf(f2788,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 )
=> ( ( !! @ 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 )
= $true ),
inference(pi_clausification,[status(thm)],[f2783]) ).
thf(f2783,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)],[f2782]) ).
thf(f2782,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 )
= $true ),
inference(forward_demodulation,[status(thm)],[f2781,f1785]) ).
thf(f2781,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)],[f2780]) ).
thf(f2780,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)],[f2779,f358]) ).
thf(f2779,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)],[f2778]) ).
thf(f2778,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)],[f2638]) ).
thf(f2960,plain,
( ! [X23: mworld] :
( ( v6 @ X23 )
= $true )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f2959]) ).
thf(f2959,definition,
( spl0_16
<=> ! [X23: mworld] :
( ( v6 @ X23 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f3550,plain,
( spl0_16
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_split_clause,[status(thm)],[f3549,f3303,f2678,f2959]) ).
thf(f2678,definition,
( spl0_15
<=> ! [X11: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( v10 @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f3303,definition,
( spl0_23
<=> ! [X1: mworld] :
( $true
= ( v20 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition]) ).
thf(f3549,plain,
( ! [X8: mworld] :
( ( v6 @ X8 )
= $true )
| ~ spl0_15
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3548]) ).
thf(f3548,plain,
( ! [X8: mworld] :
( ( $true
=> ( v6 @ X8 ) )
= $true )
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3547,f358]) ).
thf(f3547,plain,
( ! [X8: mworld,X7: mworld] :
( $true
= ( ( mrel @ X7 @ X8 )
=> ( v6 @ X8 ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3546]) ).
thf(f3546,plain,
( ! [X8: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( v6 @ Y0 ) )
@ X8 )
= $true )
| ~ spl0_15
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3541]) ).
thf(f3541,plain,
( ! [X7: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( v6 @ Y0 ) ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3540]) ).
thf(f3540,plain,
( ! [X7: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( v6 @ Y0 ) ) ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3539,f358]) ).
thf(f3539,plain,
( ! [X6: mworld,X7: mworld] :
( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( v6 @ Y0 ) ) ) )
= $true )
| ~ spl0_15
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3538]) ).
thf(f3538,plain,
( ! [X6: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v6 @ Y1 ) ) ) )
@ X7 )
= $true )
| ~ spl0_15
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3533]) ).
thf(f3533,plain,
( ! [X6: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v6 @ Y1 ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3532]) ).
thf(f3532,plain,
( ! [X6: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v6 @ Y1 ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3531,f358]) ).
thf(f3531,plain,
( ! [X6: mworld,X5: mworld] :
( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v6 @ Y1 ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3530]) ).
thf(f3530,plain,
( ! [X6: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v6 @ Y2 ) ) ) ) ) )
@ X6 ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3525]) ).
thf(f3525,plain,
( ! [X5: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v6 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3524]) ).
thf(f3524,plain,
( ! [X5: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v6 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3523,f358]) ).
thf(f3523,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 )
=> ( v6 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3522]) ).
thf(f3522,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 )
=> ( v6 @ Y3 ) ) ) ) ) ) ) )
@ X5 ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3517]) ).
thf(f3517,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 )
=> ( v6 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3516]) ).
thf(f3516,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 )
=> ( v6 @ Y3 ) ) ) ) ) ) ) ) )
| $false )
= $true )
| ~ spl0_15
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3515]) ).
thf(f3515,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 )
=> ( v6 @ Y3 ) ) ) ) ) ) ) ) )
| ~ $true ) )
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3514,f2986]) ).
thf(f2986,plain,
( ! [X12: mworld] :
( ( v10 @ X12 )
= $true )
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f2985]) ).
thf(f2985,plain,
( ! [X12: mworld] :
( $true
= ( $true
=> ( v10 @ X12 ) ) )
| ~ spl0_15 ),
inference(forward_demodulation,[status(thm)],[f2984,f358]) ).
thf(f2984,plain,
( ! [X11: mworld,X12: mworld] :
( ( ( mrel @ X11 @ X12 )
=> ( v10 @ X12 ) )
= $true )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f2983]) ).
thf(f2983,plain,
( ! [X11: mworld,X12: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( v10 @ Y0 ) )
@ X12 ) )
| ~ spl0_15 ),
inference(pi_clausification,[status(thm)],[f2679]) ).
thf(f2679,plain,
( ! [X11: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( v10 @ Y0 ) ) )
= $true )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f2678]) ).
thf(f3514,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 )
=> ( v6 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ X4 ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3513]) ).
thf(f3513,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 )
=> ( v6 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ X4 ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3512,f358]) ).
thf(f3512,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 )
=> ( v6 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ X4 ) ) )
= $true )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3511]) ).
thf(f3511,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 )
=> ( v6 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y0 ) ) )
@ X4 ) )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3506]) ).
thf(f3506,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 )
=> ( v6 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y0 ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3505]) ).
thf(f3505,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 )
=> ( v6 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y0 ) ) ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3504,f358]) ).
thf(f3504,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 )
=> ( v6 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y0 ) ) ) ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3503]) ).
thf(f3503,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 )
=> ( v6 @ Y5 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y1 ) ) ) ) )
@ X3 )
= $true )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3498]) ).
thf(f3498,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 )
=> ( v6 @ Y5 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3497]) ).
thf(f3497,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 )
=> ( v6 @ Y5 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3496,f358]) ).
thf(f3496,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 )
=> ( v6 @ Y5 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3495]) ).
thf(f3495,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 )
=> ( v6 @ Y6 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y2 ) ) ) ) ) ) )
@ X2 )
= $true )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3490]) ).
thf(f3490,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 )
=> ( v6 @ Y6 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3489]) ).
thf(f3489,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 )
=> ( v6 @ Y6 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3488,f358]) ).
thf(f3488,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( ( 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v6 @ Y6 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3485]) ).
thf(f3485,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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v6 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3436]) ).
thf(f3436,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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v6 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3435]) ).
thf(f3435,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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v6 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
| $false ) )
| ~ spl0_23 ),
inference(superposition,[status(thm)],[f3428,f2556]) ).
thf(f2556,plain,
! [X14: mworld] :
( ( v14 @ ( sK17 @ X14 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f2555]) ).
thf(f2555,plain,
! [X14: mworld] :
( ( ~ ( v14 @ ( sK17 @ X14 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2554]) ).
thf(f2554,plain,
! [X14: mworld] :
( $true
= ( ~ ( v14 @ ( sK17 @ X14 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2553,f358]) ).
thf(f2553,plain,
! [X14: mworld] :
( $true
= ( ~ ( v14 @ ( sK17 @ X14 ) )
& ( mrel @ X14 @ ( sK17 @ X14 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2552]) ).
thf(f2552,plain,
! [X14: mworld] :
( ( ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) )
@ ( sK17 @ X14 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f2544]) ).
thf(f2544,plain,
! [X14: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2543]) ).
thf(f2543,plain,
! [X14: mworld] :
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2542]) ).
thf(f2542,plain,
! [X14: mworld] :
( $true
= ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f2533,f2541]) ).
thf(f3428,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 )
=> ( v6 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( v14 @ X15 ) )
= $true )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3427]) ).
thf(f3427,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 )
=> ( v6 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( v14 @ X15 ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3426,f358]) ).
thf(f3426,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( v14 @ X15 ) ) )
= $true )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3425]) ).
thf(f3425,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) )
@ X15 )
= $true )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3420]) ).
thf(f3420,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3419]) ).
thf(f3419,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3418,f358]) ).
thf(f3418,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 )
=> ( v6 @ Y8 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3417]) ).
thf(f3417,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y1 ) ) ) ) )
@ X14 )
= $true )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3412]) ).
thf(f3412,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y1 ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3411]) ).
thf(f3411,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3410,f358]) ).
thf(f3410,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 )
=> ( v6 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3409]) ).
thf(f3409,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 )
=> ( v6 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y2 ) ) ) ) ) ) )
@ X13 ) )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3404]) ).
thf(f3404,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3403]) ).
thf(f3403,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 )
=> ( v6 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3402,f358]) ).
thf(f3402,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 )
=> ( v6 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3401]) ).
thf(f3401,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y3 ) ) ) ) ) ) ) ) )
@ X12 )
= $true )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3396]) ).
thf(f3396,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3395]) ).
thf(f3395,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3394,f358]) ).
thf(f3394,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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v6 @ Y11 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3393]) ).
thf(f3393,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 )
=> ( v6 @ Y12 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X11 ) )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3388]) ).
thf(f3388,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3387]) ).
thf(f3387,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3386,f358]) ).
thf(f3386,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3385]) ).
thf(f3385,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3380]) ).
thf(f3380,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3379]) ).
thf(f3379,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| $false ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3356]) ).
thf(f3356,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ $true ) )
| ~ spl0_23 ),
inference(backward_demodulation,[status(thm)],[f800,f3304]) ).
thf(f3304,plain,
( ! [X1: mworld] :
( $true
= ( v20 @ X1 ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[status(thm)],[f3303]) ).
thf(f800,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ X9 ) ) ),
inference(boolean_simplification,[status(thm)],[f799]) ).
thf(f799,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ X9 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f798,f358]) ).
thf(f798,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ X9 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f797]) ).
thf(f797,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y0 ) ) )
@ X9 ) ),
inference(pi_clausification,[status(thm)],[f796]) ).
thf(f796,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f795]) ).
thf(f795,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 )
=> ( v6 @ Y14 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f794,f358]) ).
thf(f794,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 )
=> ( v6 @ Y14 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f793]) ).
thf(f793,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 )
=> ( v6 @ Y15 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y1 ) ) ) ) )
@ X8 ) ),
inference(pi_clausification,[status(thm)],[f792]) ).
thf(f792,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f791]) ).
thf(f791,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 )
=> ( v6 @ Y15 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y1 ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f790,f358]) ).
thf(f790,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 )
=> ( v6 @ Y15 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f789]) ).
thf(f789,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y2 ) ) ) ) ) ) )
@ X7 )
= $true ),
inference(pi_clausification,[status(thm)],[f788]) ).
thf(f788,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f787]) ).
thf(f787,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 )
=> ( v6 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f786,f358]) ).
thf(f786,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 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v6 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f785]) ).
thf(f785,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 )
=> ( v6 @ Y17 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y3 ) ) ) ) ) ) ) ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f784]) ).
thf(f784,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f783]) ).
thf(f783,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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v6 @ Y17 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f782,f358]) ).
thf(f782,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 )
=> ( v6 @ Y17 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f781]) ).
thf(f781,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X5 )
= $true ),
inference(pi_clausification,[status(thm)],[f780]) ).
thf(f780,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f779]) ).
thf(f779,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f778,f358]) ).
thf(f778,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f777]) ).
thf(f777,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f776]) ).
thf(f776,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f775]) ).
thf(f775,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f774,f358]) ).
thf(f774,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f773]) ).
thf(f773,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f772]) ).
thf(f772,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 )
=> ( v6 @ Y20 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f771]) ).
thf(f771,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f770,f358]) ).
thf(f770,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 )
=> ( v6 @ Y20 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f769]) ).
thf(f769,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 )
=> ( v6 @ Y21 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f768]) ).
thf(f768,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f767]) ).
thf(f767,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 )
=> ( v6 @ Y21 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f766,f358]) ).
thf(f766,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f765]) ).
thf(f765,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 )
=> ( v6 @ Y22 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f341]) ).
thf(f341,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 ) ) ) ) ) ) ) ) )
| ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f286]) ).
thf(f286,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 > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v20 )
@ ( ^ [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 ) )
@ 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 > $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] :
( !! @ 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 ) ) )
@ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f233,f226,f239,f239,f239,f239,f239,f239,f239,f239,f239,f201,f213,f239,f239,f239,f239,f239,f239,f201,f239,f239,f239,f239,f201,f213,f239,f239,f239,f239]) ).
thf(f233,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f123]) ).
thf(f123,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f122]) ).
thf(f122,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f49]) ).
thf(f49,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod40) ).
thf(f3476,plain,
( ~ spl0_13
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f3475]) ).
thf(f3475,plain,
( $false
| ~ spl0_13
| ~ spl0_23 ),
inference(trivial_inequality_removal,[status(thm)],[f3474]) ).
thf(f3474,plain,
( ( $false = $true )
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3473,f2424]) ).
thf(f2424,plain,
( ! [X20: mworld] :
( ( v9 @ X20 )
= $false )
| ~ spl0_13 ),
inference(not_proxy_clausification,[status(thm)],[f2423]) ).
thf(f2423,plain,
( ! [X20: mworld] :
( $true
= ( ~ ( v9 @ X20 ) ) )
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f2422]) ).
thf(f2422,plain,
( ! [X20: mworld] :
( ( $true
=> ~ ( v9 @ X20 ) )
= $true )
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f2421,f358]) ).
thf(f2421,plain,
( ! [X19: mworld,X20: mworld] :
( $true
= ( ( mrel @ X19 @ X20 )
=> ~ ( v9 @ X20 ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f2420]) ).
thf(f2420,plain,
( ! [X19: mworld,X20: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v9 @ Y0 ) )
@ X20 ) )
| ~ spl0_13 ),
inference(pi_clausification,[status(thm)],[f2419]) ).
thf(f2419,plain,
( ! [X19: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v9 @ Y0 ) ) )
= $true )
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f2418]) ).
thf(f2418,plain,
( ! [X19: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v9 @ Y0 ) ) ) )
= $true )
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f2417,f358]) ).
thf(f2417,plain,
( ! [X18: mworld,X19: mworld] :
( ( ( mrel @ X18 @ X19 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v9 @ Y0 ) ) ) )
= $true )
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f2416]) ).
thf(f2416,plain,
( ! [X18: mworld,X19: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) )
@ X19 ) )
| ~ spl0_13 ),
inference(pi_clausification,[status(thm)],[f2414]) ).
thf(f2414,plain,
( ! [X18: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f2413]) ).
thf(f2413,definition,
( spl0_13
<=> ! [X18: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f3473,plain,
( ! [X12: mworld] :
( $true
= ( v9 @ X12 ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3472]) ).
thf(f3472,plain,
( ! [X12: mworld] :
( ( $true
=> ( v9 @ X12 ) )
= $true )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3471,f358]) ).
thf(f3471,plain,
( ! [X11: mworld,X12: mworld] :
( $true
= ( ( mrel @ X11 @ X12 )
=> ( v9 @ X12 ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3470]) ).
thf(f3470,plain,
( ! [X11: mworld,X12: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( v9 @ Y0 ) )
@ X12 ) )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3465]) ).
thf(f3465,plain,
( ! [X11: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( v9 @ Y0 ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3464]) ).
thf(f3464,plain,
( ! [X11: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( v9 @ Y0 ) ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3463,f358]) ).
thf(f3463,plain,
( ! [X10: mworld,X11: mworld] :
( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( v9 @ Y0 ) ) ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3462]) ).
thf(f3462,plain,
( ! [X10: mworld,X11: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) )
@ X11 )
= $true )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3457]) ).
thf(f3457,plain,
( ! [X10: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3456]) ).
thf(f3456,plain,
( ! [X10: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3455,f358]) ).
thf(f3455,plain,
( ! [X10: mworld,X9: mworld] :
( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3454]) ).
thf(f3454,plain,
( ! [X10: mworld,X9: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) )
@ X10 ) )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3449]) ).
thf(f3449,plain,
( ! [X9: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3448]) ).
thf(f3448,plain,
( ! [X9: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3447,f358]) ).
thf(f3447,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 )
=> ( v9 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3446]) ).
thf(f3446,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 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) )
@ X9 ) )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3441]) ).
thf(f3441,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 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3440]) ).
thf(f3440,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 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3439,f358]) ).
thf(f3439,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 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3438]) ).
thf(f3438,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 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X8 ) )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3432]) ).
thf(f3432,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 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3431]) ).
thf(f3431,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 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3430,f358]) ).
thf(f3430,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 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3429]) ).
thf(f3429,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 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3424]) ).
thf(f3424,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 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3423]) ).
thf(f3423,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 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3422,f358]) ).
thf(f3422,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 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3421]) ).
thf(f3421,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 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3416]) ).
thf(f3416,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 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3415]) ).
thf(f3415,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 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3414,f358]) ).
thf(f3414,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 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3413]) ).
thf(f3413,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 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3408]) ).
thf(f3408,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 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3407]) ).
thf(f3407,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 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3406,f358]) ).
thf(f3406,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 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3405]) ).
thf(f3405,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 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3400]) ).
thf(f3400,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 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3399]) ).
thf(f3399,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 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3398,f358]) ).
thf(f3398,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 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3397]) ).
thf(f3397,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 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3392]) ).
thf(f3392,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 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3391]) ).
thf(f3391,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 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3390,f358]) ).
thf(f3390,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 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f3389]) ).
thf(f3389,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 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ~ spl0_23 ),
inference(pi_clausification,[status(thm)],[f3378]) ).
thf(f3378,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 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(trivial_inequality_removal,[status(thm)],[f3377]) ).
thf(f3377,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 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false = $true ) )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f3361]) ).
thf(f3361,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 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) )
| ~ spl0_23 ),
inference(backward_demodulation,[status(thm)],[f2448,f3304]) ).
thf(f2448,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 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( ~ ( v20 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f2443]) ).
thf(f2443,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 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ X1 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2442]) ).
thf(f2442,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 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ X1 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2441,f358]) ).
thf(f2441,plain,
! [X0: mworld,X1: mworld] :
( ( ( mrel @ ( sK7 @ 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 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2438]) ).
thf(f2438,plain,
! [X0: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ ( sK7 @ 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 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f2431]) ).
thf(f2431,plain,
! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK7 @ 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 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2429]) ).
thf(f2429,plain,
! [X0: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK7 @ 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 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y0 ) ) ) )
| $false ) ),
inference(superposition,[status(thm)],[f2405,f1918]) ).
thf(f1918,plain,
! [X7: mworld] :
( $false
= ( v21 @ ( sK7 @ X7 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1911]) ).
thf(f1911,plain,
! [X7: mworld] :
( $true
= ( ~ ( v21 @ ( sK7 @ X7 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1910]) ).
thf(f1910,plain,
! [X7: mworld] :
( $true
= ( ~ ( v21 @ ( sK7 @ X7 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f1904,f358]) ).
thf(f1904,plain,
! [X7: mworld] :
( $true
= ( ~ ( v21 @ ( sK7 @ X7 ) )
& ( mrel @ X7 @ ( sK7 @ X7 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1903]) ).
thf(f1903,plain,
! [X7: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) )
@ ( sK7 @ X7 ) ) ),
inference(sigma_clausification,[status(thm)],[f1895]) ).
thf(f1895,plain,
! [X7: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f1894]) ).
thf(f1894,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)],[f1893]) ).
thf(f1893,plain,
! [X7: mworld] :
( $true
= ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1878,f1892]) ).
thf(f2405,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 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y0 ) ) ) )
| ( v21 @ X3 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2404]) ).
thf(f2404,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 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y0 ) ) ) )
| ( v21 @ X3 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2403,f358]) ).
thf(f2403,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 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y0 ) ) ) )
| ( v21 @ X3 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2402]) ).
thf(f2402,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 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y1 ) ) ) )
| ( v21 @ Y0 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f2310]) ).
thf(f2310,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 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y1 ) ) ) )
| ( v21 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2309]) ).
thf(f2309,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 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y1 ) ) ) )
| ( v21 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2308,f358]) ).
thf(f2308,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 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y1 ) ) ) )
| ( v21 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2307]) ).
thf(f2307,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 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y2 ) ) ) )
| ( v21 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f2302]) ).
thf(f2302,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 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y2 ) ) ) )
| ( v21 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2301]) ).
thf(f2301,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 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y2 ) ) ) )
| ( v21 @ Y1 ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2300,f358]) ).
thf(f2300,plain,
! [X0: mworld,X1: mworld] :
( ( ( 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y2 ) ) ) )
| ( v21 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2297]) ).
thf(f2297,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y3 ) ) ) )
| ( v21 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1847]) ).
thf(f1847,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y3 ) ) ) )
| ( v21 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1846]) ).
thf(f1846,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y3 ) ) ) )
| ( v21 @ Y2 ) ) ) ) ) ) ) )
| $false )
= $true ),
inference(boolean_simplification,[status(thm)],[f1842]) ).
thf(f1842,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y3 ) ) ) )
| ( v21 @ Y2 ) ) ) ) ) ) ) )
| ~ $true ) ),
inference(superposition,[status(thm)],[f575,f1822]) ).
thf(f1822,plain,
! [X4: mworld] :
( $true
= ( v24 @ ( sK4 @ X4 ) ) ),
inference(boolean_simplification,[status(thm)],[f1821]) ).
thf(f1821,plain,
! [X4: mworld] :
( ( ( v24 @ ( sK4 @ X4 ) )
& $true )
= $true ),
inference(forward_demodulation,[status(thm)],[f1820,f358]) ).
thf(f1820,plain,
! [X4: mworld] :
( $true
= ( ( v24 @ ( sK4 @ X4 ) )
& ( mrel @ X4 @ ( sK4 @ X4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1819]) ).
thf(f1819,plain,
! [X4: mworld] :
( ( ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) )
@ ( sK4 @ X4 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f1812]) ).
thf(f1812,plain,
! [X4: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1803]) ).
thf(f575,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 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y3 ) ) ) )
| ( v21 @ Y2 ) ) ) ) ) ) ) )
| ~ ( v24 @ X5 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f574]) ).
thf(f574,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y3 ) ) ) )
| ( v21 @ Y2 ) ) ) ) ) ) ) )
| ~ ( v24 @ X5 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f573,f358]) ).
thf(f573,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 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y3 ) ) ) )
| ( v21 @ Y2 ) ) ) ) ) ) ) )
| ~ ( v24 @ X5 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f572]) ).
thf(f572,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 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y4 ) ) ) )
| ( v21 @ Y3 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y0 ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f571]) ).
thf(f571,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y4 ) ) ) )
| ( v21 @ Y3 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f570]) ).
thf(f570,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 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y4 ) ) ) )
| ( v21 @ Y3 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f569,f358]) ).
thf(f569,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y4 ) ) ) )
| ( v21 @ Y3 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f568]) ).
thf(f568,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 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y5 ) ) ) )
| ( v21 @ Y4 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y1 ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f567]) ).
thf(f567,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y5 ) ) ) )
| ( v21 @ Y4 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f566]) ).
thf(f566,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 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y5 ) ) ) )
| ( v21 @ Y4 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y1 ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f565,f358]) ).
thf(f565,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 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y5 ) ) ) )
| ( v21 @ Y4 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f564]) ).
thf(f564,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y6 ) ) ) )
| ( v21 @ Y5 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f563]) ).
thf(f563,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y6 ) ) ) )
| ( v21 @ Y5 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f562]) ).
thf(f562,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 )
=> ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y6 ) ) ) )
| ( v21 @ Y5 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f561,f358]) ).
thf(f561,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y6 ) ) ) )
| ( v21 @ Y5 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f560]) ).
thf(f560,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 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y7 ) ) ) )
| ( v21 @ Y6 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f559]) ).
thf(f559,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y7 ) ) ) )
| ( v21 @ Y6 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f558]) ).
thf(f558,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 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y7 ) ) ) )
| ( v21 @ Y6 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f557,f358]) ).
thf(f557,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 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y7 ) ) ) )
| ( v21 @ Y6 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f556]) ).
thf(f556,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 )
=> ( v9 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y8 ) ) ) )
| ( v21 @ Y7 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f328]) ).
thf(f328,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v20 @ Y8 ) ) ) )
| ( v21 @ Y7 ) ) ) ) ) ) ) )
| ~ ( v24 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f250]) ).
thf(f250,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 ) )
@ ( ^ [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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v21
@ ( ^ [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 )
@ v20 )
@ ( ^ [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 ) ) )
@ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f190,f226,f239,f239,f239,f239,f239,f201,f213,f239,f239,f239,f201,f239,f201,f213,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239]) ).
thf(f190,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f99]) ).
thf(f99,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f98]) ).
thf(f98,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f38]) ).
thf(f38,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod29) ).
thf(f3354,plain,
( ~ spl0_15
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f3353]) ).
thf(f3353,plain,
( $false
| ~ spl0_15
| ~ spl0_22 ),
inference(trivial_inequality_removal,[status(thm)],[f3352]) ).
thf(f3352,plain,
( ( $false = $true )
| ~ spl0_15
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3351]) ).
thf(f3351,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3350,f2986]) ).
thf(f3350,plain,
( ! [X5: mworld] :
( ( ~ ( v10 @ X5 ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3349]) ).
thf(f3349,plain,
( ! [X5: mworld] :
( $true
= ( $true
=> ~ ( v10 @ X5 ) ) )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3348,f358]) ).
thf(f3348,plain,
( ! [X4: mworld,X5: mworld] :
( ( ( mrel @ X4 @ X5 )
=> ~ ( v10 @ X5 ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3347]) ).
thf(f3347,plain,
( ! [X4: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ~ ( v10 @ Y0 ) )
@ X5 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3346]) ).
thf(f3346,plain,
( ! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ~ ( v10 @ Y0 ) ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3345]) ).
thf(f3345,plain,
( ! [X4: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ~ ( v10 @ Y0 ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3344,f358]) ).
thf(f3344,plain,
( ! [X3: mworld,X4: mworld] :
( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ~ ( v10 @ Y0 ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3343]) ).
thf(f3343,plain,
( ! [X3: mworld,X4: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) )
@ X4 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3342]) ).
thf(f3342,plain,
( ! [X3: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3341]) ).
thf(f3341,plain,
( ! [X3: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3340,f358]) ).
thf(f3340,plain,
( ! [X2: mworld,X3: mworld] :
( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3339]) ).
thf(f3339,plain,
( ! [X2: mworld,X3: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) )
@ X3 )
= $true )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3338]) ).
thf(f3338,plain,
( ! [X2: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3337]) ).
thf(f3337,plain,
( ! [X2: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3336,f358]) ).
thf(f3336,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 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3335]) ).
thf(f3335,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 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) )
@ X2 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3334]) ).
thf(f3334,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 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3333]) ).
thf(f3333,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 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3332,f358]) ).
thf(f3332,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( mrel @ ( sK15 @ 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 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3329]) ).
thf(f3329,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK15 @ 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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X1 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3326]) ).
thf(f3326,plain,
( ! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK15 @ 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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3325]) ).
thf(f3325,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK15 @ 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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| $false )
= $true )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3324]) ).
thf(f3324,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK15 @ 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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ~ $true )
= $true )
| ~ spl0_22 ),
inference(superposition,[status(thm)],[f3321,f2336]) ).
thf(f3321,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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ X6 ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3320]) ).
thf(f3320,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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ X6 ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3319,f358]) ).
thf(f3319,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 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ X6 ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3318]) ).
thf(f3318,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 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y0 ) ) )
@ X6 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3317]) ).
thf(f3317,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 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y0 ) ) ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3316]) ).
thf(f3316,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 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y0 ) ) ) ) ) )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3315,f358]) ).
thf(f3315,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 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3314]) ).
thf(f3314,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 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) )
@ X5 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3313]) ).
thf(f3313,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 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3312]) ).
thf(f3312,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 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3311,f358]) ).
thf(f3311,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 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3310]) ).
thf(f3310,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 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) )
@ X4 )
= $true )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3309]) ).
thf(f3309,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 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f3308]) ).
thf(f3308,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 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f3307,f358]) ).
thf(f3307,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 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f3306]) ).
thf(f3306,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 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) )
@ X3 ) )
| ~ spl0_22 ),
inference(pi_clausification,[status(thm)],[f3301]) ).
thf(f3305,plain,
( spl0_22
| spl0_23 ),
inference(avatar_split_clause,[status(thm)],[f3298,f3303,f3300]) ).
thf(f3298,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v20 @ X1 ) )
| ( $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 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f3297]) ).
thf(f3297,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v20 @ X1 ) )
| ( $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 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f3295,f358]) ).
thf(f3295,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v20 @ 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 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3293]) ).
thf(f3293,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v20 @ X1 ) )
| ( $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 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f2042]) ).
thf(f2042,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 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( v20 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2037]) ).
thf(f2037,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 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ X1 ) ) ),
inference(boolean_simplification,[status(thm)],[f2036]) ).
thf(f2036,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 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ X1 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2035,f358]) ).
thf(f2035,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ( mrel @ ( sK7 @ 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 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2032]) ).
thf(f2032,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK7 @ 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 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1927]) ).
thf(f1927,plain,
! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK7 @ 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 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1924]) ).
thf(f1924,plain,
! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK7 @ 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 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y0 ) ) ) )
| $false )
= $true ),
inference(superposition,[status(thm)],[f500,f1918]) ).
thf(f500,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 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y0 ) ) ) )
| ( v21 @ X8 ) ) ),
inference(boolean_simplification,[status(thm)],[f499]) ).
thf(f499,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 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y0 ) ) ) )
| ( v21 @ X8 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f498,f358]) ).
thf(f498,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 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y0 ) ) ) )
| ( v21 @ X8 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f497]) ).
thf(f497,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 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y1 ) ) ) )
| ( v21 @ Y0 ) ) )
@ X8 ) ),
inference(pi_clausification,[status(thm)],[f496]) ).
thf(f496,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 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y1 ) ) ) )
| ( v21 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f495]) ).
thf(f495,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 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y1 ) ) ) )
| ( v21 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f494,f358]) ).
thf(f494,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 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y1 ) ) ) )
| ( v21 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f493]) ).
thf(f493,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 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y2 ) ) ) )
| ( v21 @ Y1 ) ) ) ) )
@ X7 )
= $true ),
inference(pi_clausification,[status(thm)],[f492]) ).
thf(f492,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 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y2 ) ) ) )
| ( v21 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f491]) ).
thf(f491,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 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y2 ) ) ) )
| ( v21 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f490,f358]) ).
thf(f490,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 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y2 ) ) ) )
| ( v21 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f489]) ).
thf(f489,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 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y3 ) ) ) )
| ( v21 @ Y2 ) ) ) ) ) ) )
@ X6 ) ),
inference(pi_clausification,[status(thm)],[f488]) ).
thf(f488,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 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y3 ) ) ) )
| ( v21 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f487]) ).
thf(f487,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 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y3 ) ) ) )
| ( v21 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f486,f358]) ).
thf(f486,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 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y3 ) ) ) )
| ( v21 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f485]) ).
thf(f485,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 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y4 ) ) ) )
| ( v21 @ Y3 ) ) ) ) ) ) ) ) )
@ X5 )
= $true ),
inference(pi_clausification,[status(thm)],[f484]) ).
thf(f484,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 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y4 ) ) ) )
| ( v21 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f483]) ).
thf(f483,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 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y4 ) ) ) )
| ( v21 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f482,f358]) ).
thf(f482,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 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y4 ) ) ) )
| ( v21 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f481]) ).
thf(f481,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 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y5 ) ) ) )
| ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f480]) ).
thf(f480,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 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y5 ) ) ) )
| ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f479]) ).
thf(f479,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 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y5 ) ) ) )
| ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f478,f358]) ).
thf(f478,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 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y5 ) ) ) )
| ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f477]) ).
thf(f477,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 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y6 ) ) ) )
| ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f476]) ).
thf(f476,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 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y6 ) ) ) )
| ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f475]) ).
thf(f475,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 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y6 ) ) ) )
| ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f474,f358]) ).
thf(f474,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 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y6 ) ) ) )
| ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f473]) ).
thf(f473,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 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y7 ) ) ) )
| ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f472]) ).
thf(f472,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 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y7 ) ) ) )
| ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f471]) ).
thf(f471,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 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y7 ) ) ) )
| ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f470,f358]) ).
thf(f470,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 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y7 ) ) ) )
| ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f469]) ).
thf(f469,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 )
=> ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y13 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y8 ) ) ) )
| ( v21 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f348]) ).
thf(f348,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 )
=> ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y13 ) ) ) ) ) ) ) ) ) ) ) )
| ( v20 @ Y8 ) ) ) )
| ( v21 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f284]) ).
thf(f284,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] :
( !! @ 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 ) )
@ v21
@ ( ^ [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 ) )
@ v20
@ ( ^ [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] :
( !! @ 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] :
~ ( Y0 @ Y1 )
@ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f231,f226,f239,f239,f239,f239,f239,f239,f239,f239,f201,f239,f201,f239,f239,f239,f239,f239,f201,f213,f239,f239,f239,f239,f239,f213]) ).
thf(f231,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f147]) ).
thf(f147,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f146]) ).
thf(f146,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f45]) ).
thf(f45,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod36) ).
thf(f2969,plain,
spl0_5,
inference(avatar_split_clause,[status(thm)],[f2760,f1067]) ).
thf(f1067,definition,
( spl0_5
<=> ! [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 )
=> ~ ( v3 @ Y8 ) ) ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ X17 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f2760,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 )
=> ~ ( v3 @ Y8 ) ) ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ X1 ) ) ),
inference(boolean_simplification,[status(thm)],[f2759]) ).
thf(f2759,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 )
=> ~ ( v3 @ Y8 ) ) ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ X1 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2757,f358]) ).
thf(f2757,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ( mrel @ ( sK19 @ 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 )
=> ~ ( v3 @ Y8 ) ) ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2755]) ).
thf(f2755,plain,
! [X0: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ ( sK19 @ 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 )
=> ~ ( v3 @ Y9 ) ) ) ) ) ) )
| ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f2726]) ).
thf(f2726,plain,
! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK19 @ 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 )
=> ~ ( v3 @ Y9 ) ) ) ) ) ) )
| ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2725]) ).
thf(f2725,plain,
! [X0: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK19 @ 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 )
=> ~ ( v3 @ Y9 ) ) ) ) ) ) )
| ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y0 ) ) ) )
| $false ) ),
inference(superposition,[status(thm)],[f1054,f2700]) ).
thf(f2700,plain,
! [X15: mworld] :
( ( v13 @ ( sK19 @ X15 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f2659]) ).
thf(f2659,plain,
! [X15: mworld] :
( ( ~ ( v13 @ ( sK19 @ X15 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2658]) ).
thf(f2658,plain,
! [X15: mworld] :
( $true
= ( ~ ( v13 @ ( sK19 @ X15 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2650,f358]) ).
thf(f2650,plain,
! [X15: mworld] :
( ( ~ ( v13 @ ( sK19 @ X15 ) )
& ( mrel @ X15 @ ( sK19 @ X15 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2649]) ).
thf(f2649,plain,
! [X15: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) )
@ ( sK19 @ X15 ) ) ),
inference(sigma_clausification,[status(thm)],[f2641]) ).
thf(f1054,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 )
=> ~ ( v3 @ Y9 ) ) ) ) ) ) )
| ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y0 ) ) ) )
| ( v13 @ X16 ) ) ),
inference(boolean_simplification,[status(thm)],[f1053]) ).
thf(f1053,plain,
! [X16: mworld] :
( $true
= ( $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 )
=> ~ ( v3 @ Y9 ) ) ) ) ) ) )
| ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y0 ) ) ) )
| ( v13 @ X16 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1052,f358]) ).
thf(f1052,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 )
=> ~ ( v3 @ Y9 ) ) ) ) ) ) )
| ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y0 ) ) ) )
| ( v13 @ X16 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1051]) ).
thf(f1051,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 )
=> ~ ( v3 @ Y10 ) ) ) ) ) ) )
| ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y1 ) ) ) )
| ( v13 @ Y0 ) ) )
@ X16 )
= $true ),
inference(pi_clausification,[status(thm)],[f1050]) ).
thf(f1050,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 )
=> ~ ( v3 @ Y10 ) ) ) ) ) ) )
| ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y1 ) ) ) )
| ( v13 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1049]) ).
thf(f1049,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 )
=> ~ ( v3 @ Y10 ) ) ) ) ) ) )
| ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y1 ) ) ) )
| ( v13 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1048,f358]) ).
thf(f1048,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 )
=> ~ ( v3 @ Y10 ) ) ) ) ) ) )
| ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y1 ) ) ) )
| ( v13 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1047]) ).
thf(f1047,plain,
! [X14: mworld,X15: mworld] :
( $true
= ( ^ [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 )
=> ~ ( v3 @ Y11 ) ) ) ) ) ) )
| ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y2 ) ) ) )
| ( v13 @ Y1 ) ) ) ) )
@ X15 ) ),
inference(pi_clausification,[status(thm)],[f1046]) ).
thf(f1046,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 )
=> ~ ( v3 @ Y11 ) ) ) ) ) ) )
| ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y2 ) ) ) )
| ( v13 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1045]) ).
thf(f1045,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 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v3 @ Y11 ) ) ) ) ) ) )
| ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y2 ) ) ) )
| ( v13 @ Y1 ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1044,f358]) ).
thf(f1044,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 )
=> ~ ( v3 @ Y11 ) ) ) ) ) ) )
| ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y2 ) ) ) )
| ( v13 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1043]) ).
thf(f1043,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v3 @ Y12 ) ) ) ) ) ) )
| ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y3 ) ) ) )
| ( v13 @ Y2 ) ) ) ) ) ) )
@ X14 ) ),
inference(pi_clausification,[status(thm)],[f1042]) ).
thf(f1042,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 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v3 @ Y12 ) ) ) ) ) ) )
| ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y3 ) ) ) )
| ( v13 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1041]) ).
thf(f1041,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 )
=> ~ ( v3 @ Y12 ) ) ) ) ) ) )
| ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y3 ) ) ) )
| ( v13 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1040,f358]) ).
thf(f1040,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 )
=> ~ ( v3 @ Y12 ) ) ) ) ) ) )
| ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y3 ) ) ) )
| ( v13 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1039]) ).
thf(f1039,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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v3 @ Y13 ) ) ) ) ) ) )
| ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y4 ) ) ) )
| ( v13 @ Y3 ) ) ) ) ) ) ) ) )
@ X13 )
= $true ),
inference(pi_clausification,[status(thm)],[f1038]) ).
thf(f1038,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 )
=> ~ ( v3 @ Y13 ) ) ) ) ) ) )
| ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y4 ) ) ) )
| ( v13 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1037]) ).
thf(f1037,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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v3 @ Y13 ) ) ) ) ) ) )
| ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y4 ) ) ) )
| ( v13 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1036,f358]) ).
thf(f1036,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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v3 @ Y13 ) ) ) ) ) ) )
| ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y4 ) ) ) )
| ( v13 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1035]) ).
thf(f1035,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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v3 @ Y14 ) ) ) ) ) ) )
| ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y5 ) ) ) )
| ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ),
inference(pi_clausification,[status(thm)],[f1034]) ).
thf(f1034,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 )
=> ~ ( v3 @ Y14 ) ) ) ) ) ) )
| ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y5 ) ) ) )
| ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1033]) ).
thf(f1033,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 )
=> ~ ( v3 @ Y14 ) ) ) ) ) ) )
| ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y5 ) ) ) )
| ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1032,f358]) ).
thf(f1032,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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v3 @ Y14 ) ) ) ) ) ) )
| ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y5 ) ) ) )
| ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1031]) ).
thf(f1031,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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v3 @ Y15 ) ) ) ) ) ) )
| ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y6 ) ) ) )
| ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ),
inference(pi_clausification,[status(thm)],[f1030]) ).
thf(f1030,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 )
=> ~ ( v3 @ Y15 ) ) ) ) ) ) )
| ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y6 ) ) ) )
| ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1029]) ).
thf(f1029,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 )
=> ~ ( v3 @ Y15 ) ) ) ) ) ) )
| ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y6 ) ) ) )
| ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1028,f358]) ).
thf(f1028,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 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v3 @ Y15 ) ) ) ) ) ) )
| ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y6 ) ) ) )
| ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1027]) ).
thf(f1027,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 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v3 @ Y16 ) ) ) ) ) ) )
| ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y7 ) ) ) )
| ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ),
inference(pi_clausification,[status(thm)],[f1026]) ).
thf(f1026,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 )
=> ~ ( v3 @ Y16 ) ) ) ) ) ) )
| ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y7 ) ) ) )
| ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1025]) ).
thf(f1025,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 )
=> ~ ( v3 @ Y16 ) ) ) ) ) ) )
| ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y7 ) ) ) )
| ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1024,f358]) ).
thf(f1024,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 )
=> ~ ( v3 @ Y16 ) ) ) ) ) ) )
| ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y7 ) ) ) )
| ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1023]) ).
thf(f1023,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 )
=> ~ ( v3 @ Y17 ) ) ) ) ) ) )
| ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y8 ) ) ) )
| ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 )
= $true ),
inference(pi_clausification,[status(thm)],[f1022]) ).
thf(f1022,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 )
=> ~ ( v3 @ Y17 ) ) ) ) ) ) )
| ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y8 ) ) ) )
| ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1021]) ).
thf(f1021,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 )
=> ~ ( v3 @ Y17 ) ) ) ) ) ) )
| ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y8 ) ) ) )
| ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1020,f358]) ).
thf(f1020,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 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v3 @ Y17 ) ) ) ) ) ) )
| ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y8 ) ) ) )
| ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1019]) ).
thf(f1019,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 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v3 @ Y18 ) ) ) ) ) ) )
| ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y9 ) ) ) )
| ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ),
inference(pi_clausification,[status(thm)],[f1018]) ).
thf(f1018,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 )
=> ~ ( v3 @ Y18 ) ) ) ) ) ) )
| ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y9 ) ) ) )
| ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1017]) ).
thf(f1017,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 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v3 @ Y18 ) ) ) ) ) ) )
| ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y9 ) ) ) )
| ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1016,f358]) ).
thf(f1016,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 )
=> ~ ( v3 @ Y18 ) ) ) ) ) ) )
| ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y9 ) ) ) )
| ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1015]) ).
thf(f1015,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 )
=> ~ ( v3 @ Y19 ) ) ) ) ) ) )
| ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y10 ) ) ) )
| ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true ),
inference(pi_clausification,[status(thm)],[f1014]) ).
thf(f1014,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 )
=> ~ ( v3 @ Y19 ) ) ) ) ) ) )
| ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y10 ) ) ) )
| ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1013]) ).
thf(f1013,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 )
=> ~ ( v3 @ Y19 ) ) ) ) ) ) )
| ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y10 ) ) ) )
| ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1012,f358]) ).
thf(f1012,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 )
=> ~ ( v3 @ Y19 ) ) ) ) ) ) )
| ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y10 ) ) ) )
| ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1011]) ).
thf(f1011,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 )
=> ~ ( v3 @ Y20 ) ) ) ) ) ) )
| ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y11 ) ) ) )
| ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f1010]) ).
thf(f1010,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 )
=> ~ ( v3 @ Y20 ) ) ) ) ) ) )
| ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y11 ) ) ) )
| ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1009]) ).
thf(f1009,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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ 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 )
=> ~ ( v3 @ Y20 ) ) ) ) ) ) )
| ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y11 ) ) ) )
| ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1008,f358]) ).
thf(f1008,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 )
=> ~ ( v3 @ Y20 ) ) ) ) ) ) )
| ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y11 ) ) ) )
| ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1007]) ).
thf(f1007,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 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v3 @ Y21 ) ) ) ) ) ) )
| ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y12 ) ) ) )
| ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f1006]) ).
thf(f1006,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 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v3 @ Y21 ) ) ) ) ) ) )
| ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y12 ) ) ) )
| ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1005]) ).
thf(f1005,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 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v3 @ Y21 ) ) ) ) ) ) )
| ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y12 ) ) ) )
| ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1004,f358]) ).
thf(f1004,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 )
=> ( !! @ 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 )
=> ~ ( v3 @ Y21 ) ) ) ) ) ) )
| ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y12 ) ) ) )
| ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1003]) ).
thf(f1003,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 )
=> ~ ( v3 @ Y22 ) ) ) ) ) ) )
| ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y13 ) ) ) )
| ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f1002]) ).
thf(f1002,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 )
=> ~ ( v3 @ Y22 ) ) ) ) ) ) )
| ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y13 ) ) ) )
| ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1001]) ).
thf(f1001,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 )
=> ~ ( v3 @ Y22 ) ) ) ) ) ) )
| ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y13 ) ) ) )
| ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1000,f358]) ).
thf(f1000,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 )
=> ~ ( v3 @ Y22 ) ) ) ) ) ) )
| ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y13 ) ) ) )
| ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f999]) ).
thf(f999,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 )
=> ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ~ ( v3 @ Y23 ) ) ) ) ) ) )
| ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y14 ) ) ) )
| ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f998]) ).
thf(f998,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 )
=> ~ ( v3 @ Y23 ) ) ) ) ) ) )
| ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y14 ) ) ) )
| ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f997]) ).
thf(f997,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 )
=> ~ ( v3 @ Y23 ) ) ) ) ) ) )
| ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y14 ) ) ) )
| ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f996,f358]) ).
thf(f996,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 )
=> ~ ( v3 @ Y23 ) ) ) ) ) ) )
| ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y14 ) ) ) )
| ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f995]) ).
thf(f995,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 )
=> ~ ( v3 @ Y24 ) ) ) ) ) ) )
| ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y15 ) ) ) )
| ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f994]) ).
thf(f994,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 )
=> ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ~ ( v3 @ Y24 ) ) ) ) ) ) )
| ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y15 ) ) ) )
| ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f993]) ).
thf(f993,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 )
=> ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ~ ( v3 @ Y24 ) ) ) ) ) ) )
| ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y15 ) ) ) )
| ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f992,f358]) ).
thf(f992,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 )
=> ~ ( v3 @ Y24 ) ) ) ) ) ) )
| ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y15 ) ) ) )
| ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f991]) ).
thf(f991,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 )
=> ~ ( v3 @ Y25 ) ) ) ) ) ) )
| ( v6 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y16 ) ) ) )
| ( v13 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f355]) ).
thf(f355,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 )
=> ~ ( v3 @ Y25 ) ) ) ) ) ) )
| ( v6 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ Y16 ) ) ) )
| ( v13 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f246]) ).
thf(f246,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] :
( !! @ 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 ) )
@ v13
@ ( ^ [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 ) )
@ v12
@ ( ^ [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 ) )
@ 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 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f185,f226,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f201,f239,f201,f239,f239,f239,f239,f239,f239,f201,f239,f239,f239,f213]) ).
thf(f185,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f174]) ).
thf(f174,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f173]) ).
thf(f173,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f55]) ).
thf(f55,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod46) ).
thf(f2968,plain,
( spl0_8
| ~ spl0_5
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f2715,f2675,f1067,f1324]) ).
thf(f1324,definition,
( spl0_8
<=> ! [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 )
=> ~ ( v3 @ Y7 ) ) ) ) ) ) )
| ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f2675,definition,
( spl0_14
<=> ! [X10: mworld] :
( $true
= ( ~ ( v12 @ X10 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f2715,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 )
=> ~ ( v3 @ Y7 ) ) ) ) ) ) )
| ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_5
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f2714]) ).
thf(f2714,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 )
=> ~ ( v3 @ Y7 ) ) ) ) ) ) )
| ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f2713,f358]) ).
thf(f2713,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 )
=> ~ ( v3 @ Y7 ) ) ) ) ) ) )
| ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f2712]) ).
thf(f2712,plain,
( ! [X18: mworld,X17: mworld] :
( $true
= ( ^ [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 )
=> ~ ( v3 @ Y8 ) ) ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X18 ) )
| ~ spl0_5
| ~ spl0_14 ),
inference(pi_clausification,[status(thm)],[f2688]) ).
thf(f2688,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 )
=> ~ ( v3 @ Y8 ) ) ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f2685]) ).
thf(f2685,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 )
=> ~ ( v3 @ Y8 ) ) ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| $false )
= $true )
| ~ spl0_5
| ~ spl0_14 ),
inference(backward_demodulation,[status(thm)],[f1068,f2683]) ).
thf(f2683,plain,
( ! [X10: mworld] :
( $false
= ( v12 @ X10 ) )
| ~ spl0_14 ),
inference(not_proxy_clausification,[status(thm)],[f2676]) ).
thf(f2676,plain,
( ! [X10: mworld] :
( $true
= ( ~ ( v12 @ X10 ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f2675]) ).
thf(f1068,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 )
=> ~ ( v3 @ Y8 ) ) ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v12 @ X17 ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f1067]) ).
thf(f2967,plain,
( ~ spl0_7
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f2966]) ).
thf(f2966,plain,
( $false
| ~ spl0_7
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f2965]) ).
thf(f2965,plain,
( ( $false = $true )
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f1322,f2683]) ).
thf(f1322,plain,
( ! [X17: mworld] :
( $true
= ( v12 @ X17 ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f1321]) ).
thf(f1321,definition,
( spl0_7
<=> ! [X17: mworld] :
( $true
= ( v12 @ X17 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f2964,plain,
( spl0_16
| spl0_17
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f2957,f1324,f2962,f2959]) ).
thf(f2957,plain,
( ! [X24: mworld,X23: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) )
| ( ( v6 @ X23 )
= $true ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f2956]) ).
thf(f2956,plain,
( ! [X24: mworld,X23: mworld] :
( ( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) ) )
| ( ( v6 @ X23 )
= $true ) )
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f2954,f358]) ).
thf(f2954,plain,
( ! [X24: mworld,X23: mworld] :
( ( $true
= ( ( mrel @ X23 @ X24 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) ) )
| ( ( v6 @ X23 )
= $true ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f2952]) ).
thf(f2952,plain,
( ! [X24: mworld,X23: mworld] :
( ( ( v6 @ X23 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v3 @ Y2 ) ) ) ) ) )
@ X24 ) ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f2711]) ).
thf(f2711,plain,
( ! [X23: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v3 @ Y2 ) ) ) ) ) ) ) )
| ( ( v6 @ X23 )
= $true ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f2710]) ).
thf(f2710,plain,
( ! [X23: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v3 @ Y2 ) ) ) ) ) ) )
| ( v6 @ X23 ) )
= $true )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f2709]) ).
thf(f2709,plain,
( ! [X23: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v3 @ Y2 ) ) ) ) ) ) )
| ( v6 @ X23 ) ) ) )
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f2708,f358]) ).
thf(f2708,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 )
=> ~ ( v3 @ Y2 ) ) ) ) ) ) )
| ( v6 @ X23 ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f2707]) ).
thf(f2707,plain,
( ! [X22: mworld,X23: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v3 @ Y3 ) ) ) ) ) ) )
| ( v6 @ Y0 ) ) )
@ X23 ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f2706]) ).
thf(f2706,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 )
=> ~ ( v3 @ Y3 ) ) ) ) ) ) )
| ( v6 @ Y0 ) ) ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f2705]) ).
thf(f2705,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 )
=> ~ ( v3 @ Y3 ) ) ) ) ) ) )
| ( v6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f2704,f358]) ).
thf(f2704,plain,
( ! [X21: mworld,X22: mworld] :
( ( ( 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 )
=> ~ ( v3 @ Y3 ) ) ) ) ) ) )
| ( v6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f2703]) ).
thf(f2703,plain,
( ! [X21: mworld,X22: mworld] :
( $true
= ( ^ [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 )
=> ~ ( v3 @ Y4 ) ) ) ) ) ) )
| ( v6 @ Y1 ) ) ) ) )
@ X22 ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f2699]) ).
thf(f2699,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 )
=> ~ ( v3 @ Y4 ) ) ) ) ) ) )
| ( v6 @ Y1 ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f2698]) ).
thf(f2698,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 )
=> ~ ( v3 @ Y4 ) ) ) ) ) ) )
| ( v6 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f2697,f358]) ).
thf(f2697,plain,
( ! [X21: mworld,X20: mworld] :
( $true
= ( ( 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 )
=> ~ ( v3 @ Y4 ) ) ) ) ) ) )
| ( v6 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f2696]) ).
thf(f2696,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 )
=> ~ ( v3 @ Y5 ) ) ) ) ) ) )
| ( v6 @ Y2 ) ) ) ) ) ) )
@ X21 ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f2667]) ).
thf(f2667,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 )
=> ~ ( v3 @ Y5 ) ) ) ) ) ) )
| ( v6 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f2666]) ).
thf(f2666,plain,
( ! [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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v3 @ Y5 ) ) ) ) ) ) )
| ( v6 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f2665,f358]) ).
thf(f2665,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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v3 @ Y5 ) ) ) ) ) ) )
| ( v6 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f2664]) ).
thf(f2664,plain,
( ! [X19: mworld,X20: mworld] :
( $true
= ( ^ [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 )
=> ~ ( v3 @ Y6 ) ) ) ) ) ) )
| ( v6 @ Y3 ) ) ) ) ) ) ) ) )
@ X20 ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f2663]) ).
thf(f2663,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 )
=> ~ ( v3 @ Y6 ) ) ) ) ) ) )
| ( v6 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f2662]) ).
thf(f2662,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 )
=> ~ ( v3 @ Y6 ) ) ) ) ) ) )
| ( v6 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f2661,f358]) ).
thf(f2661,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 )
=> ~ ( v3 @ Y6 ) ) ) ) ) ) )
| ( v6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f2660]) ).
thf(f2660,plain,
( ! [X18: mworld,X19: mworld] :
( $true
= ( ^ [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 )
=> ~ ( v3 @ Y7 ) ) ) ) ) ) )
| ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X19 ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f1325]) ).
thf(f1325,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 )
=> ~ ( v3 @ Y7 ) ) ) ) ) ) )
| ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f1324]) ).
thf(f2680,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f2673,f2678,f2675]) ).
thf(f2673,plain,
! [X10: mworld,X11: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( v10 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( v12 @ X10 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2672]) ).
thf(f2672,plain,
! [X10: mworld,X11: mworld] :
( ( $true
= ( ~ ( v12 @ X10 ) ) )
| ( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( v10 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2671,f358]) ).
thf(f2671,plain,
! [X10: mworld,X11: mworld] :
( ( $true
= ( ~ ( v12 @ X10 ) ) )
| ( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( v10 @ Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2668]) ).
thf(f2668,plain,
! [X10: mworld,X11: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v10 @ Y1 ) ) ) )
@ X11 ) )
| ( $true
= ( ~ ( v12 @ X10 ) ) ) ),
inference(pi_clausification,[status(thm)],[f2214]) ).
thf(f2214,plain,
! [X10: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v10 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( v12 @ X10 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2209]) ).
thf(f2209,plain,
! [X10: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v10 @ Y1 ) ) ) ) )
| ~ ( v12 @ X10 ) ) ),
inference(boolean_simplification,[status(thm)],[f2208]) ).
thf(f2208,plain,
! [X10: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v10 @ Y1 ) ) ) ) )
| ~ ( v12 @ X10 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2207,f358]) ).
thf(f2207,plain,
! [X10: mworld,X9: mworld] :
( $true
= ( ( mrel @ X9 @ X10 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v10 @ Y1 ) ) ) ) )
| ~ ( v12 @ X10 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2206]) ).
thf(f2206,plain,
! [X10: mworld,X9: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v10 @ Y2 ) ) ) ) )
| ~ ( v12 @ Y0 ) ) )
@ X10 ) ),
inference(pi_clausification,[status(thm)],[f2201]) ).
thf(f2201,plain,
! [X9: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v10 @ Y2 ) ) ) ) )
| ~ ( v12 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2200]) ).
thf(f2200,plain,
! [X9: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v10 @ Y2 ) ) ) ) )
| ~ ( v12 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2199,f358]) ).
thf(f2199,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 )
=> ( v10 @ Y2 ) ) ) ) )
| ~ ( v12 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2198]) ).
thf(f2198,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 )
=> ( v10 @ Y3 ) ) ) ) )
| ~ ( v12 @ Y1 ) ) ) ) )
@ X9 ) ),
inference(pi_clausification,[status(thm)],[f2193]) ).
thf(f2193,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 )
=> ( v10 @ Y3 ) ) ) ) )
| ~ ( v12 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2192]) ).
thf(f2192,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 )
=> ( v10 @ Y3 ) ) ) ) )
| ~ ( v12 @ Y1 ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2191,f358]) ).
thf(f2191,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 )
=> ( v10 @ Y3 ) ) ) ) )
| ~ ( v12 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2190]) ).
thf(f2190,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 )
=> ( v10 @ Y4 ) ) ) ) )
| ~ ( v12 @ Y2 ) ) ) ) ) ) )
@ X8 ) ),
inference(pi_clausification,[status(thm)],[f2185]) ).
thf(f2185,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 )
=> ( v10 @ Y4 ) ) ) ) )
| ~ ( v12 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2184]) ).
thf(f2184,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 )
=> ( v10 @ Y4 ) ) ) ) )
| ~ ( v12 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2183,f358]) ).
thf(f2183,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 )
=> ( v10 @ Y4 ) ) ) ) )
| ~ ( v12 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2182]) ).
thf(f2182,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 )
=> ( v10 @ Y5 ) ) ) ) )
| ~ ( v12 @ Y3 ) ) ) ) ) ) ) ) )
@ X7 ) ),
inference(pi_clausification,[status(thm)],[f2175]) ).
thf(f2175,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 )
=> ( v10 @ Y5 ) ) ) ) )
| ~ ( v12 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2174]) ).
thf(f2174,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 )
=> ( v10 @ Y5 ) ) ) ) )
| ~ ( v12 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2173,f358]) ).
thf(f2173,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 )
=> ( v10 @ Y5 ) ) ) ) )
| ~ ( v12 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2172]) ).
thf(f2172,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 )
=> ( v10 @ Y6 ) ) ) ) )
| ~ ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f2170]) ).
thf(f2170,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 )
=> ( v10 @ Y6 ) ) ) ) )
| ~ ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2169]) ).
thf(f2169,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 )
=> ( v10 @ Y6 ) ) ) ) )
| ~ ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2168,f358]) ).
thf(f2168,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 )
=> ( v10 @ Y6 ) ) ) ) )
| ~ ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2167]) ).
thf(f2167,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 )
=> ( v10 @ Y7 ) ) ) ) )
| ~ ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f2100]) ).
thf(f2100,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 )
=> ( v10 @ Y7 ) ) ) ) )
| ~ ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2099]) ).
thf(f2099,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 )
=> ( v10 @ Y7 ) ) ) ) )
| ~ ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2098,f358]) ).
thf(f2098,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 )
=> ( v10 @ Y7 ) ) ) ) )
| ~ ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2097]) ).
thf(f2097,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 )
=> ( v10 @ Y8 ) ) ) ) )
| ~ ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f2092]) ).
thf(f2092,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 )
=> ( v10 @ Y8 ) ) ) ) )
| ~ ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2091]) ).
thf(f2091,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 )
=> ( v10 @ Y8 ) ) ) ) )
| ~ ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2090,f358]) ).
thf(f2090,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 )
=> ( v10 @ Y8 ) ) ) ) )
| ~ ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2089]) ).
thf(f2089,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 )
=> ( v10 @ Y9 ) ) ) ) )
| ~ ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f2082]) ).
thf(f2082,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 )
=> ( v10 @ Y9 ) ) ) ) )
| ~ ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2081]) ).
thf(f2081,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 )
=> ( v10 @ Y9 ) ) ) ) )
| ~ ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2080,f358]) ).
thf(f2080,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 )
=> ( v10 @ Y9 ) ) ) ) )
| ~ ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2079]) ).
thf(f2079,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 )
=> ( v10 @ Y10 ) ) ) ) )
| ~ ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f2072]) ).
thf(f2072,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 )
=> ( v10 @ Y10 ) ) ) ) )
| ~ ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2071]) ).
thf(f2071,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 )
=> ( v10 @ Y10 ) ) ) ) )
| ~ ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2070,f358]) ).
thf(f2070,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ( mrel @ ( sK11 @ 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 )
=> ( v10 @ Y10 ) ) ) ) )
| ~ ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2067]) ).
thf(f2067,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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v10 @ Y11 ) ) ) ) )
| ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f2059]) ).
thf(f2059,plain,
! [X0: mworld] :
( $true
= ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v10 @ Y11 ) ) ) ) )
| ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2058]) ).
thf(f2058,plain,
! [X0: mworld] :
( $true
= ( ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v10 @ Y11 ) ) ) ) )
| ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| $false ) ),
inference(superposition,[status(thm)],[f2049,f1993]) ).
thf(f1993,plain,
! [X6: mworld] :
( $false
= ( v22 @ ( sK11 @ X6 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1992]) ).
thf(f1992,plain,
! [X6: mworld] :
( ( ~ ( v22 @ ( sK11 @ X6 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1991]) ).
thf(f1991,plain,
! [X6: mworld] :
( ( ~ ( v22 @ ( sK11 @ X6 ) )
& $true )
= $true ),
inference(forward_demodulation,[status(thm)],[f1990,f358]) ).
thf(f1990,plain,
! [X6: mworld] :
( $true
= ( ~ ( v22 @ ( sK11 @ X6 ) )
& ( mrel @ X6 @ ( sK11 @ X6 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1989]) ).
thf(f1989,plain,
! [X6: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) )
@ ( sK11 @ X6 ) ) ),
inference(sigma_clausification,[status(thm)],[f1984]) ).
thf(f1984,plain,
! [X6: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1983]) ).
thf(f1983,plain,
! [X6: mworld] :
( $true
= ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1860,f1982]) ).
thf(f1982,plain,
! [X6: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f1860]) ).
thf(f2049,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 )
=> ( v10 @ Y11 ) ) ) ) )
| ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ X1 ) ) ),
inference(boolean_simplification,[status(thm)],[f2048]) ).
thf(f2048,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 )
=> ( v10 @ Y11 ) ) ) ) )
| ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ X1 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2047,f358]) ).
thf(f2047,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ( 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 )
=> ( v10 @ Y11 ) ) ) ) )
| ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2044]) ).
thf(f2044,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ^ [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 )
=> ( v10 @ Y12 ) ) ) ) )
| ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1963]) ).
thf(f1963,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 )
=> ( v10 @ Y12 ) ) ) ) )
| ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1962]) ).
thf(f1962,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 )
=> ( v10 @ Y12 ) ) ) ) )
| ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) ) )
| $false )
= $true ),
inference(boolean_simplification,[status(thm)],[f1957]) ).
thf(f1957,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 )
=> ( v10 @ Y12 ) ) ) ) )
| ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) ) )
| ~ $true ) ),
inference(superposition,[status(thm)],[f467,f1949]) ).
thf(f1949,plain,
! [X5: mworld] :
( $true
= ( v23 @ ( sK8 @ X5 ) ) ),
inference(boolean_simplification,[status(thm)],[f1948]) ).
thf(f1948,plain,
! [X5: mworld] :
( $true
= ( ( v23 @ ( sK8 @ X5 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f1947,f358]) ).
thf(f1947,plain,
! [X5: mworld] :
( $true
= ( ( v23 @ ( sK8 @ X5 ) )
& ( mrel @ X5 @ ( sK8 @ X5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1946]) ).
thf(f1946,plain,
! [X5: mworld] :
( ( ^ [Y0: mworld] :
( ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) )
@ ( sK8 @ X5 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f1936]) ).
thf(f467,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 )
=> ( v10 @ Y12 ) ) ) ) )
| ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) ) )
| ~ ( v23 @ X6 ) ) ),
inference(boolean_simplification,[status(thm)],[f466]) ).
thf(f466,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 )
=> ( v10 @ Y12 ) ) ) ) )
| ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) ) )
| ~ ( v23 @ X6 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f465,f358]) ).
thf(f465,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 )
=> ( v10 @ Y12 ) ) ) ) )
| ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) ) )
| ~ ( v23 @ X6 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f464]) ).
thf(f464,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 )
=> ( v10 @ Y13 ) ) ) ) )
| ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) )
| ~ ( v23 @ Y0 ) ) )
@ X6 ) ),
inference(pi_clausification,[status(thm)],[f463]) ).
thf(f463,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 )
=> ( v10 @ Y13 ) ) ) ) )
| ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) )
| ~ ( v23 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f462]) ).
thf(f462,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 )
=> ( v10 @ Y13 ) ) ) ) )
| ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) )
| ~ ( v23 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f461,f358]) ).
thf(f461,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 )
=> ( v10 @ Y13 ) ) ) ) )
| ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) )
| ~ ( v23 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f460]) ).
thf(f460,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 )
=> ( v10 @ Y14 ) ) ) ) )
| ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y2 ) ) ) )
| ~ ( v23 @ Y1 ) ) ) ) )
@ X5 )
= $true ),
inference(pi_clausification,[status(thm)],[f459]) ).
thf(f459,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 )
=> ( v10 @ Y14 ) ) ) ) )
| ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y2 ) ) ) )
| ~ ( v23 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f458]) ).
thf(f458,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 )
=> ( v10 @ Y14 ) ) ) ) )
| ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y2 ) ) ) )
| ~ ( v23 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f457,f358]) ).
thf(f457,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 )
=> ( v10 @ Y14 ) ) ) ) )
| ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y2 ) ) ) )
| ~ ( v23 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f456]) ).
thf(f456,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 )
=> ( v10 @ Y15 ) ) ) ) )
| ~ ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y3 ) ) ) )
| ~ ( v23 @ Y2 ) ) ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f455]) ).
thf(f455,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 )
=> ( v10 @ Y15 ) ) ) ) )
| ~ ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y3 ) ) ) )
| ~ ( v23 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f454]) ).
thf(f454,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 )
=> ( v10 @ Y15 ) ) ) ) )
| ~ ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y3 ) ) ) )
| ~ ( v23 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f453,f358]) ).
thf(f453,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 )
=> ( v10 @ Y15 ) ) ) ) )
| ~ ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y3 ) ) ) )
| ~ ( v23 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f452]) ).
thf(f452,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 )
=> ( v10 @ Y16 ) ) ) ) )
| ~ ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) )
| ~ ( v23 @ Y3 ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f451]) ).
thf(f451,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 )
=> ( v10 @ Y16 ) ) ) ) )
| ~ ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) )
| ~ ( v23 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f450]) ).
thf(f450,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 )
=> ( v10 @ Y16 ) ) ) ) )
| ~ ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) )
| ~ ( v23 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f449,f358]) ).
thf(f449,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 )
=> ( v10 @ Y16 ) ) ) ) )
| ~ ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) )
| ~ ( v23 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f448]) ).
thf(f448,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 )
=> ( v10 @ Y17 ) ) ) ) )
| ~ ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) )
| ~ ( v23 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f447]) ).
thf(f447,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 )
=> ( v10 @ Y17 ) ) ) ) )
| ~ ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) )
| ~ ( v23 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f446]) ).
thf(f446,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 )
=> ( v10 @ Y17 ) ) ) ) )
| ~ ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) )
| ~ ( v23 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f445,f358]) ).
thf(f445,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 )
=> ( v10 @ Y17 ) ) ) ) )
| ~ ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) )
| ~ ( v23 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f444]) ).
thf(f444,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 )
=> ( v10 @ Y18 ) ) ) ) )
| ~ ( v12 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y6 ) ) ) )
| ~ ( v23 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f307]) ).
thf(f307,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 )
=> ( v10 @ Y18 ) ) ) ) )
| ~ ( v12 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v22 @ Y6 ) ) ) )
| ~ ( v23 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f289]) ).
thf(f289,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] :
( !! @ 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 )
@ v23 )
@ ( ^ [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 ) ) )
@ ( ^ [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 )
@ v12 )
@ ( ^ [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 ) ) )
@ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f236,f226,f239,f239,f239,f239,f239,f239,f201,f213,f239,f201,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f201,f213,f239,f239]) ).
thf(f236,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f139]) ).
thf(f139,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f138]) ).
thf(f138,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f43]) ).
thf(f43,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod34) ).
thf(f2415,plain,
( spl0_7
| spl0_13
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f2411,f833,f2413,f1321]) ).
thf(f833,definition,
( spl0_4
<=> ! [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 ) ) ) ) ) ) )
| ( v12 @ Y2 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f2411,plain,
( ! [X18: mworld,X17: mworld] :
( ( $true
= ( v12 @ X17 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) ) )
= $true ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f2410]) ).
thf(f2410,plain,
( ! [X18: mworld,X17: mworld] :
( ( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v12 @ X17 ) ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f2408,f358]) ).
thf(f2408,plain,
( ! [X18: mworld,X17: mworld] :
( ( $true
= ( v12 @ X17 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f2406]) ).
thf(f2406,plain,
( ! [X18: mworld,X17: mworld] :
( ( $true
= ( v12 @ X17 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v9 @ Y2 ) ) ) ) ) )
@ X18 )
= $true ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f2160]) ).
thf(f2160,plain,
( ! [X17: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v9 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $true
= ( v12 @ X17 ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f2159]) ).
thf(f2159,plain,
( ! [X17: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v9 @ Y2 ) ) ) ) ) ) )
| ( v12 @ X17 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f2158]) ).
thf(f2158,plain,
( ! [X17: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v9 @ Y2 ) ) ) ) ) ) )
| ( v12 @ X17 ) ) ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f2157,f358]) ).
thf(f2157,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 )
=> ~ ( v9 @ Y2 ) ) ) ) ) ) )
| ( v12 @ X17 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f2156]) ).
thf(f2156,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 )
=> ~ ( v9 @ Y3 ) ) ) ) ) ) )
| ( v12 @ Y0 ) ) )
@ X17 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f2155]) ).
thf(f2155,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 )
=> ~ ( v9 @ Y3 ) ) ) ) ) ) )
| ( v12 @ Y0 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f2154]) ).
thf(f2154,plain,
( ! [X16: mworld] :
( $true
= ( $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 )
=> ~ ( v9 @ Y3 ) ) ) ) ) ) )
| ( v12 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f2153,f358]) ).
thf(f2153,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 )
=> ~ ( v9 @ Y3 ) ) ) ) ) ) )
| ( v12 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f2152]) ).
thf(f2152,plain,
( ! [X16: mworld,X15: mworld] :
( $true
= ( ^ [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 )
=> ~ ( v9 @ Y4 ) ) ) ) ) ) )
| ( v12 @ Y1 ) ) ) ) )
@ X16 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f2151]) ).
thf(f2151,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 )
=> ~ ( v9 @ Y4 ) ) ) ) ) ) )
| ( v12 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f2150]) ).
thf(f2150,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 )
=> ~ ( v9 @ Y4 ) ) ) ) ) ) )
| ( v12 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f2149,f358]) ).
thf(f2149,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 )
=> ~ ( v9 @ Y4 ) ) ) ) ) ) )
| ( v12 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f2148]) ).
thf(f2148,plain,
( ! [X14: mworld,X15: mworld] :
( $true
= ( ^ [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 ) ) ) ) ) ) )
| ( v12 @ Y2 ) ) ) ) ) ) )
@ X15 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f834]) ).
thf(f834,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 ) ) ) ) ) ) )
| ( v12 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f833]) ).
thf(f2141,plain,
spl0_4,
inference(avatar_split_clause,[status(thm)],[f2140,f833]) ).
thf(f2140,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 )
=> ~ ( v9 @ Y5 ) ) ) ) ) ) )
| ( v12 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2139]) ).
thf(f2139,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 )
=> ~ ( v9 @ Y5 ) ) ) ) ) ) )
| ( v12 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2138,f358]) ).
thf(f2138,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ( mrel @ ( sK12 @ 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 )
=> ~ ( v9 @ Y5 ) ) ) ) ) ) )
| ( v12 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2135]) ).
thf(f2135,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ 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 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) )
| ( v12 @ Y3 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f2126]) ).
thf(f2126,plain,
! [X0: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ 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 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) )
| ( v12 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2125]) ).
thf(f2125,plain,
! [X0: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ 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 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) )
| ( v12 @ Y3 ) ) ) ) ) ) ) ) ) )
| $false ) ),
inference(superposition,[status(thm)],[f2023,f2118]) ).
thf(f2118,plain,
! [X12: mworld] :
( $false
= ( v16 @ ( sK12 @ X12 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f2117]) ).
thf(f2117,plain,
! [X12: mworld] :
( $true
= ( ~ ( v16 @ ( sK12 @ X12 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2116]) ).
thf(f2116,plain,
! [X12: mworld] :
( $true
= ( ~ ( v16 @ ( sK12 @ X12 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2110,f358]) ).
thf(f2110,plain,
! [X12: mworld] :
( $true
= ( ~ ( v16 @ ( sK12 @ X12 ) )
& ( mrel @ X12 @ ( sK12 @ X12 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2109]) ).
thf(f2109,plain,
! [X12: mworld] :
( ( ^ [Y0: mworld] :
( ~ ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) )
@ ( sK12 @ X12 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f2108]) ).
thf(f2108,plain,
! [X12: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2107]) ).
thf(f2107,plain,
! [X12: mworld] :
( ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f2104,f2106]) ).
thf(f2106,plain,
! [X12: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2104]) ).
thf(f2104,plain,
! [X12: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2103]) ).
thf(f2103,plain,
! [X12: mworld] :
( ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f2096,f2102]) ).
thf(f2023,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 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) )
| ( v12 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( v16 @ X5 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2022]) ).
thf(f2022,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 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) )
| ( v12 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( v16 @ X5 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2021,f358]) ).
thf(f2021,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 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) )
| ( v12 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( v16 @ X5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2020]) ).
thf(f2020,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 )
=> ~ ( v9 @ Y7 ) ) ) ) ) ) )
| ( v12 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y0 ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f2019]) ).
thf(f2019,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 )
=> ~ ( v9 @ Y7 ) ) ) ) ) ) )
| ( v12 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2018]) ).
thf(f2018,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 )
=> ~ ( v9 @ Y7 ) ) ) ) ) ) )
| ( v12 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2017,f358]) ).
thf(f2017,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 )
=> ~ ( v9 @ Y7 ) ) ) ) ) ) )
| ( v12 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2016]) ).
thf(f2016,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 )
=> ~ ( v9 @ Y8 ) ) ) ) ) ) )
| ( v12 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y1 ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f2015]) ).
thf(f2015,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 )
=> ~ ( v9 @ Y8 ) ) ) ) ) ) )
| ( v12 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2014]) ).
thf(f2014,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 )
=> ~ ( v9 @ Y8 ) ) ) ) ) ) )
| ( v12 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y1 ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2013,f358]) ).
thf(f2013,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 )
=> ~ ( v9 @ Y8 ) ) ) ) ) ) )
| ( v12 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2012]) ).
thf(f2012,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 )
=> ~ ( v9 @ Y9 ) ) ) ) ) ) )
| ( v12 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y2 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f2011]) ).
thf(f2011,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 )
=> ~ ( v9 @ Y9 ) ) ) ) ) ) )
| ( v12 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2010]) ).
thf(f2010,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 )
=> ~ ( v9 @ Y9 ) ) ) ) ) ) )
| ( v12 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2009,f358]) ).
thf(f2009,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 )
=> ~ ( v9 @ Y9 ) ) ) ) ) ) )
| ( v12 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2008]) ).
thf(f2008,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 )
=> ~ ( v9 @ Y10 ) ) ) ) ) ) )
| ( v12 @ Y7 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y3 ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f2001]) ).
thf(f2001,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 )
=> ~ ( v9 @ Y10 ) ) ) ) ) ) )
| ( v12 @ Y7 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2000]) ).
thf(f2000,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 )
=> ~ ( v9 @ Y10 ) ) ) ) ) ) )
| ( v12 @ Y7 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1999,f358]) ).
thf(f1999,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ( mrel @ ( sK6 @ 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 )
=> ~ ( v9 @ Y10 ) ) ) ) ) ) )
| ( v12 @ Y7 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1996]) ).
thf(f1996,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK6 @ 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 )
=> ~ ( v9 @ Y11 ) ) ) ) ) ) )
| ( v12 @ Y8 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1934]) ).
thf(f1934,plain,
! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK6 @ 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 )
=> ~ ( v9 @ Y11 ) ) ) ) ) ) )
| ( v12 @ Y8 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1933]) ).
thf(f1933,plain,
! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK6 @ 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 )
=> ~ ( v9 @ Y11 ) ) ) ) ) ) )
| ( v12 @ Y8 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| $false )
= $true ),
inference(boolean_simplification,[status(thm)],[f1929]) ).
thf(f1929,plain,
! [X0: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK6 @ 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 )
=> ~ ( v9 @ Y11 ) ) ) ) ) ) )
| ( v12 @ Y8 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ~ $true ) ),
inference(superposition,[status(thm)],[f554,f1913]) ).
thf(f1913,plain,
! [X7: mworld] :
( $true
= ( v21 @ ( sK6 @ X7 ) ) ),
inference(boolean_simplification,[status(thm)],[f1912]) ).
thf(f1912,plain,
! [X7: mworld] :
( $true
= ( ( v21 @ ( sK6 @ X7 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f1900,f358]) ).
thf(f1900,plain,
! [X7: mworld] :
( ( ( v21 @ ( sK6 @ X7 ) )
& ( mrel @ X7 @ ( sK6 @ X7 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1899]) ).
thf(f1899,plain,
! [X7: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) )
@ ( sK6 @ X7 ) ) ),
inference(sigma_clausification,[status(thm)],[f1898]) ).
thf(f1898,plain,
! [X7: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1897]) ).
thf(f1897,plain,
! [X7: mworld] :
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f1894,f1895]) ).
thf(f554,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 )
=> ~ ( v9 @ Y11 ) ) ) ) ) ) )
| ( v12 @ Y8 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ X8 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f553]) ).
thf(f553,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 ) ) ) ) ) ) )
| ( v12 @ Y8 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ X8 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f552,f358]) ).
thf(f552,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 ) ) ) ) ) ) )
| ( v12 @ Y8 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ X8 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f551]) ).
thf(f551,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 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) )
| ( v12 @ Y9 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y0 ) ) )
@ X8 ) ),
inference(pi_clausification,[status(thm)],[f550]) ).
thf(f550,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 ) ) ) ) ) ) )
| ( v12 @ Y9 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f549]) ).
thf(f549,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 ) ) ) ) ) ) )
| ( v12 @ Y9 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f548,f358]) ).
thf(f548,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 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) )
| ( v12 @ Y9 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f547]) ).
thf(f547,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 )
=> ~ ( v9 @ Y13 ) ) ) ) ) ) )
| ( v12 @ Y10 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y1 ) ) ) ) )
@ X7 ) ),
inference(pi_clausification,[status(thm)],[f546]) ).
thf(f546,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 ) ) ) ) ) ) )
| ( v12 @ Y10 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f545]) ).
thf(f545,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 )
=> ~ ( v9 @ Y13 ) ) ) ) ) ) )
| ( v12 @ Y10 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y1 ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f544,f358]) ).
thf(f544,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 ) ) ) ) ) ) )
| ( v12 @ Y10 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f543]) ).
thf(f543,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 )
=> ~ ( v9 @ Y14 ) ) ) ) ) ) )
| ( v12 @ Y11 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y2 ) ) ) ) ) ) )
@ X6 ) ),
inference(pi_clausification,[status(thm)],[f542]) ).
thf(f542,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 ) ) ) ) ) ) )
| ( v12 @ Y11 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f541]) ).
thf(f541,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 ) ) ) ) ) ) )
| ( v12 @ Y11 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f540,f358]) ).
thf(f540,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 ) ) ) ) ) ) )
| ( v12 @ Y11 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f539]) ).
thf(f539,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 ) ) ) ) ) ) )
| ( v12 @ Y12 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y3 ) ) ) ) ) ) ) ) )
@ X5 )
= $true ),
inference(pi_clausification,[status(thm)],[f538]) ).
thf(f538,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 ) ) ) ) ) ) )
| ( v12 @ Y12 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f537]) ).
thf(f537,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 )
=> ~ ( v9 @ Y15 ) ) ) ) ) ) )
| ( v12 @ Y12 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f536,f358]) ).
thf(f536,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 )
=> ~ ( v9 @ Y15 ) ) ) ) ) ) )
| ( v12 @ Y12 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f535]) ).
thf(f535,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 )
=> ~ ( v9 @ Y16 ) ) ) ) ) ) )
| ( v12 @ Y13 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f534]) ).
thf(f534,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 )
=> ~ ( v9 @ Y16 ) ) ) ) ) ) )
| ( v12 @ Y13 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f533]) ).
thf(f533,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 )
=> ~ ( v9 @ Y16 ) ) ) ) ) ) )
| ( v12 @ Y13 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f532,f358]) ).
thf(f532,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 ) ) ) ) ) ) )
| ( v12 @ Y13 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f531]) ).
thf(f531,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 ) ) ) ) ) ) )
| ( v12 @ Y14 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f530]) ).
thf(f530,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 ) ) ) ) ) ) )
| ( v12 @ Y14 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f529]) ).
thf(f529,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 ) ) ) ) ) ) )
| ( v12 @ Y14 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f528,f358]) ).
thf(f528,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 ) ) ) ) ) ) )
| ( v12 @ Y14 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f527]) ).
thf(f527,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 ) ) ) ) ) ) )
| ( v12 @ Y15 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f526]) ).
thf(f526,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 ) ) ) ) ) ) )
| ( v12 @ Y15 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f525]) ).
thf(f525,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 )
=> ~ ( v9 @ Y18 ) ) ) ) ) ) )
| ( v12 @ Y15 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f524,f358]) ).
thf(f524,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 ) ) ) ) ) ) )
| ( v12 @ Y15 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f523]) ).
thf(f523,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 ) ) ) ) ) ) )
| ( v12 @ Y16 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y12 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f327]) ).
thf(f327,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 ) ) ) ) ) ) )
| ( v12 @ Y16 ) ) ) ) ) ) ) ) ) )
| ( v16 @ Y12 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f274]) ).
thf(f274,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] :
( !! @ 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 > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ 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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v12
@ ( ^ [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 )
@ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f218,f226,f239,f239,f239,f239,f239,f239,f239,f239,f201,f213,f239,f239,f239,f239,f239,f201,f239,f239,f239,f239,f201,f239,f239,f239,f213]) ).
thf(f218,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f145]) ).
thf(f145,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f144]) ).
thf(f144,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f48]) ).
thf(f48,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod39) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO905^6 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n025.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 14:53:57 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SYO905^6 : TPTP v9.2.1. Released v8.1.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : QBF-CNFSSS-K=4 C=50 V=4 D=6.3
% 0.16/0.39 % Version : [BP13] axioms.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.16/0.39 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.16/0.39 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.16/0.39 % Source : [TPTP]
% 0.16/0.39 % Names : SYM362+1 [QMLTP]
% 0.16/0.39
% 0.16/0.39 % Status : ContradictoryAxioms
% 0.16/0.39 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.70 v8.2.0, 0.62 v8.1.0
% 0.16/0.39 % Syntax : Number of formulae : 100 ( 9 unt; 39 typ; 8 def)
% 0.16/0.39 % Number of atoms : 1880 ( 8 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 159 ( 30 avg)
% 0.16/0.39 % Number of connectives : 1834 ( 1 ~; 1 |; 2 &;1827 @)
% 0.16/0.39 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 85 ( 26 avg)
% 0.16/0.39 % Number of types : 2 ( 1 usr)
% 0.16/0.39 % Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 41 ( 38 usr; 3 con; 0-3 aty)
% 0.16/0.39 % Number of variables : 40 ( 36 ^; 3 !; 1 ?; 40 :)
% 0.16/0.39 % SPC : TH0_CAX_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.16/0.39 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.16/0.39 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.16/0.39 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.16/0.39 % $modalities == $modal_system_S5U].
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(mworld,type,
% 0.16/0.39 mworld: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(mrel_type,type,
% 0.16/0.39 mrel: mworld > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mactual_type,type,
% 0.16/0.39 mactual: mworld ).
% 0.16/0.39
% 0.16/0.39 thf(mlocal_type,type,
% 0.16/0.39 mlocal: ( mworld > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mlocal_def,definition,
% 0.16/0.39 ( mlocal
% 0.16/0.39 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mnot_type,type,
% 0.16/0.39 mnot: ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mand_type,type,
% 0.16/0.39 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mor_type,type,
% 0.16/0.39 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mimplies_type,type,
% 0.16/0.39 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mequiv_type,type,
% 0.16/0.39 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mnot_def,definition,
% 0.16/0.39 ( mnot
% 0.16/0.39 = ( ^ [A: mworld > $o,W: mworld] :
% 0.16/0.39 ~ ( A @ W ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mand_def,definition,
% 0.16/0.39 ( mand
% 0.16/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.39 ( ( A @ W )
% 0.16/0.39 & ( B @ W ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mor_def,definition,
% 0.16/0.39 ( mor
% 0.16/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.39 ( ( A @ W )
% 0.16/0.39 | ( B @ W ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mimplies_def,definition,
% 0.16/0.39 ( mimplies
% 0.16/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.39 ( ( A @ W )
% 0.16/0.39 => ( B @ W ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mequiv_def,definition,
% 0.16/0.39 ( mequiv
% 0.16/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.39 ( ( A @ W )
% 0.16/0.39 <=> ( B @ W ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mbox_type,type,
% 0.16/0.39 mbox: ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mbox_def,definition,
% 0.16/0.39 ( mbox
% 0.16/0.39 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.16/0.39 ! [V: mworld] :
% 0.16/0.39 ( ( mrel @ W @ V )
% 0.16/0.39 => ( Phi @ V ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mdia_type,type,
% 0.16/0.39 mdia: ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mdia_def,definition,
% 0.16/0.39 ( mdia
% 0.16/0.39 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.16/0.39 ? [V: mworld] :
% 0.16/0.39 ( ( mrel @ W @ V )
% 0.16/0.39 & ( Phi @ V ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mrel_universal,axiom,
% 0.16/0.39 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 0.16/0.39
% 0.16/0.39 %%% This output was generated by tptputils, version 1.2.
% 0.16/0.39 %%% Generated on Wed Apr 27 15:40:50 CEST 2022 using command 'downgrade(tff)'.
% 0.16/0.39 thf(v1_decl,type,
% 0.16/0.39 v1: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v2_decl,type,
% 0.16/0.39 v2: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v3_decl,type,
% 0.16/0.39 v3: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v4_decl,type,
% 0.16/0.39 v4: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v5_decl,type,
% 0.16/0.39 v5: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v6_decl,type,
% 0.16/0.39 v6: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v7_decl,type,
% 0.16/0.39 v7: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v8_decl,type,
% 0.16/0.39 v8: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v9_decl,type,
% 0.16/0.39 v9: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v10_decl,type,
% 0.16/0.39 v10: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v12_decl,type,
% 0.16/0.39 v12: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v11_decl,type,
% 0.16/0.39 v11: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v14_decl,type,
% 0.16/0.39 v14: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v13_decl,type,
% 0.16/0.39 v13: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v16_decl,type,
% 0.16/0.39 v16: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v15_decl,type,
% 0.16/0.39 v15: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v18_decl,type,
% 0.16/0.39 v18: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v17_decl,type,
% 0.16/0.39 v17: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v19_decl,type,
% 0.16/0.39 v19: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v21_decl,type,
% 0.16/0.39 v21: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v20_decl,type,
% 0.16/0.39 v20: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v23_decl,type,
% 0.16/0.39 v23: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v22_decl,type,
% 0.16/0.39 v22: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v25_decl,type,
% 0.16/0.39 v25: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v24_decl,type,
% 0.16/0.39 v24: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v27_decl,type,
% 0.16/0.39 v27: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v26_decl,type,
% 0.16/0.39 v26: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(v28_decl,type,
% 0.16/0.39 v28: mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mod1,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod2,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mbox @ ( mnot @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod3,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod4,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod5,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v5 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod6,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod7,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( 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 @ ( mor @ ( mnot @ v9 ) @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod8,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v11 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod9,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod10,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod11,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod12,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod13,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod14,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod15,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod16,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod17,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( 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 @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod18,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod19,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mnot @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod20,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod21,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v17 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod22,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod23,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v18 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod24,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v19 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod25,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod26,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v8 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod27,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod28,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod29,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod30,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod31,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod32,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v18 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod33,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod34,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod35,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod36,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod37,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod38,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod39,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod40,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod41,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod42,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod43,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod44,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v11 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod45,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v11 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod46,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod47,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v2 ) @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod48,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v7 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod49,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v11 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v8 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v5 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mod50,axiom,
% 0.16/0.39 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v11 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v7 @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(alt1,axiom,
% 0.16/0.39 ( mlocal
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
% 0.16/0.39 @ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) )
% 0.16/0.39 @ ( mdia
% 0.16/0.39 @ ^ [W: mworld] : $true ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(result1,conjecture,
% 0.16/0.39 ( mlocal
% 0.16/0.39 @ ^ [W: mworld] : $false ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 2.45/1.55 ---- Embedded in THF ---
% 2.45/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.45/1.55 %%% Generated on Tue Feb 24 14:53:58 EST 2026
% 2.45/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 2.45/1.55 %%% Logic specification used:
% 2.45/1.55 %%% thf(spec, logic, $$dhol).
% 2.45/1.55
% 2.45/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2DTF26726.p
% See solution above
% 2.45/1.55 ------------------------
% 2.45/1.57 ---- Cleaned THF ---
% 2.45/1.58 thf(mworld,type,
% 2.45/1.58 mworld: $tType ).
% 2.45/1.58
% 2.45/1.58 thf(mrel_type,type,
% 2.45/1.58 mrel: mworld > mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(mactual_type,type,
% 2.45/1.58 mactual: mworld ).
% 2.45/1.58
% 2.45/1.58 thf(mlocal_type,type,
% 2.45/1.58 mlocal: ( mworld > $o ) > $o ).
% 2.45/1.58
% 2.45/1.58 thf(mlocal_def,definition,
% 2.45/1.58 ( mlocal
% 2.45/1.58 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mnot_type,type,
% 2.45/1.58 mnot: ( mworld > $o ) > mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(mand_type,type,
% 2.45/1.58 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(mor_type,type,
% 2.45/1.58 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(mimplies_type,type,
% 2.45/1.58 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(mequiv_type,type,
% 2.45/1.58 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(mnot_def,definition,
% 2.45/1.58 ( mnot
% 2.45/1.58 = ( ^ [A: mworld > $o,W: mworld] :
% 2.45/1.58 ~ ( A @ W ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mand_def,definition,
% 2.45/1.58 ( mand
% 2.45/1.58 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.45/1.58 ( ( A @ W )
% 2.45/1.58 & ( B @ W ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mor_def,definition,
% 2.45/1.58 ( mor
% 2.45/1.58 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.45/1.58 ( ( A @ W )
% 2.45/1.58 | ( B @ W ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mimplies_def,definition,
% 2.45/1.58 ( mimplies
% 2.45/1.58 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.45/1.58 ( ( A @ W )
% 2.45/1.58 => ( B @ W ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mequiv_def,definition,
% 2.45/1.58 ( mequiv
% 2.45/1.58 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.45/1.58 ( ( A @ W )
% 2.45/1.58 <=> ( B @ W ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mbox_type,type,
% 2.45/1.58 mbox: ( mworld > $o ) > mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(mbox_def,definition,
% 2.45/1.58 ( mbox
% 2.45/1.58 = ( ^ [Phi: mworld > $o,W: mworld] :
% 2.45/1.58 ! [V: mworld] :
% 2.45/1.58 ( ( mrel @ W @ V )
% 2.45/1.58 => ( Phi @ V ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mdia_type,type,
% 2.45/1.58 mdia: ( mworld > $o ) > mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(mdia_def,definition,
% 2.45/1.58 ( mdia
% 2.45/1.58 = ( ^ [Phi: mworld > $o,W: mworld] :
% 2.45/1.58 ? [V: mworld] :
% 2.45/1.58 ( ( mrel @ W @ V )
% 2.45/1.58 & ( Phi @ V ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mrel_universal,axiom,
% 2.45/1.58 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 2.45/1.58
% 2.45/1.58 thf(v1_decl,type,
% 2.45/1.58 v1: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v2_decl,type,
% 2.45/1.58 v2: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v3_decl,type,
% 2.45/1.58 v3: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v4_decl,type,
% 2.45/1.58 v4: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v5_decl,type,
% 2.45/1.58 v5: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v6_decl,type,
% 2.45/1.58 v6: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v7_decl,type,
% 2.45/1.58 v7: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v8_decl,type,
% 2.45/1.58 v8: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v9_decl,type,
% 2.45/1.58 v9: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v10_decl,type,
% 2.45/1.58 v10: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v12_decl,type,
% 2.45/1.58 v12: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v11_decl,type,
% 2.45/1.58 v11: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v14_decl,type,
% 2.45/1.58 v14: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v13_decl,type,
% 2.45/1.58 v13: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v16_decl,type,
% 2.45/1.58 v16: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v15_decl,type,
% 2.45/1.58 v15: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v18_decl,type,
% 2.45/1.58 v18: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v17_decl,type,
% 2.45/1.58 v17: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v19_decl,type,
% 2.45/1.58 v19: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v21_decl,type,
% 2.45/1.58 v21: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v20_decl,type,
% 2.45/1.58 v20: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v23_decl,type,
% 2.45/1.58 v23: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v22_decl,type,
% 2.45/1.58 v22: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v25_decl,type,
% 2.45/1.58 v25: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v24_decl,type,
% 2.45/1.58 v24: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v27_decl,type,
% 2.45/1.58 v27: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v26_decl,type,
% 2.45/1.58 v26: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(v28_decl,type,
% 2.45/1.58 v28: mworld > $o ).
% 2.45/1.58
% 2.45/1.58 thf(mod1,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod2,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mbox @ ( mnot @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod3,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod4,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod5,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v5 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod6,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod7,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( 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 @ ( mor @ ( mnot @ v9 ) @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod8,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v11 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod9,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod10,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod11,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod12,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod13,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod14,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod15,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod16,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod17,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( 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 @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod18,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod19,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mnot @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod20,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod21,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v17 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod22,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod23,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v18 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod24,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v19 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod25,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod26,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v8 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod27,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod28,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod29,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod30,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod31,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod32,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v18 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod33,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod34,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod35,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod36,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod37,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod38,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod39,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod40,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod41,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod42,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod43,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod44,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v11 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod45,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v11 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod46,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod47,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v2 ) @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod48,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v7 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod49,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v11 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v8 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v5 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(mod50,axiom,
% 2.45/1.58 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v11 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v7 @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(alt1,axiom,
% 2.45/1.58 ( mlocal
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mand
% 2.45/1.58 @ ( mbox
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
% 2.45/1.58 @ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) )
% 2.45/1.58 @ ( mdia
% 2.45/1.58 @ ^ [W: mworld] : $true ) ) ) ).
% 2.45/1.58
% 2.45/1.58 thf(result1,conjecture,
% 2.45/1.58 ( mlocal
% 2.45/1.58 @ ^ [W: mworld] : $false ) ).
% 2.45/1.58 ------------------------
% 2.55/1.61 % (26824)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/183Mi)
% 2.55/1.61 % (26826)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_26726 for (2999ds/27Mi)
% 2.55/1.61 % (26829)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_26726 for (2999ds/275Mi)
% 2.55/1.61 % (26825)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_26726 for (2999ds/4Mi)
% 2.55/1.61 % (26828)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_26726 for (2999ds/2Mi)
% 2.55/1.61 % (26827)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/2Mi)
% 2.55/1.61 % (26830)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/18Mi)
% 2.55/1.61 % (26827)Instruction limit reached!
% 2.55/1.61 % (26827)------------------------------
% 2.55/1.61 % (26827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.61 % (26827)Termination reason: Unknown
% 2.55/1.61 % (26827)Termination phase: shuffling
% 2.55/1.61 % (26828)Instruction limit reached!
% 2.55/1.61 % (26828)------------------------------
% 2.55/1.61 % (26828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.61 % (26828)Termination reason: Unknown
% 2.55/1.61 % (26828)Termination phase: shuffling
% 2.55/1.61
% 2.55/1.61 % (26828)Memory used [KB]: 1151
% 2.55/1.61 % (26828)Time elapsed: 0.003 s
% 2.55/1.61 % (26828)Instructions burned: 2 (million)
% 2.55/1.61 % (26828)------------------------------
% 2.55/1.61 % (26828)------------------------------
% 2.55/1.61
% 2.55/1.61 % (26827)Memory used [KB]: 1151
% 2.55/1.61 % (26827)Time elapsed: 0.003 s
% 2.55/1.61 % (26827)Instructions burned: 2 (million)
% 2.55/1.61 % (26827)------------------------------
% 2.55/1.61 % (26827)------------------------------
% 2.55/1.61 % (26825)Instruction limit reached!
% 2.55/1.61 % (26825)------------------------------
% 2.55/1.61 % (26825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.61 % (26825)Termination reason: Unknown
% 2.55/1.61 % (26825)Termination phase: shuffling
% 2.55/1.61
% 2.55/1.61 % (26825)Memory used [KB]: 1151
% 2.55/1.61 % (26825)Time elapsed: 0.004 s
% 2.55/1.61 % (26825)Instructions burned: 4 (million)
% 2.55/1.61 % (26825)------------------------------
% 2.55/1.61 % (26825)------------------------------
% 2.55/1.61 % (26830)Instruction limit reached!
% 2.55/1.61 % (26830)------------------------------
% 2.55/1.61 % (26830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.61 % (26830)Termination reason: Unknown
% 2.55/1.61 % (26830)Termination phase: shuffling
% 2.55/1.61
% 2.55/1.61 % (26830)Memory used [KB]: 1151
% 2.55/1.61 % (26830)Time elapsed: 0.009 s
% 2.55/1.61 % (26830)Instructions burned: 18 (million)
% 2.55/1.61 % (26830)------------------------------
% 2.55/1.61 % (26830)------------------------------
% 2.55/1.62 % (26826)Instruction limit reached!
% 2.55/1.62 % (26826)------------------------------
% 2.55/1.62 % (26826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.62 % (26826)Termination reason: Unknown
% 2.55/1.62 % (26826)Termination phase: shuffling
% 2.55/1.62
% 2.55/1.62 % (26826)Memory used [KB]: 1151
% 2.55/1.62 % (26826)Time elapsed: 0.013 s
% 2.55/1.62 % (26826)Instructions burned: 28 (million)
% 2.55/1.62 % (26826)------------------------------
% 2.55/1.62 % (26826)------------------------------
% 2.55/1.62 % (26831)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/3Mi)
% 2.55/1.62 % (26832)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_26726 for (2999ds/37Mi)
% 2.55/1.63 % (26833)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_26726 for (2999ds/15Mi)
% 2.55/1.63 % (26831)Instruction limit reached!
% 2.55/1.63 % (26831)------------------------------
% 2.55/1.63 % (26831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.63 % (26831)Termination reason: Unknown
% 2.55/1.63 % (26831)Termination phase: shuffling
% 2.55/1.63
% 2.55/1.63 % (26831)Memory used [KB]: 1151
% 2.55/1.63 % (26831)Time elapsed: 0.003 s
% 2.55/1.63 % (26831)Instructions burned: 4 (million)
% 2.55/1.63 % (26831)------------------------------
% 2.55/1.63 % (26831)------------------------------
% 2.55/1.63 % (26829)Refutation not found, incomplete strategy
% 2.55/1.63 % (26829)------------------------------
% 2.55/1.63 % (26829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.63 % (26829)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.63
% 2.55/1.63
% 2.55/1.63 % (26829)Memory used [KB]: 5756
% 2.55/1.63 % (26829)Time elapsed: 0.024 s
% 2.55/1.63 % (26829)Instructions burned: 56 (million)
% 2.55/1.63 % (26829)------------------------------
% 2.55/1.63 % (26829)------------------------------
% 2.55/1.63 % (26834)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_26726 for (2999ds/3Mi)
% 2.55/1.63 % (26833)Instruction limit reached!
% 2.55/1.63 % (26833)------------------------------
% 2.55/1.63 % (26833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.63 % (26833)Termination reason: Unknown
% 2.55/1.63 % (26833)Termination phase: shuffling
% 2.55/1.63
% 2.55/1.63 % (26833)Memory used [KB]: 1151
% 2.55/1.63 % (26833)Time elapsed: 0.007 s
% 2.55/1.63 % (26833)Instructions burned: 15 (million)
% 2.55/1.63 % (26833)------------------------------
% 2.55/1.63 % (26833)------------------------------
% 2.55/1.63 % (26834)Instruction limit reached!
% 2.55/1.63 % (26834)------------------------------
% 2.55/1.63 % (26834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.63 % (26834)Termination reason: Unknown
% 2.55/1.63 % (26834)Termination phase: shuffling
% 2.55/1.63
% 2.55/1.63 % (26834)Memory used [KB]: 1151
% 2.55/1.63 % (26834)Time elapsed: 0.003 s
% 2.55/1.63 % (26834)Instructions burned: 5 (million)
% 2.55/1.63 % (26834)------------------------------
% 2.55/1.63 % (26834)------------------------------
% 2.55/1.63 % (26835)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_26726 for (2999ds/1041Mi)
% 2.55/1.64 % (26832)Instruction limit reached!
% 2.55/1.64 % (26832)------------------------------
% 2.55/1.64 % (26832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.64 % (26832)Termination reason: Unknown
% 2.55/1.64 % (26832)Termination phase: Function definition elimination
% 2.55/1.64
% 2.55/1.64 % (26832)Memory used [KB]: 1407
% 2.55/1.64 % (26832)Time elapsed: 0.017 s
% 2.55/1.64 % (26832)Instructions burned: 39 (million)
% 2.55/1.64 % (26832)------------------------------
% 2.55/1.64 % (26832)------------------------------
% 2.55/1.64 % (26836)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/7Mi)
% 2.55/1.64 % (26836)Instruction limit reached!
% 2.55/1.64 % (26836)------------------------------
% 2.55/1.64 % (26836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.64 % (26836)Termination reason: Unknown
% 2.55/1.64 % (26836)Termination phase: shuffling
% 2.55/1.64
% 2.55/1.64 % (26836)Memory used [KB]: 1151
% 2.55/1.64 % (26836)Time elapsed: 0.004 s
% 2.55/1.64 % (26836)Instructions burned: 7 (million)
% 2.55/1.64 % (26836)------------------------------
% 2.55/1.64 % (26836)------------------------------
% 2.55/1.65 % (26837)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/16Mi)
% 2.55/1.65 % (26838)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_26726 for (2999ds/3Mi)
% 2.55/1.65 % (26839)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_26726 for (2999ds/3Mi)
% 2.55/1.65 % (26838)Instruction limit reached!
% 2.55/1.65 % (26838)------------------------------
% 2.55/1.65 % (26838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.65 % (26838)Termination reason: Unknown
% 2.55/1.65 % (26838)Termination phase: shuffling
% 2.55/1.65
% 2.55/1.65 % (26838)Memory used [KB]: 1151
% 2.55/1.65 % (26838)Time elapsed: 0.003 s
% 2.55/1.65 % (26838)Instructions burned: 4 (million)
% 2.55/1.65 % (26838)------------------------------
% 2.55/1.65 % (26838)------------------------------
% 2.55/1.65 % (26839)Instruction limit reached!
% 2.55/1.65 % (26839)------------------------------
% 2.55/1.65 % (26839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.65 % (26839)Termination reason: Unknown
% 2.55/1.65 % (26839)Termination phase: shuffling
% 2.55/1.65
% 2.55/1.65 % (26839)Memory used [KB]: 1151
% 2.55/1.65 % (26839)Time elapsed: 0.003 s
% 2.55/1.65 % (26839)Instructions burned: 4 (million)
% 2.55/1.65 % (26839)------------------------------
% 2.55/1.65 % (26839)------------------------------
% 2.55/1.65 % (26837)Instruction limit reached!
% 2.55/1.65 % (26837)------------------------------
% 2.55/1.65 % (26837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.65 % (26837)Termination reason: Unknown
% 2.55/1.65 % (26837)Termination phase: shuffling
% 2.55/1.65
% 2.55/1.65 % (26837)Memory used [KB]: 1151
% 2.55/1.65 % (26837)Time elapsed: 0.008 s
% 2.55/1.65 % (26837)Instructions burned: 17 (million)
% 2.55/1.65 % (26837)------------------------------
% 2.55/1.65 % (26837)------------------------------
% 2.55/1.66 % (26840)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/7Mi)
% 2.55/1.66 % (26840)Instruction limit reached!
% 2.55/1.66 % (26840)------------------------------
% 2.55/1.66 % (26840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.66 % (26840)Termination reason: Unknown
% 2.55/1.66 % (26840)Termination phase: shuffling
% 2.55/1.66
% 2.55/1.66 % (26840)Memory used [KB]: 1151
% 2.55/1.66 % (26840)Time elapsed: 0.005 s
% 2.55/1.66 % (26840)Instructions burned: 9 (million)
% 2.55/1.66 % (26840)------------------------------
% 2.55/1.66 % (26840)------------------------------
% 2.55/1.66 % (26841)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/3Mi)
% 2.55/1.66 % (26841)Instruction limit reached!
% 2.55/1.66 % (26841)------------------------------
% 2.55/1.66 % (26841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.66 % (26841)Termination reason: Unknown
% 2.55/1.66 % (26841)Termination phase: shuffling
% 2.55/1.66
% 2.55/1.66 % (26841)Memory used [KB]: 1151
% 2.55/1.66 % (26841)Time elapsed: 0.003 s
% 2.55/1.66 % (26841)Instructions burned: 4 (million)
% 2.55/1.66 % (26841)------------------------------
% 2.55/1.66 % (26841)------------------------------
% 2.55/1.66 % (26842)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/4Mi)
% 2.55/1.67 % (26843)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/18Mi)
% 2.55/1.67 % (26842)Instruction limit reached!
% 2.55/1.67 % (26842)------------------------------
% 2.55/1.67 % (26842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.67 % (26842)Termination reason: Unknown
% 2.55/1.67 % (26842)Termination phase: shuffling
% 2.55/1.67
% 2.55/1.67 % (26842)Memory used [KB]: 1151
% 2.55/1.67 % (26842)Time elapsed: 0.003 s
% 2.55/1.67 % (26842)Instructions burned: 4 (million)
% 2.55/1.67 % (26842)------------------------------
% 2.55/1.67 % (26842)------------------------------
% 2.55/1.67 % (26844)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/710Mi)
% 2.55/1.67 % (26843)Instruction limit reached!
% 2.55/1.67 % (26843)------------------------------
% 2.55/1.67 % (26843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.67 % (26843)Termination reason: Unknown
% 2.55/1.67 % (26843)Termination phase: shuffling
% 2.55/1.67
% 2.55/1.67 % (26843)Memory used [KB]: 1151
% 2.55/1.67 % (26843)Time elapsed: 0.008 s
% 2.55/1.67 % (26843)Instructions burned: 18 (million)
% 2.55/1.67 % (26843)------------------------------
% 2.55/1.67 % (26843)------------------------------
% 2.55/1.68 % (26845)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/6Mi)
% 2.55/1.68 % (26846)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_26726 for (2999ds/902Mi)
% 2.55/1.68 % (26845)Instruction limit reached!
% 2.55/1.68 % (26845)------------------------------
% 2.55/1.68 % (26845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.68 % (26845)Termination reason: Unknown
% 2.55/1.68 % (26845)Termination phase: shuffling
% 2.55/1.68
% 2.55/1.68 % (26845)Memory used [KB]: 1151
% 2.55/1.68 % (26845)Time elapsed: 0.004 s
% 2.55/1.68 % (26845)Instructions burned: 7 (million)
% 2.55/1.68 % (26845)------------------------------
% 2.55/1.68 % (26845)------------------------------
% 2.55/1.68 % (26824)Instruction limit reached!
% 2.55/1.68 % (26824)------------------------------
% 2.55/1.68 % (26824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.68 % (26824)Termination reason: Unknown
% 2.55/1.68 % (26824)Termination phase: Saturation
% 2.55/1.68
% 2.55/1.68 % (26824)Memory used [KB]: 6140
% 2.55/1.68 % (26824)Time elapsed: 0.075 s
% 2.55/1.68 % (26824)Instructions burned: 184 (million)
% 2.55/1.68 % (26824)------------------------------
% 2.55/1.68 % (26824)------------------------------
% 2.55/1.68 % (26847)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_26726 for (2999ds/21Mi)
% 2.55/1.69 % (26848)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/5Mi)
% 2.55/1.69 % (26847)Instruction limit reached!
% 2.55/1.69 % (26847)------------------------------
% 2.55/1.69 % (26847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.69 % (26847)Termination reason: Unknown
% 2.55/1.69 % (26847)Termination phase: shuffling
% 2.55/1.69
% 2.55/1.69 % (26847)Memory used [KB]: 1279
% 2.55/1.69 % (26847)Time elapsed: 0.009 s
% 2.55/1.69 % (26847)Instructions burned: 21 (million)
% 2.55/1.69 % (26847)------------------------------
% 2.55/1.69 % (26847)------------------------------
% 2.55/1.69 % (26848)Instruction limit reached!
% 2.55/1.69 % (26848)------------------------------
% 2.55/1.69 % (26848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.69 % (26848)Termination reason: Unknown
% 2.55/1.69 % (26848)Termination phase: shuffling
% 2.55/1.69
% 2.55/1.69 % (26844)Refutation not found, incomplete strategy
% 2.55/1.69 % (26844)------------------------------
% 2.55/1.69 % (26844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.69 % (26848)Memory used [KB]: 1279
% 2.55/1.69 % (26848)Time elapsed: 0.004 s
% 2.55/1.69 % (26848)Instructions burned: 7 (million)
% 2.55/1.69 % (26848)------------------------------
% 2.55/1.69 % (26848)------------------------------
% 2.55/1.69 % (26844)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.69
% 2.55/1.69
% 2.55/1.69 % (26844)Memory used [KB]: 5756
% 2.55/1.69 % (26844)Time elapsed: 0.023 s
% 2.55/1.69 % (26844)Instructions burned: 56 (million)
% 2.55/1.69 % (26844)------------------------------
% 2.55/1.69 % (26844)------------------------------
% 2.55/1.69 % (26849)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_26726 for (2999ds/6Mi)
% 2.55/1.70 % (26850)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/377Mi)
% 2.55/1.70 % (26849)Instruction limit reached!
% 2.55/1.70 % (26849)------------------------------
% 2.55/1.70 % (26849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.70 % (26849)Termination reason: Unknown
% 2.55/1.70 % (26849)Termination phase: shuffling
% 2.55/1.70
% 2.55/1.70 % (26849)Memory used [KB]: 1151
% 2.55/1.70 % (26849)Time elapsed: 0.004 s
% 2.55/1.70 % (26849)Instructions burned: 6 (million)
% 2.55/1.70 % (26849)------------------------------
% 2.55/1.70 % (26849)------------------------------
% 2.55/1.71 % (26851)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_26726 for (2999ds/779Mi)
% 2.55/1.71 % (26852)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_26726 for (2999ds/19Mi)
% 2.55/1.71 % (26853)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26726 for (2999ds/879Mi)
% 2.55/1.71 % (26846)Refutation not found, incomplete strategy
% 2.55/1.71 % (26846)------------------------------
% 2.55/1.71 % (26846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.71 % (26846)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.71
% 2.55/1.71
% 2.55/1.71 % (26846)Memory used [KB]: 5884
% 2.55/1.71 % (26846)Time elapsed: 0.033 s
% 2.55/1.71 % (26846)Instructions burned: 78 (million)
% 2.55/1.71 % (26846)------------------------------
% 2.55/1.71 % (26846)------------------------------
% 2.55/1.71 % (26854)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26726 for (2998ds/17Mi)
% 2.55/1.72 % (26852)Instruction limit reached!
% 2.55/1.72 % (26852)------------------------------
% 2.55/1.72 % (26852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.72 % (26852)Termination reason: Unknown
% 2.55/1.72 % (26852)Termination phase: SInE selection
% 2.55/1.72
% 2.55/1.72 % (26852)Memory used [KB]: 1279
% 2.55/1.72 % (26852)Time elapsed: 0.010 s
% 2.55/1.72 % (26852)Instructions burned: 21 (million)
% 2.55/1.72 % (26852)------------------------------
% 2.55/1.72 % (26852)------------------------------
% 2.55/1.72 % (26851)Refutation not found, incomplete strategy
% 2.55/1.72 % (26851)------------------------------
% 2.55/1.72 % (26851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.72 % (26851)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.72
% 2.55/1.72
% 2.55/1.72 % (26851)Memory used [KB]: 5756
% 2.55/1.72 % (26851)Time elapsed: 0.015 s
% 2.55/1.72 % (26851)Instructions burned: 34 (million)
% 2.55/1.72 % (26851)------------------------------
% 2.55/1.72 % (26851)------------------------------
% 2.55/1.72 % (26854)Instruction limit reached!
% 2.55/1.72 % (26854)------------------------------
% 2.55/1.72 % (26854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.72 % (26854)Termination reason: Unknown
% 2.55/1.72 % (26854)Termination phase: shuffling
% 2.55/1.72
% 2.55/1.72 % (26854)Memory used [KB]: 1151
% 2.55/1.72 % (26854)Time elapsed: 0.008 s
% 2.55/1.72 % (26854)Instructions burned: 17 (million)
% 2.55/1.72 % (26854)------------------------------
% 2.55/1.72 % (26854)------------------------------
% 2.55/1.73 % (26855)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26726 for (2998ds/3Mi)
% 2.55/1.73 % (26855)Instruction limit reached!
% 2.55/1.73 % (26855)------------------------------
% 2.55/1.73 % (26855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.73 % (26855)Termination reason: Unknown
% 2.55/1.73 % (26855)Termination phase: shuffling
% 2.55/1.73
% 2.55/1.73 % (26855)Memory used [KB]: 1151
% 2.55/1.73 % (26855)Time elapsed: 0.003 s
% 2.55/1.73 % (26855)Instructions burned: 4 (million)
% 2.55/1.73 % (26855)------------------------------
% 2.55/1.73 % (26855)------------------------------
% 2.55/1.73 % (26856)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26726 for (2998ds/30Mi)
% 2.55/1.74 % (26857)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26726 for (2998ds/127Mi)
% 2.55/1.74 % (26858)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26726 for (2998ds/100Mi)
% 2.55/1.74 % (26856)Instruction limit reached!
% 2.55/1.74 % (26856)------------------------------
% 2.55/1.74 % (26856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.74 % (26856)Termination reason: Unknown
% 2.55/1.74 % (26856)Termination phase: shuffling
% 2.55/1.74
% 2.55/1.74 % (26856)Memory used [KB]: 1279
% 2.55/1.74 % (26856)Time elapsed: 0.013 s
% 2.55/1.74 % (26856)Instructions burned: 31 (million)
% 2.55/1.74 % (26856)------------------------------
% 2.55/1.74 % (26856)------------------------------
% 2.55/1.74 % (26859)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_26726 for (2998ds/3Mi)
% 2.55/1.75 % (26859)Instruction limit reached!
% 2.55/1.75 % (26859)------------------------------
% 2.55/1.75 % (26859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.75 % (26859)Termination reason: Unknown
% 2.55/1.75 % (26859)Termination phase: shuffling
% 2.55/1.75
% 2.55/1.75 % (26859)Memory used [KB]: 1151
% 2.55/1.75 % (26859)Time elapsed: 0.003 s
% 2.55/1.75 % (26859)Instructions burned: 4 (million)
% 2.55/1.75 % (26859)------------------------------
% 2.55/1.75 % (26859)------------------------------
% 2.55/1.76 % (26860)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_26726 for (2998ds/20Mi)
% 2.55/1.76 % (26861)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_26726 for (2998ds/86Mi)
% 2.55/1.77 % (26860)Instruction limit reached!
% 2.55/1.77 % (26860)------------------------------
% 2.55/1.77 % (26860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.77 % (26860)Termination reason: Unknown
% 2.55/1.77 % (26860)Termination phase: shuffling
% 2.55/1.77
% 2.55/1.77 % (26860)Memory used [KB]: 1279
% 2.55/1.77 % (26860)Time elapsed: 0.009 s
% 2.55/1.77 % (26860)Instructions burned: 20 (million)
% 2.55/1.77 % (26860)------------------------------
% 2.55/1.77 % (26860)------------------------------
% 2.55/1.78 % (26858)Instruction limit reached!
% 2.55/1.78 % (26858)------------------------------
% 2.55/1.78 % (26858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.78 % (26858)Termination reason: Unknown
% 2.55/1.78 % (26858)Termination phase: Property scanning
% 2.55/1.78
% 2.55/1.78 % (26858)Memory used [KB]: 1407
% 2.55/1.78 % (26858)Time elapsed: 0.042 s
% 2.55/1.78 % (26858)Instructions burned: 100 (million)
% 2.55/1.78 % (26858)------------------------------
% 2.55/1.78 % (26858)------------------------------
% 2.55/1.78 % (26862)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_26726 for (2998ds/107Mi)
% 2.55/1.79 % (26857)Instruction limit reached!
% 2.55/1.79 % (26857)------------------------------
% 2.55/1.79 % (26857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.79 % (26857)Termination reason: Unknown
% 2.55/1.79 % (26857)Termination phase: Property scanning
% 2.55/1.79
% 2.55/1.79 % (26857)Memory used [KB]: 1407
% 2.55/1.79 % (26857)Time elapsed: 0.052 s
% 2.55/1.79 % (26857)Instructions burned: 127 (million)
% 2.55/1.79 % (26857)------------------------------
% 2.55/1.79 % (26857)------------------------------
% 2.55/1.79 % (26863)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_26726 for (2998ds/39Mi)
% 2.55/1.80 % (26861)Instruction limit reached!
% 2.55/1.80 % (26861)------------------------------
% 2.55/1.80 % (26861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.80 % (26861)Termination reason: Unknown
% 2.55/1.80 % (26861)Termination phase: Property scanning
% 2.55/1.80
% 2.55/1.80 % (26861)Memory used [KB]: 1407
% 2.55/1.80 % (26861)Time elapsed: 0.036 s
% 2.55/1.80 % (26861)Instructions burned: 88 (million)
% 2.55/1.80 % (26861)------------------------------
% 2.55/1.80 % (26861)------------------------------
% 2.55/1.80 % (26864)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_26726 for (2998ds/448Mi)
% 2.55/1.81 % (26863)Instruction limit reached!
% 2.55/1.81 % (26863)------------------------------
% 2.55/1.81 % (26863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.81 % (26863)Termination reason: Unknown
% 2.55/1.81 % (26863)Termination phase: Function definition elimination
% 2.55/1.81
% 2.55/1.81 % (26863)Memory used [KB]: 1407
% 2.55/1.81 % (26863)Time elapsed: 0.018 s
% 2.55/1.81 % (26863)Instructions burned: 41 (million)
% 2.55/1.81 % (26863)------------------------------
% 2.55/1.81 % (26863)------------------------------
% 2.55/1.81 % (26865)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_26726 for (2998ds/46Mi)
% 2.55/1.81 % (26864)Refutation not found, incomplete strategy
% 2.55/1.81 % (26864)------------------------------
% 2.55/1.81 % (26864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.81 % (26864)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.81
% 2.55/1.81
% 2.55/1.81 % (26864)Memory used [KB]: 5756
% 2.55/1.81 % (26864)Time elapsed: 0.037 s
% 2.55/1.81 % (26864)Instructions burned: 29 (million)
% 2.55/1.81 % (26864)------------------------------
% 2.55/1.81 % (26864)------------------------------
% 2.55/1.82 % (26862)Instruction limit reached!
% 2.55/1.82 % (26862)------------------------------
% 2.55/1.82 % (26862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.82 % (26862)Termination reason: Unknown
% 2.55/1.82 % (26862)Termination phase: Saturation
% 2.55/1.82
% 2.55/1.82 % (26862)Memory used [KB]: 5884
% 2.55/1.82 % (26862)Time elapsed: 0.043 s
% 2.55/1.82 % (26862)Instructions burned: 109 (million)
% 2.55/1.82 % (26862)------------------------------
% 2.55/1.82 % (26862)------------------------------
% 2.55/1.82 % (26866)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_26726 for (2997ds/98Mi)
% 2.55/1.83 % (26867)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_26726 for (2997ds/507Mi)
% 2.55/1.83 % (26865)Instruction limit reached!
% 2.55/1.83 % (26865)------------------------------
% 2.55/1.83 % (26865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.83 % (26865)Termination reason: Unknown
% 2.55/1.83 % (26865)Termination phase: Property scanning
% 2.55/1.83
% 2.55/1.83 % (26865)Memory used [KB]: 1279
% 2.55/1.83 % (26865)Time elapsed: 0.020 s
% 2.55/1.83 % (26865)Instructions burned: 48 (million)
% 2.55/1.83 % (26865)------------------------------
% 2.55/1.83 % (26865)------------------------------
% 2.55/1.84 % (26868)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_26726 for (2997ds/149Mi)
% 2.55/1.84 % (26850)Instruction limit reached!
% 2.55/1.84 % (26850)------------------------------
% 2.55/1.84 % (26850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.84 % (26850)Termination reason: Unknown
% 2.55/1.84 % (26850)Termination phase: Saturation
% 2.55/1.84
% 2.55/1.84 % (26850)Memory used [KB]: 6268
% 2.55/1.84 % (26850)Time elapsed: 0.146 s
% 2.55/1.84 % (26850)Instructions burned: 377 (million)
% 2.55/1.84 % (26850)------------------------------
% 2.55/1.84 % (26850)------------------------------
% 2.55/1.85 % (26869)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_26726 for (2997ds/39Mi)
% 2.55/1.86 % (26870)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_26726 for (2997ds/6Mi)
% 2.55/1.86 % (26870)Instruction limit reached!
% 2.55/1.86 % (26870)------------------------------
% 2.55/1.86 % (26870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.86 % (26870)Termination reason: Unknown
% 2.55/1.86 % (26870)Termination phase: shuffling
% 2.55/1.86
% 2.55/1.86 % (26870)Memory used [KB]: 1151
% 2.55/1.86 % (26870)Time elapsed: 0.004 s
% 2.55/1.86 % (26870)Instructions burned: 6 (million)
% 2.55/1.86 % (26870)------------------------------
% 2.55/1.86 % (26870)------------------------------
% 2.55/1.86 % (26869)Instruction limit reached!
% 2.55/1.86 % (26869)------------------------------
% 2.55/1.86 % (26869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.86 % (26869)Termination reason: Unknown
% 2.55/1.86 % (26869)Termination phase: shuffling
% 2.55/1.86
% 2.55/1.86 % (26869)Memory used [KB]: 1279
% 2.55/1.86 % (26869)Time elapsed: 0.017 s
% 2.55/1.86 % (26869)Instructions burned: 41 (million)
% 2.55/1.86 % (26869)------------------------------
% 2.55/1.86 % (26869)------------------------------
% 2.55/1.87 % (26866)Instruction limit reached!
% 2.55/1.87 % (26866)------------------------------
% 2.55/1.87 % (26866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.87 % (26866)Termination reason: Unknown
% 2.55/1.87 % (26866)Termination phase: Property scanning
% 2.55/1.87
% 2.55/1.87 % (26866)Memory used [KB]: 1407
% 2.55/1.87 % (26866)Time elapsed: 0.042 s
% 2.55/1.87 % (26866)Instructions burned: 100 (million)
% 2.55/1.87 % (26866)------------------------------
% 2.55/1.87 % (26866)------------------------------
% 2.55/1.88 % (26871)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_26726 for (2997ds/1087Mi)
% 2.55/1.88 % (26872)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_26726 for (2997ds/47Mi)
% 2.55/1.88 % (26873)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_26726 for (2997ds/44Mi)
% 2.55/1.89 % (26873)Refutation not found, incomplete strategy
% 2.55/1.89 % (26873)------------------------------
% 2.55/1.89 % (26873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.89 % (26873)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.89
% 2.55/1.89
% 2.55/1.89 % (26873)Memory used [KB]: 1279
% 2.55/1.89 % (26873)Time elapsed: 0.012 s
% 2.55/1.89 % (26873)Instructions burned: 26 (million)
% 2.55/1.89 % (26873)------------------------------
% 2.55/1.89 % (26873)------------------------------
% 2.55/1.90 % (26872)Instruction limit reached!
% 2.55/1.90 % (26872)------------------------------
% 2.55/1.90 % (26872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.90 % (26872)Termination reason: Unknown
% 2.55/1.90 % (26872)Termination phase: Property scanning
% 2.55/1.90
% 2.55/1.90 % (26872)Memory used [KB]: 1279
% 2.55/1.90 % (26872)Time elapsed: 0.020 s
% 2.55/1.90 % (26872)Instructions burned: 48 (million)
% 2.55/1.90 % (26872)------------------------------
% 2.55/1.90 % (26872)------------------------------
% 2.55/1.90 % (26871)Refutation not found, incomplete strategy
% 2.55/1.90 % (26871)------------------------------
% 2.55/1.90 % (26871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.90 % (26871)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.90
% 2.55/1.90
% 2.55/1.90 % (26871)Memory used [KB]: 5756
% 2.55/1.90 % (26871)Time elapsed: 0.024 s
% 2.55/1.90 % (26871)Instructions burned: 58 (million)
% 2.55/1.90 % (26871)------------------------------
% 2.55/1.90 % (26871)------------------------------
% 2.55/1.90 % (26868)Instruction limit reached!
% 2.55/1.90 % (26868)------------------------------
% 2.55/1.90 % (26868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.90 % (26868)Termination reason: Unknown
% 2.55/1.90 % (26868)Termination phase: Saturation
% 2.55/1.90
% 2.55/1.90 % (26868)Memory used [KB]: 6140
% 2.55/1.90 % (26868)Time elapsed: 0.062 s
% 2.55/1.90 % (26868)Instructions burned: 151 (million)
% 2.55/1.90 % (26868)------------------------------
% 2.55/1.90 % (26868)------------------------------
% 2.55/1.91 % (26874)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_26726 for (2996ds/432Mi)
% 2.55/1.91 % (26875)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_26726 for (2996ds/62Mi)
% 2.55/1.91 % (26876)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_26726 for (2996ds/31Mi)
% 2.55/1.92 % (26877)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_26726 for (2996ds/96Mi)
% 2.55/1.93 % (26876)Instruction limit reached!
% 2.55/1.93 % (26876)------------------------------
% 2.55/1.93 % (26876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.93 % (26876)Termination reason: Unknown
% 2.55/1.93 % (26876)Termination phase: shuffling
% 2.55/1.93
% 2.55/1.93 % (26876)Memory used [KB]: 1279
% 2.55/1.93 % (26876)Time elapsed: 0.014 s
% 2.55/1.93 % (26876)Instructions burned: 33 (million)
% 2.55/1.93 % (26876)------------------------------
% 2.55/1.93 % (26876)------------------------------
% 2.55/1.94 % (26875)Instruction limit reached!
% 2.55/1.94 % (26875)------------------------------
% 2.55/1.94 % (26875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.94 % (26875)Termination reason: Unknown
% 2.55/1.94 % (26875)Termination phase: Property scanning
% 2.55/1.94
% 2.55/1.94 % (26875)Memory used [KB]: 1407
% 2.55/1.94 % (26875)Time elapsed: 0.027 s
% 2.55/1.94 % (26875)Instructions burned: 63 (million)
% 2.55/1.94 % (26875)------------------------------
% 2.55/1.94 % (26875)------------------------------
% 2.55/1.94 % (26878)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_26726 for (2996ds/453Mi)
% 2.55/1.95 % (26877)Instruction limit reached!
% 2.55/1.95 % (26877)------------------------------
% 2.55/1.95 % (26877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.95 % (26877)Termination reason: Unknown
% 2.55/1.95 % (26877)Termination phase: Property scanning
% 2.55/1.95
% 2.55/1.95 % (26877)Memory used [KB]: 1407
% 2.55/1.95 % (26877)Time elapsed: 0.039 s
% 2.55/1.95 % (26877)Instructions burned: 97 (million)
% 2.55/1.95 % (26877)------------------------------
% 2.55/1.95 % (26877)------------------------------
% 2.55/1.95 % (26879)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_26726 for (2996ds/71Mi)
% 2.55/1.97 % (26880)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_26726 for (2996ds/83Mi)
% 2.55/1.98 % (26879)Instruction limit reached!
% 2.55/1.98 % (26879)------------------------------
% 2.55/1.98 % (26879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.98 % (26879)Termination reason: Unknown
% 2.55/1.98 % (26879)Termination phase: Function definition elimination
% 2.55/1.98
% 2.55/1.98 % (26879)Memory used [KB]: 1407
% 2.55/1.98 % (26879)Time elapsed: 0.030 s
% 2.55/1.98 % (26879)Instructions burned: 73 (million)
% 2.55/1.98 % (26879)------------------------------
% 2.55/1.98 % (26879)------------------------------
% 2.55/1.99 % (26880)Refutation not found, incomplete strategy
% 2.55/1.99 % (26880)------------------------------
% 2.55/1.99 % (26880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.99 % (26880)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.99
% 2.55/1.99
% 2.55/1.99 % (26880)Memory used [KB]: 5756
% 2.55/1.99 % (26880)Time elapsed: 0.024 s
% 2.55/1.99 % (26880)Instructions burned: 59 (million)
% 2.55/1.99 % (26880)------------------------------
% 2.55/1.99 % (26880)------------------------------
% 2.55/2.00 % (26881)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_26726 for (2996ds/11Mi)
% 2.55/2.00 % (26867)Refutation not found, incomplete strategy
% 2.55/2.00 % (26867)------------------------------
% 2.55/2.00 % (26867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/2.00 % (26867)Termination reason: Refutation not found, incomplete strategy
% 2.55/2.00
% 2.55/2.00
% 2.55/2.00 % (26867)Memory used [KB]: 7547
% 2.55/2.00 % (26867)Time elapsed: 0.173 s
% 2.55/2.00 % (26867)Instructions burned: 470 (million)
% 2.55/2.00 % (26867)------------------------------
% 2.55/2.00 % (26867)------------------------------
% 2.55/2.00 % (26881)Instruction limit reached!
% 2.55/2.00 % (26881)------------------------------
% 2.55/2.00 % (26881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/2.00 % (26881)Termination reason: Unknown
% 2.55/2.00 % (26881)Termination phase: Property scanning
% 2.55/2.00
% 2.55/2.00 % (26881)Memory used [KB]: 1279
% 2.55/2.01 % (26881)Time elapsed: 0.007 s
% 2.55/2.01 % (26881)Instructions burned: 12 (million)
% 2.55/2.01 % (26881)------------------------------
% 2.55/2.01 % (26881)------------------------------
% 2.55/2.01 % (26882)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_26726 for (2995ds/41Mi)
% 2.55/2.02 % (26883)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26726 for (2995ds/6Mi)
% 2.55/2.02 % (26884)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_26726 for (2995ds/150Mi)
% 2.55/2.02 % (26883)Instruction limit reached!
% 2.55/2.02 % (26883)------------------------------
% 2.55/2.02 % (26883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/2.02 % (26883)Termination reason: Unknown
% 2.55/2.02 % (26883)Termination phase: shuffling
% 2.55/2.02
% 2.55/2.02 % (26883)Memory used [KB]: 1151
% 2.55/2.02 % (26883)Time elapsed: 0.004 s
% 2.55/2.02 % (26883)Instructions burned: 6 (million)
% 2.55/2.02 % (26883)------------------------------
% 2.55/2.02 % (26883)------------------------------
% 5.51/2.03 % (26882)Instruction limit reached!
% 5.51/2.03 % (26882)------------------------------
% 5.51/2.03 % (26882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.03 % (26882)Termination reason: Unknown
% 5.51/2.03 % (26882)Termination phase: Function definition elimination
% 5.51/2.03
% 5.51/2.03 % (26882)Memory used [KB]: 1407
% 5.51/2.03 % (26882)Time elapsed: 0.018 s
% 5.51/2.03 % (26882)Instructions burned: 41 (million)
% 5.51/2.03 % (26882)------------------------------
% 5.51/2.03 % (26882)------------------------------
% 5.51/2.04 % (26885)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_26726 for (2995ds/343Mi)
% 5.51/2.04 % (26835)Instruction limit reached!
% 5.51/2.04 % (26835)------------------------------
% 5.51/2.04 % (26835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.04 % (26835)Termination reason: Unknown
% 5.51/2.04 % (26835)Termination phase: Saturation
% 5.51/2.04
% 5.51/2.04 % (26835)Memory used [KB]: 7931
% 5.51/2.04 % (26835)Time elapsed: 0.406 s
% 5.51/2.04 % (26835)Instructions burned: 1041 (million)
% 5.51/2.04 % (26835)------------------------------
% 5.51/2.04 % (26835)------------------------------
% 5.51/2.04 % (26886)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_26726 for (2995ds/109Mi)
% 5.51/2.06 % (26887)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_26726 for (2995ds/253Mi)
% 5.51/2.06 % (26853)Instruction limit reached!
% 5.51/2.06 % (26853)------------------------------
% 5.51/2.06 % (26853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.06 % (26853)Termination reason: Unknown
% 5.51/2.06 % (26853)Termination phase: Saturation
% 5.51/2.06
% 5.51/2.06 % (26853)Memory used [KB]: 6780
% 5.51/2.06 % (26853)Time elapsed: 0.354 s
% 5.51/2.06 % (26853)Instructions burned: 879 (million)
% 5.51/2.06 % (26853)------------------------------
% 5.51/2.06 % (26853)------------------------------
% 5.51/2.06 % (26885)Refutation not found, incomplete strategy
% 5.51/2.06 % (26885)------------------------------
% 5.51/2.06 % (26885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.06 % (26885)Termination reason: Refutation not found, incomplete strategy
% 5.51/2.06
% 5.51/2.06
% 5.51/2.06 % (26885)Memory used [KB]: 5756
% 5.51/2.06 % (26885)Time elapsed: 0.025 s
% 5.51/2.06 % (26885)Instructions burned: 62 (million)
% 5.51/2.06 % (26885)------------------------------
% 5.51/2.06 % (26885)------------------------------
% 5.51/2.07 % (26874)Instruction limit reached!
% 5.51/2.07 % (26874)------------------------------
% 5.51/2.07 % (26874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.07 % (26874)Termination reason: Unknown
% 5.51/2.07 % (26874)Termination phase: Saturation
% 5.51/2.07
% 5.51/2.07 % (26874)Memory used [KB]: 3070
% 5.51/2.07 % (26874)Time elapsed: 0.159 s
% 5.51/2.07 % (26874)Instructions burned: 434 (million)
% 5.51/2.07 % (26874)------------------------------
% 5.51/2.07 % (26874)------------------------------
% 5.51/2.08 % (26888)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_26726 for (2995ds/140Mi)
% 5.51/2.08 % (26887)Refutation not found, incomplete strategy
% 5.51/2.08 % (26887)------------------------------
% 5.51/2.08 % (26887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.08 % (26887)Termination reason: Refutation not found, incomplete strategy
% 5.51/2.08
% 5.51/2.08
% 5.51/2.08 % (26887)Memory used [KB]: 5756
% 5.51/2.08 % (26887)Time elapsed: 0.023 s
% 5.51/2.08 % (26887)Instructions burned: 56 (million)
% 5.51/2.08 % (26887)------------------------------
% 5.51/2.08 % (26887)------------------------------
% 5.51/2.08 % (26889)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_26726 for (2995ds/614Mi)
% 5.51/2.08 % (26884)Instruction limit reached!
% 5.51/2.08 % (26884)------------------------------
% 5.51/2.08 % (26884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.08 % (26884)Termination reason: Unknown
% 5.51/2.08 % (26884)Termination phase: Saturation
% 5.51/2.08
% 5.51/2.08 % (26884)Memory used [KB]: 6012
% 5.51/2.08 % (26884)Time elapsed: 0.063 s
% 5.51/2.08 % (26884)Instructions burned: 152 (million)
% 5.51/2.08 % (26884)------------------------------
% 5.51/2.08 % (26884)------------------------------
% 5.51/2.08 % (26890)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_26726 for (2995ds/202Mi)
% 5.51/2.09 % (26886)Instruction limit reached!
% 5.51/2.09 % (26886)------------------------------
% 5.51/2.09 % (26886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.09 % (26886)Termination reason: Unknown
% 5.51/2.09 % (26886)Termination phase: Property scanning
% 5.51/2.09
% 5.51/2.09 % (26886)Memory used [KB]: 1407
% 5.51/2.09 % (26886)Time elapsed: 0.045 s
% 5.51/2.09 % (26886)Instructions burned: 110 (million)
% 5.51/2.09 % (26886)------------------------------
% 5.51/2.09 % (26886)------------------------------
% 5.51/2.09 % (26891)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_26726 for (2995ds/339Mi)
% 5.51/2.10 % (26892)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_26726 for (2995ds/283Mi)
% 5.51/2.10 % (26893)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_26726 for (2995ds/134Mi)
% 5.51/2.11 % (26890)Refutation not found, incomplete strategy
% 5.51/2.11 % (26890)------------------------------
% 5.51/2.11 % (26890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.11 % (26890)Termination reason: Refutation not found, incomplete strategy
% 5.51/2.11
% 5.51/2.11
% 5.51/2.11 % (26890)Memory used [KB]: 5756
% 5.51/2.11 % (26890)Time elapsed: 0.024 s
% 5.51/2.11 % (26890)Instructions burned: 58 (million)
% 5.51/2.11 % (26890)------------------------------
% 5.51/2.11 % (26890)------------------------------
% 5.51/2.11 % (26878)Instruction limit reached!
% 5.51/2.11 % (26878)------------------------------
% 5.51/2.11 % (26878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.11 % (26878)Termination reason: Unknown
% 5.51/2.11 % (26878)Termination phase: Saturation
% 5.51/2.11
% 5.51/2.11 % (26878)Memory used [KB]: 7547
% 5.51/2.11 % (26878)Time elapsed: 0.167 s
% 5.51/2.11 % (26878)Instructions burned: 454 (million)
% 5.51/2.11 % (26878)------------------------------
% 5.51/2.11 % (26878)------------------------------
% 5.51/2.12 % (26891)Refutation not found, incomplete strategy
% 5.51/2.12 % (26891)------------------------------
% 5.51/2.12 % (26891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.12 % (26891)Termination reason: Refutation not found, incomplete strategy
% 5.51/2.12
% 5.51/2.12
% 5.51/2.12 % (26891)Memory used [KB]: 5756
% 5.51/2.12 % (26891)Time elapsed: 0.025 s
% 5.51/2.12 % (26891)Instructions burned: 59 (million)
% 5.51/2.12 % (26891)------------------------------
% 5.51/2.12 % (26891)------------------------------
% 5.51/2.12 % (26888)Refutation not found, incomplete strategy
% 5.51/2.12 % (26888)------------------------------
% 5.51/2.12 % (26888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.12 % (26888)Termination reason: Refutation not found, incomplete strategy
% 5.51/2.12
% 5.51/2.12
% 5.51/2.12 % (26888)Memory used [KB]: 5884
% 5.51/2.12 % (26888)Time elapsed: 0.044 s
% 5.51/2.12 % (26888)Instructions burned: 115 (million)
% 5.51/2.12 % (26888)------------------------------
% 5.51/2.12 % (26888)------------------------------
% 5.51/2.12 % (26894)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_26726 for (2994ds/298Mi)
% 5.51/2.12 % (26895)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_26726 for (2994ds/192Mi)
% 6.09/2.13 % (26896)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_26726 for (2994ds/258Mi)
% 6.09/2.14 % (26897)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_26726 for (2994ds/90Mi)
% 6.09/2.16 % (26893)Instruction limit reached!
% 6.09/2.16 % (26893)------------------------------
% 6.09/2.16 % (26893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.16 % (26893)Termination reason: Unknown
% 6.09/2.16 % (26893)Termination phase: Property scanning
% 6.09/2.16
% 6.09/2.16 % (26893)Memory used [KB]: 1407
% 6.09/2.16 % (26893)Time elapsed: 0.055 s
% 6.09/2.16 % (26893)Instructions burned: 135 (million)
% 6.09/2.16 % (26893)------------------------------
% 6.09/2.16 % (26893)------------------------------
% 6.09/2.17 % (26897)Instruction limit reached!
% 6.09/2.17 % (26897)------------------------------
% 6.09/2.17 % (26897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.17 % (26897)Termination reason: Unknown
% 6.09/2.17 % (26897)Termination phase: Property scanning
% 6.09/2.17
% 6.09/2.17 % (26897)Memory used [KB]: 1407
% 6.09/2.17 % (26897)Time elapsed: 0.037 s
% 6.09/2.17 % (26897)Instructions burned: 91 (million)
% 6.09/2.17 % (26897)------------------------------
% 6.09/2.17 % (26897)------------------------------
% 6.09/2.17 % (26898)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_26726 for (2994ds/231Mi)
% 6.09/2.19 % (26899)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_26726 for (2994ds/458Mi)
% 6.21/2.20 % (26895)Instruction limit reached!
% 6.21/2.20 % (26895)------------------------------
% 6.21/2.20 % (26895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.20 % (26895)Termination reason: Unknown
% 6.21/2.20 % (26895)Termination phase: Saturation
% 6.21/2.20
% 6.21/2.20 % (26895)Memory used [KB]: 1791
% 6.21/2.20 % (26895)Time elapsed: 0.077 s
% 6.21/2.20 % (26895)Instructions burned: 193 (million)
% 6.21/2.20 % (26895)------------------------------
% 6.21/2.20 % (26895)------------------------------
% 6.21/2.20 % (26892)Instruction limit reached!
% 6.21/2.20 % (26892)------------------------------
% 6.21/2.20 % (26892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.20 % (26892)Termination reason: Unknown
% 6.21/2.20 % (26892)Termination phase: Saturation
% 6.21/2.20
% 6.21/2.20 % (26892)Memory used [KB]: 6652
% 6.21/2.20 % (26892)Time elapsed: 0.108 s
% 6.21/2.20 % (26892)Instructions burned: 285 (million)
% 6.21/2.20 % (26892)------------------------------
% 6.21/2.20 % (26892)------------------------------
% 6.21/2.22 % (26900)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_26726 for (2993ds/31Mi)
% 6.21/2.22 % (26901)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_26726 for (2993ds/297Mi)
% 6.21/2.23 % (26900)Instruction limit reached!
% 6.21/2.23 % (26900)------------------------------
% 6.21/2.23 % (26900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.23 % (26900)Termination reason: Unknown
% 6.21/2.23 % (26900)Termination phase: shuffling
% 6.21/2.23
% 6.21/2.23 % (26900)Memory used [KB]: 1279
% 6.21/2.23 % (26900)Time elapsed: 0.014 s
% 6.21/2.23 % (26900)Instructions burned: 32 (million)
% 6.21/2.23 % (26900)------------------------------
% 6.21/2.23 % (26900)------------------------------
% 6.21/2.23 % (26896)Instruction limit reached!
% 6.21/2.23 % (26896)------------------------------
% 6.21/2.23 % (26896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.23 % (26896)Termination reason: Unknown
% 6.21/2.23 % (26896)Termination phase: Saturation
% 6.21/2.23
% 6.21/2.23 % (26896)Memory used [KB]: 2046
% 6.21/2.23 % (26896)Time elapsed: 0.100 s
% 6.21/2.23 % (26896)Instructions burned: 259 (million)
% 6.21/2.23 % (26896)------------------------------
% 6.21/2.23 % (26896)------------------------------
% 6.21/2.23 % (26894)Instruction limit reached!
% 6.21/2.23 % (26894)------------------------------
% 6.21/2.23 % (26894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.23 % (26894)Termination reason: Unknown
% 6.21/2.23 % (26894)Termination phase: Saturation
% 6.21/2.23
% 6.21/2.23 % (26894)Memory used [KB]: 6652
% 6.21/2.23 % (26894)Time elapsed: 0.113 s
% 6.21/2.23 % (26894)Instructions burned: 298 (million)
% 6.21/2.23 % (26894)------------------------------
% 6.21/2.23 % (26894)------------------------------
% 6.21/2.23 % (26901)Refutation not found, incomplete strategy
% 6.21/2.23 % (26901)------------------------------
% 6.21/2.23 % (26901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.23 % (26901)Termination reason: Refutation not found, incomplete strategy
% 6.21/2.23
% 6.21/2.23
% 6.21/2.23 % (26901)Memory used [KB]: 5756
% 6.21/2.23 % (26901)Time elapsed: 0.013 s
% 6.21/2.23 % (26901)Instructions burned: 28 (million)
% 6.21/2.23 % (26901)------------------------------
% 6.21/2.23 % (26901)------------------------------
% 6.21/2.25 % (26902)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_26726 for (2993ds/987Mi)
% 6.21/2.25 % (26903)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_26726 for (2993ds/182Mi)
% 6.21/2.25 % (26904)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_26726 for (2993ds/182Mi)
% 6.21/2.25 % (26905)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_26726 for (2993ds/154Mi)
% 6.21/2.26 % (26898)Instruction limit reached!
% 6.21/2.26 % (26898)------------------------------
% 6.21/2.26 % (26898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.26 % (26898)Termination reason: Unknown
% 6.21/2.26 % (26898)Termination phase: Saturation
% 6.21/2.26
% 6.21/2.26 % (26898)Memory used [KB]: 6524
% 6.21/2.26 % (26898)Time elapsed: 0.091 s
% 6.21/2.26 % (26898)Instructions burned: 233 (million)
% 6.21/2.26 % (26898)------------------------------
% 6.21/2.26 % (26898)------------------------------
% 6.21/2.28 % (26906)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_26726 for (2993ds/79Mi)
% 6.83/2.31 % (26889)Instruction limit reached!
% 6.83/2.31 % (26889)------------------------------
% 6.83/2.31 % (26889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.31 % (26889)Termination reason: Unknown
% 6.83/2.31 % (26889)Termination phase: Saturation
% 6.83/2.31
% 6.83/2.31 % (26889)Memory used [KB]: 6652
% 6.83/2.31 % (26889)Time elapsed: 0.230 s
% 6.83/2.31 % (26889)Instructions burned: 615 (million)
% 6.83/2.31 % (26889)------------------------------
% 6.83/2.31 % (26889)------------------------------
% 6.83/2.31 % (26906)Instruction limit reached!
% 6.83/2.31 % (26906)------------------------------
% 6.83/2.31 % (26906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.31 % (26906)Termination reason: Unknown
% 6.83/2.31 % (26906)Termination phase: Property scanning
% 6.83/2.31
% 6.83/2.31 % (26906)Memory used [KB]: 1407
% 6.83/2.31 % (26906)Time elapsed: 0.033 s
% 6.83/2.31 % (26906)Instructions burned: 81 (million)
% 6.83/2.31 % (26906)------------------------------
% 6.83/2.31 % (26906)------------------------------
% 6.83/2.31 % (26905)Instruction limit reached!
% 6.83/2.31 % (26905)------------------------------
% 6.83/2.31 % (26905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.31 % (26905)Termination reason: Unknown
% 6.83/2.31 % (26905)Termination phase: Saturation
% 6.83/2.31
% 6.83/2.31 % (26905)Memory used [KB]: 1663
% 6.83/2.31 % (26905)Time elapsed: 0.063 s
% 6.83/2.31 % (26905)Instructions burned: 154 (million)
% 6.83/2.31 % (26905)------------------------------
% 6.83/2.31 % (26905)------------------------------
% 6.83/2.32 % (26903)Instruction limit reached!
% 6.83/2.32 % (26903)------------------------------
% 6.83/2.32 % (26903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.32 % (26903)Termination reason: Unknown
% 6.83/2.32 % (26903)Termination phase: Saturation
% 6.83/2.32
% 6.83/2.32 % (26903)Memory used [KB]: 6140
% 6.83/2.32 % (26903)Time elapsed: 0.074 s
% 6.83/2.32 % (26903)Instructions burned: 183 (million)
% 6.83/2.32 % (26903)------------------------------
% 6.83/2.32 % (26903)------------------------------
% 6.83/2.32 % (26907)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_26726 for (2992ds/216Mi)
% 6.83/2.33 % (26908)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_26726 for (2992ds/114Mi)
% 6.83/2.33 % (26909)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_26726 for (2992ds/922Mi)
% 6.83/2.33 % (26904)Instruction limit reached!
% 6.83/2.33 % (26904)------------------------------
% 6.83/2.33 % (26904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.33 % (26904)Termination reason: Unknown
% 6.83/2.33 % (26904)Termination phase: Saturation
% 6.83/2.33
% 6.83/2.33 % (26904)Memory used [KB]: 6268
% 6.83/2.33 % (26904)Time elapsed: 0.082 s
% 6.83/2.33 % (26904)Instructions burned: 182 (million)
% 6.83/2.33 % (26904)------------------------------
% 6.83/2.33 % (26904)------------------------------
% 6.83/2.34 % (26907)Refutation not found, incomplete strategy
% 6.83/2.34 % (26907)------------------------------
% 6.83/2.34 % (26907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.34 % (26907)Termination reason: Refutation not found, incomplete strategy
% 6.83/2.34
% 6.83/2.34
% 6.83/2.34 % (26907)Memory used [KB]: 5756
% 6.83/2.34 % (26907)Time elapsed: 0.015 s
% 6.83/2.34 % (26907)Instructions burned: 31 (million)
% 6.83/2.34 % (26907)------------------------------
% 6.83/2.34 % (26907)------------------------------
% 6.83/2.34 % (26910)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_26726 for (2992ds/182Mi)
% 6.83/2.35 % (26911)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_26726 for (2992ds/164Mi)
% 6.83/2.35 % (26909)Refutation not found, incomplete strategy
% 6.83/2.35 % (26909)------------------------------
% 6.83/2.35 % (26909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.35 % (26909)Termination reason: Refutation not found, incomplete strategy
% 6.83/2.35
% 6.83/2.35
% 6.83/2.35 % (26909)Memory used [KB]: 5756
% 6.83/2.35 % (26909)Time elapsed: 0.023 s
% 6.83/2.35 % (26909)Instructions burned: 56 (million)
% 6.83/2.35 % (26909)------------------------------
% 6.83/2.35 % (26909)------------------------------
% 6.83/2.35 % (26912)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_26726 for (2992ds/50Mi)
% 6.83/2.35 % (26911)Refutation not found, incomplete strategy
% 6.83/2.35 % (26911)------------------------------
% 6.83/2.35 % (26911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.35 % (26911)Termination reason: Refutation not found, incomplete strategy
% 6.83/2.35
% 6.83/2.35
% 6.83/2.35 % (26911)Memory used [KB]: 1279
% 6.83/2.35 % (26911)Time elapsed: 0.009 s
% 6.83/2.35 % (26911)Instructions burned: 26 (million)
% 6.83/2.35 % (26911)------------------------------
% 6.83/2.35 % (26911)------------------------------
% 6.83/2.36 % (26899)Instruction limit reached!
% 6.83/2.36 % (26899)------------------------------
% 6.83/2.36 % (26899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.36 % (26899)Termination reason: Unknown
% 6.83/2.36 % (26899)Termination phase: Saturation
% 6.83/2.36
% 6.83/2.36 % (26899)Memory used [KB]: 6396
% 6.83/2.36 % (26899)Time elapsed: 0.173 s
% 6.83/2.36 % (26899)Instructions burned: 459 (million)
% 6.83/2.36 % (26899)------------------------------
% 6.83/2.36 % (26899)------------------------------
% 6.83/2.37 % (26914)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_26726 for (2992ds/1021Mi)
% 6.83/2.37 % (26913)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_26726 for (2992ds/368Mi)
% 6.83/2.37 % (26908)Instruction limit reached!
% 6.83/2.37 % (26908)------------------------------
% 6.83/2.37 % (26908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.37 % (26908)Termination reason: Unknown
% 6.83/2.37 % (26908)Termination phase: Property scanning
% 6.83/2.37
% 6.83/2.37 % (26908)Memory used [KB]: 1407
% 6.83/2.37 % (26908)Time elapsed: 0.047 s
% 6.83/2.37 % (26908)Instructions burned: 115 (million)
% 6.83/2.37 % (26908)------------------------------
% 6.83/2.37 % (26908)------------------------------
% 6.83/2.37 % (26912)Instruction limit reached!
% 6.83/2.37 % (26912)------------------------------
% 6.83/2.37 % (26912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.37 % (26912)Termination reason: Unknown
% 6.83/2.37 % (26912)Termination phase: Property scanning
% 6.83/2.37
% 6.83/2.37 % (26912)Memory used [KB]: 1407
% 6.83/2.37 % (26912)Time elapsed: 0.022 s
% 6.83/2.37 % (26912)Instructions burned: 51 (million)
% 6.83/2.37 % (26912)------------------------------
% 6.83/2.37 % (26912)------------------------------
% 6.83/2.38 % (26915)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_26726 for (2992ds/267Mi)
% 6.83/2.39 % (26916)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_26726 for (2992ds/204Mi)
% 6.83/2.39 % (26917)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_26726 for (2992ds/26Mi)
% 7.76/2.40 % (26917)Instruction limit reached!
% 7.76/2.40 % (26917)------------------------------
% 7.76/2.40 % (26917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.40 % (26917)Termination reason: Unknown
% 7.76/2.40 % (26917)Termination phase: Property scanning
% 7.76/2.40
% 7.76/2.40 % (26917)Memory used [KB]: 1279
% 7.76/2.40 % (26917)Time elapsed: 0.013 s
% 7.76/2.40 % (26917)Instructions burned: 27 (million)
% 7.76/2.40 % (26917)------------------------------
% 7.76/2.40 % (26917)------------------------------
% 7.76/2.41 % (26910)Instruction limit reached!
% 7.76/2.41 % (26910)------------------------------
% 7.76/2.41 % (26910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.41 % (26910)Termination reason: Unknown
% 7.76/2.41 % (26910)Termination phase: Saturation
% 7.76/2.41
% 7.76/2.41 % (26910)Memory used [KB]: 6268
% 7.76/2.41 % (26910)Time elapsed: 0.073 s
% 7.76/2.41 % (26910)Instructions burned: 184 (million)
% 7.76/2.41 % (26910)------------------------------
% 7.76/2.41 % (26910)------------------------------
% 7.76/2.42 % (26918)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_26726 for (2991ds/53Mi)
% 7.76/2.42 % (26919)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_26726 for (2991ds/4436Mi)
% 7.76/2.44 % (26918)Instruction limit reached!
% 7.76/2.44 % (26918)------------------------------
% 7.76/2.44 % (26918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.44 % (26918)Termination reason: Unknown
% 7.76/2.44 % (26918)Termination phase: Property scanning
% 7.76/2.44
% 7.76/2.44 % (26918)Memory used [KB]: 1407
% 7.76/2.44 % (26918)Time elapsed: 0.023 s
% 7.76/2.44 % (26918)Instructions burned: 53 (million)
% 7.76/2.44 % (26918)------------------------------
% 7.76/2.44 % (26918)------------------------------
% 7.76/2.45 % (26919)Refutation not found, incomplete strategy
% 7.76/2.45 % (26919)------------------------------
% 7.76/2.45 % (26919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.45 % (26919)Termination reason: Refutation not found, incomplete strategy
% 7.76/2.45
% 7.76/2.45
% 7.76/2.45 % (26919)Memory used [KB]: 5756
% 7.76/2.45 % (26919)Time elapsed: 0.024 s
% 7.76/2.45 % (26919)Instructions burned: 58 (million)
% 7.76/2.45 % (26919)------------------------------
% 7.76/2.45 % (26919)------------------------------
% 7.76/2.46 % (26920)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_26726 for (2991ds/1539Mi)
% 7.76/2.46 % (26921)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_26726 for (2991ds/408Mi)
% 7.76/2.47 % (26916)Instruction limit reached!
% 7.76/2.47 % (26916)------------------------------
% 7.76/2.47 % (26916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.47 % (26916)Termination reason: Unknown
% 7.76/2.47 % (26916)Termination phase: Saturation
% 7.76/2.47
% 7.76/2.47 % (26916)Memory used [KB]: 6268
% 7.76/2.47 % (26916)Time elapsed: 0.080 s
% 7.76/2.47 % (26916)Instructions burned: 204 (million)
% 7.76/2.47 % (26916)------------------------------
% 7.76/2.47 % (26916)------------------------------
% 7.76/2.48 % (26915)Instruction limit reached!
% 7.76/2.48 % (26915)------------------------------
% 7.76/2.48 % (26915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.76/2.48 % (26915)Termination reason: Unknown
% 7.76/2.48 % (26915)Termination phase: Saturation
% 7.76/2.48
% 7.76/2.48 % (26915)Memory used [KB]: 6524
% 7.76/2.48 % (26915)Time elapsed: 0.102 s
% 7.76/2.48 % (26915)Instructions burned: 269 (million)
% 7.76/2.48 % (26915)------------------------------
% 7.76/2.48 % (26915)------------------------------
% 7.76/2.48 % (26922)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_26726 for (2991ds/5205Mi)
% 7.76/2.49 % (26923)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_26726 for (2991ds/1913Mi)
% 8.16/2.51 % (26913)Instruction limit reached!
% 8.16/2.51 % (26913)------------------------------
% 8.16/2.51 % (26913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.51 % (26913)Termination reason: Unknown
% 8.16/2.51 % (26913)Termination phase: Saturation
% 8.16/2.51
% 8.16/2.51 % (26913)Memory used [KB]: 6268
% 8.16/2.51 % (26913)Time elapsed: 0.142 s
% 8.16/2.51 % (26913)Instructions burned: 368 (million)
% 8.16/2.51 % (26913)------------------------------
% 8.16/2.51 % (26913)------------------------------
% 8.16/2.53 % (26924)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_26726 for (2990ds/4350Mi)
% 8.16/2.55 % (26921)Refutation not found, incomplete strategy
% 8.16/2.55 % (26921)------------------------------
% 8.16/2.55 % (26921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.55 % (26921)Termination reason: Refutation not found, incomplete strategy
% 8.16/2.55
% 8.16/2.55
% 8.16/2.55 % (26921)Memory used [KB]: 6396
% 8.16/2.55 % (26921)Time elapsed: 0.091 s
% 8.16/2.55 % (26921)Instructions burned: 198 (million)
% 8.16/2.55 % (26921)------------------------------
% 8.16/2.55 % (26921)------------------------------
% 8.16/2.57 % (26924)Refutation not found, incomplete strategy
% 8.16/2.57 % (26924)------------------------------
% 8.16/2.57 % (26924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.57 % (26924)Termination reason: Refutation not found, incomplete strategy
% 8.16/2.57
% 8.16/2.57
% 8.16/2.57 % (26924)Memory used [KB]: 5884
% 8.16/2.57 % (26924)Time elapsed: 0.043 s
% 8.16/2.57 % (26924)Instructions burned: 114 (million)
% 8.16/2.57 % (26924)------------------------------
% 8.16/2.57 % (26924)------------------------------
% 8.16/2.57 % (26925)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_26726 for (2990ds/68Mi)
% 8.16/2.58 % (26926)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_26726 for (2990ds/358Mi)
% 8.48/2.60 % (26925)Instruction limit reached!
% 8.48/2.60 % (26925)------------------------------
% 8.48/2.60 % (26925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.60 % (26925)Termination reason: Unknown
% 8.48/2.60 % (26925)Termination phase: Property scanning
% 8.48/2.60
% 8.48/2.60 % (26925)Memory used [KB]: 1279
% 8.48/2.60 % (26925)Time elapsed: 0.028 s
% 8.48/2.60 % (26925)Instructions burned: 68 (million)
% 8.48/2.60 % (26925)------------------------------
% 8.48/2.60 % (26925)------------------------------
% 8.48/2.60 % (26923)Refutation not found, incomplete strategy
% 8.48/2.60 % (26923)------------------------------
% 8.48/2.60 % (26923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.60 % (26923)Termination reason: Refutation not found, incomplete strategy
% 8.48/2.60
% 8.48/2.60
% 8.48/2.60 % (26923)Memory used [KB]: 2302
% 8.48/2.60 % (26923)Time elapsed: 0.110 s
% 8.48/2.60 % (26923)Instructions burned: 266 (million)
% 8.48/2.60 % (26923)------------------------------
% 8.48/2.60 % (26923)------------------------------
% 8.48/2.61 % (26926)Refutation not found, incomplete strategy
% 8.48/2.61 % (26926)------------------------------
% 8.48/2.61 % (26926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.61 % (26926)Termination reason: Refutation not found, incomplete strategy
% 8.48/2.61
% 8.48/2.61
% 8.48/2.61 % (26926)Memory used [KB]: 5756
% 8.48/2.61 % (26926)Time elapsed: 0.026 s
% 8.48/2.61 % (26926)Instructions burned: 64 (million)
% 8.48/2.61 % (26926)------------------------------
% 8.48/2.61 % (26926)------------------------------
% 8.48/2.61 % (26927)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_26726 for (2989ds/31Mi)
% 8.48/2.62 % (26928)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_26726 for (2989ds/279Mi)
% 8.48/2.63 % (26927)Instruction limit reached!
% 8.48/2.63 % (26927)------------------------------
% 8.48/2.63 % (26927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.63 % (26927)Termination reason: Unknown
% 8.48/2.63 % (26927)Termination phase: shuffling
% 8.48/2.63
% 8.48/2.63 % (26927)Memory used [KB]: 1279
% 8.48/2.63 % (26927)Time elapsed: 0.014 s
% 8.48/2.63 % (26927)Instructions burned: 33 (million)
% 8.48/2.63 % (26927)------------------------------
% 8.48/2.63 % (26927)------------------------------
% 8.48/2.63 % (26929)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_26726 for (2989ds/258Mi)
% 8.48/2.63 % (26928)Refutation not found, incomplete strategy
% 8.48/2.63 % (26928)------------------------------
% 8.48/2.63 % (26928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.63 % (26928)Termination reason: Refutation not found, incomplete strategy
% 8.48/2.63
% 8.48/2.63
% 8.48/2.63 % (26928)Memory used [KB]: 5756
% 8.48/2.63 % (26928)Time elapsed: 0.011 s
% 8.48/2.63 % (26928)Instructions burned: 24 (million)
% 8.48/2.63 % (26928)------------------------------
% 8.48/2.63 % (26928)------------------------------
% 8.48/2.63 % (26902)Instruction limit reached!
% 8.48/2.63 % (26902)------------------------------
% 8.48/2.63 % (26902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.63 % (26902)Termination reason: Unknown
% 8.48/2.63 % (26902)Termination phase: Saturation
% 8.48/2.63
% 8.48/2.63 % (26902)Memory used [KB]: 8059
% 8.48/2.63 % (26902)Time elapsed: 0.386 s
% 8.48/2.63 % (26902)Instructions burned: 988 (million)
% 8.48/2.63 % (26902)------------------------------
% 8.48/2.63 % (26902)------------------------------
% 8.48/2.64 % (26930)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_26726 for (2989ds/26Mi)
% 8.48/2.64 % (26931)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_26726 for (2989ds/995Mi)
% 8.48/2.65 % (26932)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_26726 for (2989ds/373Mi)
% 8.48/2.65 % (26930)Instruction limit reached!
% 8.48/2.65 % (26930)------------------------------
% 8.48/2.65 % (26930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.65 % (26930)Termination reason: Unknown
% 8.48/2.65 % (26930)Termination phase: Property scanning
% 8.48/2.65
% 8.48/2.65 % (26930)Memory used [KB]: 1279
% 8.48/2.65 % (26930)Time elapsed: 0.013 s
% 8.48/2.65 % (26930)Instructions burned: 28 (million)
% 8.48/2.65 % (26930)------------------------------
% 8.48/2.65 % (26930)------------------------------
% 8.48/2.67 % (26933)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_26726 for (2989ds/253Mi)
% 9.19/2.74 % (26929)Instruction limit reached!
% 9.19/2.74 % (26929)------------------------------
% 9.19/2.74 % (26929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.74 % (26929)Termination reason: Unknown
% 9.19/2.74 % (26929)Termination phase: Saturation
% 9.19/2.74
% 9.19/2.74 % (26929)Memory used [KB]: 7036
% 9.19/2.74 % (26929)Time elapsed: 0.115 s
% 9.19/2.74 % (26929)Instructions burned: 258 (million)
% 9.19/2.74 % (26929)------------------------------
% 9.19/2.74 % (26929)------------------------------
% 9.19/2.75 % (26914)Instruction limit reached!
% 9.19/2.75 % (26914)------------------------------
% 9.19/2.75 % (26914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.75 % (26914)Termination reason: Unknown
% 9.19/2.75 % (26914)Termination phase: Saturation
% 9.19/2.75
% 9.19/2.75 % (26914)Memory used [KB]: 7164
% 9.19/2.75 % (26914)Time elapsed: 0.388 s
% 9.19/2.75 % (26914)Instructions burned: 1022 (million)
% 9.19/2.75 % (26914)------------------------------
% 9.19/2.75 % (26914)------------------------------
% 9.19/2.76 % (26934)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_26726 for (2988ds/832Mi)
% 9.19/2.77 % (26933)Instruction limit reached!
% 9.19/2.77 % (26933)------------------------------
% 9.19/2.77 % (26933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.77 % (26933)Termination reason: Unknown
% 9.19/2.77 % (26933)Termination phase: Saturation
% 9.19/2.77
% 9.19/2.77 % (26933)Memory used [KB]: 6524
% 9.19/2.77 % (26933)Time elapsed: 0.098 s
% 9.19/2.77 % (26933)Instructions burned: 255 (million)
% 9.19/2.77 % (26933)------------------------------
% 9.19/2.77 % (26933)------------------------------
% 9.19/2.77 % (26935)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_26726 for (2988ds/668Mi)
% 9.19/2.78 % (26936)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_26726 for (2988ds/40Mi)
% 9.19/2.79 % (26932)Instruction limit reached!
% 9.19/2.79 % (26932)------------------------------
% 9.19/2.79 % (26932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.79 % (26932)Termination reason: Unknown
% 9.19/2.79 % (26932)Termination phase: Saturation
% 9.19/2.79
% 9.19/2.79 % (26932)Memory used [KB]: 6396
% 9.19/2.79 % (26932)Time elapsed: 0.146 s
% 9.19/2.79 % (26932)Instructions burned: 373 (million)
% 9.19/2.79 % (26932)------------------------------
% 9.19/2.79 % (26932)------------------------------
% 9.19/2.79 % (26934)Refutation not found, incomplete strategy
% 9.19/2.79 % (26934)------------------------------
% 9.19/2.79 % (26934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.79 % (26934)Termination reason: Refutation not found, incomplete strategy
% 9.19/2.79
% 9.19/2.79
% 9.19/2.79 % (26934)Memory used [KB]: 6012
% 9.19/2.79 % (26934)Time elapsed: 0.039 s
% 9.19/2.79 % (26934)Instructions burned: 90 (million)
% 9.19/2.79 % (26934)------------------------------
% 9.19/2.79 % (26934)------------------------------
% 10.04/2.80 % (26936)Instruction limit reached!
% 10.04/2.80 % (26936)------------------------------
% 10.04/2.80 % (26936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.04/2.80 % (26936)Termination reason: Unknown
% 10.04/2.80 % (26936)Termination phase: Function definition elimination
% 10.04/2.80
% 10.04/2.80 % (26936)Memory used [KB]: 1407
% 10.04/2.80 % (26936)Time elapsed: 0.018 s
% 10.04/2.80 % (26936)Instructions burned: 41 (million)
% 10.04/2.80 % (26936)------------------------------
% 10.04/2.80 % (26936)------------------------------
% 10.04/2.81 % (26937)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_26726 for (2988ds/294Mi)
% 10.04/2.81 % (26938)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_26726 for (2988ds/187Mi)
% 10.04/2.81 % (26939)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_26726 for (2987ds/371Mi)
% 10.04/2.84 % (26939)Refutation not found, incomplete strategy
% 10.04/2.84 % (26939)------------------------------
% 10.04/2.84 % (26939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.04/2.84 % (26939)Termination reason: Refutation not found, incomplete strategy
% 10.04/2.84
% 10.04/2.84
% 10.04/2.84 % (26939)Memory used [KB]: 5756
% 10.04/2.84 % (26939)Time elapsed: 0.024 s
% 10.04/2.84 % (26939)Instructions burned: 58 (million)
% 10.04/2.84 % (26939)------------------------------
% 10.04/2.84 % (26939)------------------------------
% 10.04/2.84 % (26937)Refutation not found, incomplete strategy
% 10.04/2.84 % (26937)------------------------------
% 10.04/2.84 % (26937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.04/2.84 % (26937)Termination reason: Refutation not found, incomplete strategy
% 10.04/2.84
% 10.04/2.84
% 10.04/2.84 % (26937)Memory used [KB]: 5884
% 10.04/2.84 % (26937)Time elapsed: 0.031 s
% 10.04/2.84 % (26937)Instructions burned: 81 (million)
% 10.04/2.84 % (26937)------------------------------
% 10.04/2.84 % (26937)------------------------------
% 10.04/2.85 % (26941)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_26726 for (2987ds/70Mi)
% 10.04/2.85 % (26940)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_26726 for (2987ds/1827Mi)
% 10.04/2.88 % (26941)Instruction limit reached!
% 10.04/2.88 % (26941)------------------------------
% 10.04/2.88 % (26941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.04/2.88 % (26941)Termination reason: Unknown
% 10.04/2.88 % (26941)Termination phase: Property scanning
% 10.04/2.88
% 10.04/2.88 % (26941)Memory used [KB]: 1407
% 10.04/2.88 % (26941)Time elapsed: 0.030 s
% 10.04/2.88 % (26941)Instructions burned: 70 (million)
% 10.04/2.88 % (26941)------------------------------
% 10.04/2.88 % (26941)------------------------------
% 10.04/2.88 % (26938)Instruction limit reached!
% 10.04/2.88 % (26938)------------------------------
% 10.04/2.88 % (26938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.04/2.88 % (26938)Termination reason: Unknown
% 10.04/2.88 % (26938)Termination phase: Saturation
% 10.04/2.88
% 10.04/2.88 % (26938)Memory used [KB]: 6140
% 10.04/2.88 % (26938)Time elapsed: 0.076 s
% 10.04/2.88 % (26938)Instructions burned: 187 (million)
% 10.04/2.88 % (26938)------------------------------
% 10.04/2.88 % (26938)------------------------------
% 10.29/2.90 % (26942)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_26726 for (2987ds/316Mi)
% 10.29/2.90 % (26943)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_26726 for (2986ds/932Mi)
% 10.29/3.02 % (26942)Instruction limit reached!
% 10.29/3.02 % (26942)------------------------------
% 10.29/3.02 % (26942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.29/3.02 % (26942)Termination reason: Unknown
% 10.29/3.02 % (26942)Termination phase: Saturation
% 10.29/3.02
% 10.29/3.02 % (26942)Memory used [KB]: 2302
% 10.29/3.02 % (26942)Time elapsed: 0.119 s
% 10.29/3.02 % (26942)Instructions burned: 316 (million)
% 10.29/3.02 % (26942)------------------------------
% 10.29/3.02 % (26942)------------------------------
% 10.29/3.02 % (26935)Instruction limit reached!
% 10.29/3.02 % (26935)------------------------------
% 10.29/3.02 % (26935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.29/3.02 % (26935)Termination reason: Unknown
% 10.29/3.02 % (26935)Termination phase: Saturation
% 10.29/3.02
% 10.29/3.02 % (26935)Memory used [KB]: 12409
% 10.29/3.02 % (26935)Time elapsed: 0.256 s
% 10.29/3.02 % (26935)Instructions burned: 669 (million)
% 10.29/3.02 % (26935)------------------------------
% 10.29/3.02 % (26935)------------------------------
% 10.29/3.03 % (26931)Instruction limit reached!
% 10.29/3.03 % (26931)------------------------------
% 10.29/3.03 % (26931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.29/3.03 % (26931)Termination reason: Unknown
% 10.29/3.03 % (26931)Termination phase: Saturation
% 10.29/3.03
% 10.29/3.03 % (26931)Memory used [KB]: 7931
% 10.29/3.03 % (26931)Time elapsed: 0.382 s
% 10.29/3.03 % (26931)Instructions burned: 996 (million)
% 10.29/3.03 % (26931)------------------------------
% 10.29/3.03 % (26931)------------------------------
% 12.50/3.03 % (26944)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_26726 for (2985ds/4714Mi)
% 12.50/3.04 % (26920)Instruction limit reached!
% 12.50/3.04 % (26920)------------------------------
% 12.50/3.04 % (26920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.50/3.04 % (26920)Termination reason: Unknown
% 12.50/3.04 % (26920)Termination phase: Saturation
% 12.50/3.04
% 12.50/3.04 % (26920)Memory used [KB]: 8187
% 12.50/3.04 % (26920)Time elapsed: 0.584 s
% 12.50/3.04 % (26920)Instructions burned: 1539 (million)
% 12.50/3.04 % (26920)------------------------------
% 12.50/3.04 % (26920)------------------------------
% 12.50/3.04 % (26945)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_26726 for (2985ds/8250Mi)
% 12.50/3.04 % (26946)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_26726 for (2985ds/770Mi)
% 12.50/3.05 % (26947)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_26726 for (2985ds/794Mi)
% 12.50/3.06 % (26946)Refutation not found, incomplete strategy
% 12.50/3.06 % (26946)------------------------------
% 12.50/3.06 % (26946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.50/3.06 % (26946)Termination reason: Refutation not found, incomplete strategy
% 12.50/3.06
% 12.50/3.06
% 12.50/3.06 % (26946)Memory used [KB]: 5756
% 12.50/3.06 % (26946)Time elapsed: 0.024 s
% 12.50/3.06 % (26946)Instructions burned: 55 (million)
% 12.50/3.06 % (26946)------------------------------
% 12.50/3.06 % (26946)------------------------------
% 12.50/3.08 % (26948)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_26726 for (2985ds/464Mi)
% 13.10/3.20 % (26944)Refutation not found, incomplete strategy
% 13.10/3.20 % (26944)------------------------------
% 13.10/3.20 % (26944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.10/3.20 % (26944)Termination reason: Refutation not found, incomplete strategy
% 13.10/3.20
% 13.10/3.20
% 13.10/3.20 % (26944)Memory used [KB]: 7547
% 13.10/3.20 % (26944)Time elapsed: 0.170 s
% 13.10/3.20 % (26944)Instructions burned: 464 (million)
% 13.10/3.20 % (26944)------------------------------
% 13.10/3.20 % (26944)------------------------------
% 13.10/3.22 % (26949)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_26726 for (2983ds/1376Mi)
% 13.10/3.27 % (26948)Instruction limit reached!
% 13.10/3.27 % (26948)------------------------------
% 13.10/3.27 % (26948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.10/3.27 % (26948)Termination reason: Unknown
% 13.10/3.27 % (26948)Termination phase: Saturation
% 13.10/3.27
% 13.10/3.27 % (26948)Memory used [KB]: 6268
% 13.10/3.27 % (26948)Time elapsed: 0.191 s
% 13.10/3.27 % (26948)Instructions burned: 466 (million)
% 13.10/3.27 % (26948)------------------------------
% 13.10/3.27 % (26948)------------------------------
% 13.10/3.29 % (26943)Instruction limit reached!
% 13.10/3.29 % (26943)------------------------------
% 13.10/3.29 % (26943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.10/3.29 % (26943)Termination reason: Unknown
% 13.10/3.29 % (26943)Termination phase: Saturation
% 13.10/3.29
% 13.10/3.29 % (26943)Memory used [KB]: 7931
% 13.10/3.29 % (26943)Time elapsed: 0.379 s
% 13.10/3.29 % (26943)Instructions burned: 933 (million)
% 13.10/3.29 % (26943)------------------------------
% 13.10/3.29 % (26943)------------------------------
% 13.10/3.29 % (26950)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_26726 for (2983ds/906Mi)
% 13.80/3.30 % (26951)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_26726 for (2982ds/434Mi)
% 13.80/3.33 % (26951)Refutation not found, incomplete strategy
% 13.80/3.33 % (26951)------------------------------
% 13.80/3.33 % (26951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.80/3.33 % (26951)Termination reason: Refutation not found, incomplete strategy
% 13.80/3.33
% 13.80/3.33
% 13.80/3.33 % (26951)Memory used [KB]: 5756
% 13.80/3.33 % (26951)Time elapsed: 0.024 s
% 13.80/3.33 % (26951)Instructions burned: 56 (million)
% 13.80/3.33 % (26951)------------------------------
% 13.80/3.33 % (26951)------------------------------
% 13.80/3.34 % (26952)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_26726 for (2982ds/865Mi)
% 13.80/3.35 % (26952)Refutation not found, incomplete strategy
% 13.80/3.35 % (26952)------------------------------
% 13.80/3.35 % (26952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.80/3.35 % (26952)Termination reason: Refutation not found, incomplete strategy
% 13.80/3.35
% 13.80/3.35
% 13.80/3.35 % (26952)Memory used [KB]: 5756
% 13.80/3.35 % (26952)Time elapsed: 0.012 s
% 13.80/3.35 % (26952)Instructions burned: 24 (million)
% 13.80/3.35 % (26952)------------------------------
% 13.80/3.35 % (26952)------------------------------
% 13.80/3.36 % (26947)Instruction limit reached!
% 13.80/3.36 % (26947)------------------------------
% 13.80/3.36 % (26947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.80/3.36 % (26947)Termination reason: Unknown
% 13.80/3.36 % (26947)Termination phase: Saturation
% 13.80/3.36
% 13.80/3.36 % (26947)Memory used [KB]: 2430
% 13.80/3.36 % (26947)Time elapsed: 0.306 s
% 13.80/3.36 % (26947)Instructions burned: 795 (million)
% 13.80/3.36 % (26947)------------------------------
% 13.80/3.36 % (26947)------------------------------
% 13.80/3.37 % (26953)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_26726 for (2982ds/593Mi)
% 13.80/3.37 % (26954)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_26726 for (2982ds/443Mi)
% 14.57/3.55 % (26954)Instruction limit reached!
% 14.57/3.55 % (26954)------------------------------
% 14.57/3.55 % (26954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.55 % (26954)Termination reason: Unknown
% 14.57/3.55 % (26954)Termination phase: Saturation
% 14.57/3.55
% 14.57/3.55 % (26954)Memory used [KB]: 6396
% 14.57/3.55 % (26954)Time elapsed: 0.174 s
% 14.57/3.55 % (26954)Instructions burned: 443 (million)
% 14.57/3.55 % (26954)------------------------------
% 14.57/3.55 % (26954)------------------------------
% 14.57/3.56 % (26955)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_26726 for (2980ds/594Mi)
% 14.57/3.59 % (26955)Refutation not found, incomplete strategy
% 14.57/3.59 % (26955)------------------------------
% 14.57/3.59 % (26955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.59 % (26955)Termination reason: Refutation not found, incomplete strategy
% 14.57/3.59
% 14.57/3.59
% 14.57/3.59 % (26955)Memory used [KB]: 5756
% 14.57/3.59 % (26955)Time elapsed: 0.025 s
% 14.57/3.59 % (26955)Instructions burned: 58 (million)
% 14.57/3.59 % (26955)------------------------------
% 14.57/3.59 % (26955)------------------------------
% 14.57/3.59 % (26953)Instruction limit reached!
% 14.57/3.59 % (26953)------------------------------
% 14.57/3.59 % (26953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.59 % (26953)Termination reason: Unknown
% 14.57/3.59 % (26953)Termination phase: Saturation
% 14.57/3.59
% 14.57/3.59 % (26953)Memory used [KB]: 7675
% 14.57/3.59 % (26953)Time elapsed: 0.222 s
% 14.57/3.59 % (26953)Instructions burned: 594 (million)
% 14.57/3.59 % (26953)------------------------------
% 14.57/3.59 % (26953)------------------------------
% 15.24/3.60 % (26956)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_26726 for (2979ds/327Mi)
% 15.24/3.61 % (26957)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_26726 for (2979ds/5411Mi)
% 15.24/3.63 % (26957)Refutation not found, incomplete strategy
% 15.24/3.63 % (26957)------------------------------
% 15.24/3.63 % (26957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.24/3.63 % (26957)Termination reason: Refutation not found, incomplete strategy
% 15.24/3.63
% 15.24/3.63
% 15.24/3.63 % (26957)Memory used [KB]: 5756
% 15.24/3.63 % (26957)Time elapsed: 0.023 s
% 15.24/3.63 % (26957)Instructions burned: 56 (million)
% 15.24/3.63 % (26957)------------------------------
% 15.24/3.63 % (26957)------------------------------
% 15.24/3.64 % (26950)Instruction limit reached!
% 15.24/3.64 % (26950)------------------------------
% 15.24/3.64 % (26950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.24/3.64 % (26950)Termination reason: Unknown
% 15.24/3.64 % (26950)Termination phase: Saturation
% 15.24/3.64
% 15.24/3.64 % (26950)Memory used [KB]: 7036
% 15.24/3.64 % (26950)Time elapsed: 0.351 s
% 15.24/3.64 % (26950)Instructions burned: 906 (million)
% 15.24/3.64 % (26950)------------------------------
% 15.24/3.64 % (26950)------------------------------
% 15.24/3.65 % (26958)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_26726 for (2979ds/1762Mi)
% 15.24/3.65 % (26959)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_26726 for (2979ds/96Mi)
% 15.24/3.67 % (26940)Instruction limit reached!
% 15.24/3.67 % (26940)------------------------------
% 15.24/3.67 % (26940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.24/3.67 % (26940)Termination reason: Unknown
% 15.24/3.67 % (26940)Termination phase: Saturation
% 15.24/3.67
% 15.24/3.67 % (26940)Memory used [KB]: 8059
% 15.24/3.67 % (26940)Time elapsed: 0.844 s
% 15.24/3.67 % (26940)Instructions burned: 1829 (million)
% 15.24/3.67 % (26940)------------------------------
% 15.24/3.67 % (26940)------------------------------
% 15.24/3.69 % (26960)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_26726 for (2979ds/503Mi)
% 15.24/3.69 % (26959)Instruction limit reached!
% 15.24/3.69 % (26959)------------------------------
% 15.24/3.69 % (26959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.24/3.69 % (26959)Termination reason: Unknown
% 15.24/3.69 % (26959)Termination phase: Property scanning
% 15.24/3.69
% 15.24/3.69 % (26959)Memory used [KB]: 1407
% 15.24/3.69 % (26959)Time elapsed: 0.041 s
% 15.24/3.69 % (26959)Instructions burned: 96 (million)
% 15.24/3.69 % (26959)------------------------------
% 15.24/3.69 % (26959)------------------------------
% 15.88/3.71 % (26961)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_26726 for (2978ds/90Mi)
% 15.88/3.71 % (26960)Refutation not found, incomplete strategy
% 15.88/3.71 % (26960)------------------------------
% 15.88/3.71 % (26960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/3.71 % (26960)Termination reason: Refutation not found, incomplete strategy
% 15.88/3.71
% 15.88/3.71
% 15.88/3.71 % (26960)Memory used [KB]: 5756
% 15.88/3.71 % (26960)Time elapsed: 0.024 s
% 15.88/3.71 % (26960)Instructions burned: 55 (million)
% 15.88/3.71 % (26960)------------------------------
% 15.88/3.71 % (26960)------------------------------
% 15.88/3.73 % (26962)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_26726 for (2978ds/593Mi)
% 15.88/3.74 % (26961)Instruction limit reached!
% 15.88/3.74 % (26961)------------------------------
% 15.88/3.74 % (26961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/3.74 % (26961)Termination reason: Unknown
% 15.88/3.74 % (26961)Termination phase: Property scanning
% 15.88/3.74
% 15.88/3.74 % (26961)Memory used [KB]: 1407
% 15.88/3.74 % (26961)Time elapsed: 0.037 s
% 15.88/3.74 % (26961)Instructions burned: 90 (million)
% 15.88/3.74 % (26961)------------------------------
% 15.88/3.74 % (26961)------------------------------
% 15.88/3.75 % (26956)Instruction limit reached!
% 15.88/3.75 % (26956)------------------------------
% 15.88/3.75 % (26956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/3.75 % (26956)Termination reason: Unknown
% 15.88/3.75 % (26956)Termination phase: Saturation
% 15.88/3.75
% 15.88/3.75 % (26956)Memory used [KB]: 6780
% 15.88/3.75 % (26956)Time elapsed: 0.147 s
% 15.88/3.75 % (26956)Instructions burned: 328 (million)
% 15.88/3.75 % (26956)------------------------------
% 15.88/3.75 % (26956)------------------------------
% 15.88/3.76 % (26963)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_26726 for (2978ds/1512Mi)
% 15.88/3.77 % (26964)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_26726 for (2978ds/569Mi)
% 16.25/3.80 % (26949)Instruction limit reached!
% 16.25/3.80 % (26949)------------------------------
% 16.25/3.80 % (26949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.25/3.80 % (26963)Refutation not found, incomplete strategy
% 16.25/3.80 % (26963)------------------------------
% 16.25/3.80 % (26963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.25/3.80 % (26963)Termination reason: Refutation not found, incomplete strategy
% 16.25/3.80
% 16.25/3.80
% 16.25/3.80 % (26963)Memory used [KB]: 6012
% 16.25/3.80 % (26963)Time elapsed: 0.041 s
% 16.25/3.80 % (26963)Instructions burned: 93 (million)
% 16.25/3.80 % (26963)------------------------------
% 16.25/3.80 % (26963)------------------------------
% 16.25/3.80 % (26949)Termination reason: Unknown
% 16.25/3.80 % (26949)Termination phase: Saturation
% 16.25/3.80
% 16.25/3.80 % (26949)Memory used [KB]: 8059
% 16.25/3.80 % (26949)Time elapsed: 0.583 s
% 16.25/3.80 % (26949)Instructions burned: 1377 (million)
% 16.25/3.80 % (26949)------------------------------
% 16.25/3.80 % (26949)------------------------------
% 16.25/3.82 % (26966)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_26726 for (2977ds/562Mi)
% 16.25/3.82 % (26965)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_26726 for (2977ds/501Mi)
% 16.25/3.83 % (26966)Refutation not found, incomplete strategy
% 16.25/3.83 % (26966)------------------------------
% 16.25/3.83 % (26966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.25/3.83 % (26966)Termination reason: Refutation not found, incomplete strategy
% 16.25/3.83
% 16.25/3.83
% 16.25/3.83 % (26966)Memory used [KB]: 5756
% 16.25/3.83 % (26966)Time elapsed: 0.012 s
% 16.25/3.83 % (26966)Instructions burned: 24 (million)
% 16.25/3.83 % (26966)------------------------------
% 16.25/3.83 % (26966)------------------------------
% 16.25/3.84 % (26967)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_26726 for (2977ds/406Mi)
% 17.03/3.95 % (26962)Instruction limit reached!
% 17.03/3.95 % (26962)------------------------------
% 17.03/3.95 % (26962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.03/3.95 % (26962)Termination reason: Unknown
% 17.03/3.95 % (26962)Termination phase: Saturation
% 17.03/3.95
% 17.03/3.95 % (26962)Memory used [KB]: 6780
% 17.03/3.95 % (26962)Time elapsed: 0.228 s
% 17.03/3.95 % (26962)Instructions burned: 594 (million)
% 17.03/3.95 % (26962)------------------------------
% 17.03/3.95 % (26962)------------------------------
% 17.03/3.97 % (26968)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_26726 for (2976ds/582Mi)
% 17.03/3.98 % (26964)Instruction limit reached!
% 17.03/3.98 % (26964)------------------------------
% 17.03/3.98 % (26964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.03/3.98 % (26964)Termination reason: Unknown
% 17.03/3.98 % (26964)Termination phase: Saturation
% 17.03/3.98
% 17.03/3.98 % (26964)Memory used [KB]: 7675
% 17.03/3.98 % (26964)Time elapsed: 0.214 s
% 17.03/3.98 % (26964)Instructions burned: 569 (million)
% 17.03/3.98 % (26964)------------------------------
% 17.03/3.98 % (26964)------------------------------
% 17.03/4.00 % (26969)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_26726 for (2976ds/456Mi)
% 17.03/4.01 % (26965)Refutation not found, incomplete strategy
% 17.03/4.01 % (26965)------------------------------
% 17.03/4.01 % (26965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.03/4.01 % (26965)Termination reason: Refutation not found, incomplete strategy
% 17.03/4.01
% 17.03/4.01
% 17.03/4.01 % (26965)Memory used [KB]: 7547
% 17.03/4.01 % (26965)Time elapsed: 0.182 s
% 17.03/4.01 % (26965)Instructions burned: 495 (million)
% 17.03/4.01 % (26965)------------------------------
% 17.03/4.01 % (26965)------------------------------
% 17.03/4.03 % (26967)Instruction limit reached!
% 17.03/4.03 % (26967)------------------------------
% 17.03/4.03 % (26967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.03/4.03 % (26967)Termination reason: Unknown
% 17.03/4.03 % (26967)Termination phase: Saturation
% 17.03/4.03
% 17.03/4.03 % (26967)Memory used [KB]: 7419
% 17.03/4.03 % (26967)Time elapsed: 0.184 s
% 17.03/4.03 % (26967)Instructions burned: 407 (million)
% 17.03/4.03 % (26967)------------------------------
% 17.03/4.03 % (26967)------------------------------
% 17.03/4.03 % (26970)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_26726 for (2975ds/393Mi)
% 19.30/4.04 % (26971)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_26726 for (2975ds/1335Mi)
% 19.30/4.05 % (26971)Refutation not found, incomplete strategy
% 19.30/4.05 % (26971)------------------------------
% 19.30/4.05 % (26971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.30/4.05 % (26971)Termination reason: Refutation not found, incomplete strategy
% 19.30/4.05
% 19.30/4.05
% 19.30/4.05 % (26971)Memory used [KB]: 5756
% 19.30/4.05 % (26971)Time elapsed: 0.014 s
% 19.30/4.05 % (26971)Instructions burned: 30 (million)
% 19.30/4.05 % (26971)------------------------------
% 19.30/4.05 % (26971)------------------------------
% 19.30/4.07 % (26972)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_26726 for (2975ds/3373Mi)
% 20.04/4.16 % (26969)Instruction limit reached!
% 20.04/4.16 % (26969)------------------------------
% 20.04/4.16 % (26969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.04/4.16 % (26969)Termination reason: Unknown
% 20.04/4.16 % (26969)Termination phase: Saturation
% 20.04/4.16
% 20.04/4.16 % (26969)Memory used [KB]: 2942
% 20.04/4.16 % (26969)Time elapsed: 0.169 s
% 20.04/4.16 % (26969)Instructions burned: 456 (million)
% 20.04/4.16 % (26969)------------------------------
% 20.04/4.16 % (26969)------------------------------
% 20.04/4.17 % (26970)Instruction limit reached!
% 20.04/4.17 % (26970)------------------------------
% 20.04/4.17 % (26970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.04/4.17 % (26970)Termination reason: Unknown
% 20.04/4.17 % (26970)Termination phase: Saturation
% 20.04/4.17
% 20.04/4.17 % (26970)Memory used [KB]: 7419
% 20.04/4.17 % (26970)Time elapsed: 0.146 s
% 20.04/4.17 % (26970)Instructions burned: 394 (million)
% 20.04/4.17 % (26970)------------------------------
% 20.04/4.17 % (26970)------------------------------
% 20.04/4.18 % (26973)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_26726 for (2974ds/474Mi)
% 20.04/4.19 % (26974)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_26726 for (2974ds/157Mi)
% 20.52/4.20 % (26968)Instruction limit reached!
% 20.52/4.20 % (26968)------------------------------
% 20.52/4.20 % (26968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.20 % (26968)Termination reason: Unknown
% 20.52/4.20 % (26968)Termination phase: Saturation
% 20.52/4.20
% 20.52/4.20 % (26968)Memory used [KB]: 6780
% 20.52/4.20 % (26968)Time elapsed: 0.229 s
% 20.52/4.20 % (26968)Instructions burned: 584 (million)
% 20.52/4.20 % (26968)------------------------------
% 20.52/4.20 % (26968)------------------------------
% 20.52/4.22 % (26975)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_26726 for (2973ds/590Mi)
% 20.52/4.24 % (26975)Refutation not found, incomplete strategy
% 20.52/4.24 % (26975)------------------------------
% 20.52/4.24 % (26975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.24 % (26975)Termination reason: Refutation not found, incomplete strategy
% 20.52/4.24
% 20.52/4.24
% 20.52/4.24 % (26975)Memory used [KB]: 5756
% 20.52/4.24 % (26975)Time elapsed: 0.026 s
% 20.52/4.24 % (26975)Instructions burned: 62 (million)
% 20.52/4.24 % (26975)------------------------------
% 20.52/4.24 % (26975)------------------------------
% 20.52/4.25 % (26974)Instruction limit reached!
% 20.52/4.25 % (26974)------------------------------
% 20.52/4.25 % (26974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.25 % (26974)Termination reason: Unknown
% 20.52/4.25 % (26974)Termination phase: Saturation
% 20.52/4.25
% 20.52/4.25 % (26974)Memory used [KB]: 6140
% 20.52/4.25 % (26974)Time elapsed: 0.065 s
% 20.52/4.25 % (26974)Instructions burned: 158 (million)
% 20.52/4.25 % (26974)------------------------------
% 20.52/4.25 % (26974)------------------------------
% 20.52/4.26 % (26976)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_26726 for (2973ds/104Mi)
% 20.52/4.27 % (26977)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_26726 for (2973ds/414Mi)
% 20.95/4.30 % (26976)Instruction limit reached!
% 20.95/4.30 % (26976)------------------------------
% 20.95/4.30 % (26976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.95/4.30 % (26976)Termination reason: Unknown
% 20.95/4.30 % (26976)Termination phase: Property scanning
% 20.95/4.30
% 20.95/4.30 % (26976)Memory used [KB]: 1407
% 20.95/4.30 % (26976)Time elapsed: 0.043 s
% 20.95/4.30 % (26976)Instructions burned: 104 (million)
% 20.95/4.30 % (26976)------------------------------
% 20.95/4.30 % (26976)------------------------------
% 20.95/4.31 % (26978)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_26726 for (2972ds/715Mi)
% 20.95/4.35 % (26973)Instruction limit reached!
% 20.95/4.35 % (26973)------------------------------
% 20.95/4.35 % (26973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.95/4.35 % (26973)Termination reason: Unknown
% 20.95/4.35 % (26973)Termination phase: Saturation
% 20.95/4.35
% 20.95/4.35 % (26973)Memory used [KB]: 7547
% 20.95/4.35 % (26973)Time elapsed: 0.177 s
% 20.95/4.35 % (26973)Instructions burned: 476 (million)
% 20.95/4.35 % (26973)------------------------------
% 20.95/4.35 % (26973)------------------------------
% 20.95/4.36 % (26958)Instruction limit reached!
% 20.95/4.36 % (26958)------------------------------
% 20.95/4.36 % (26958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.95/4.36 % (26958)Termination reason: Unknown
% 20.95/4.36 % (26958)Termination phase: Saturation
% 20.95/4.36
% 20.95/4.36 % (26958)Memory used [KB]: 8315
% 20.95/4.36 % (26958)Time elapsed: 0.711 s
% 20.95/4.36 % (26958)Instructions burned: 1763 (million)
% 20.95/4.36 % (26958)------------------------------
% 20.95/4.36 % (26958)------------------------------
% 20.95/4.37 % (26980)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_26726 for (2972ds/1213Mi)
% 20.95/4.38 % (26979)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_26726 for (2972ds/961Mi)
% 21.46/4.42 % (26977)Instruction limit reached!
% 21.46/4.42 % (26977)------------------------------
% 21.46/4.42 % (26977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.46/4.42 % (26977)Termination reason: Unknown
% 21.46/4.42 % (26977)Termination phase: Saturation
% 21.46/4.42
% 21.46/4.42 % (26977)Memory used [KB]: 7419
% 21.46/4.42 % (26977)Time elapsed: 0.156 s
% 21.46/4.42 % (26977)Instructions burned: 416 (million)
% 21.46/4.42 % (26977)------------------------------
% 21.46/4.42 % (26977)------------------------------
% 21.46/4.44 % (26981)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_26726 for (2971ds/1979Mi)
% 21.83/4.55 % (26922)Instruction limit reached!
% 21.83/4.55 % (26922)------------------------------
% 21.83/4.55 % (26922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.83/4.55 % (26922)Termination reason: Unknown
% 21.83/4.55 % (26922)Termination phase: Saturation
% 21.83/4.55
% 21.83/4.55 % (26922)Memory used [KB]: 9210
% 21.83/4.55 % (26922)Time elapsed: 2.067 s
% 21.83/4.55 % (26922)Instructions burned: 5206 (million)
% 21.83/4.55 % (26922)------------------------------
% 21.83/4.55 % (26922)------------------------------
% 21.83/4.56 % (26982)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_26726 for (2970ds/481Mi)
% 21.83/4.58 % (26979)Refutation not found, incomplete strategy
% 21.83/4.58 % (26979)------------------------------
% 21.83/4.58 % (26979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.83/4.58 % (26979)Termination reason: Refutation not found, incomplete strategy
% 21.83/4.58
% 21.83/4.58
% 21.83/4.58 % (26979)Memory used [KB]: 7547
% 21.83/4.58 % (26979)Time elapsed: 0.205 s
% 21.83/4.58 % (26979)Instructions burned: 540 (million)
% 21.83/4.58 % (26979)------------------------------
% 21.83/4.58 % (26979)------------------------------
% 21.83/4.59 % (26978)Instruction limit reached!
% 21.83/4.59 % (26978)------------------------------
% 21.83/4.59 % (26978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.83/4.59 % (26978)Termination reason: Unknown
% 21.83/4.59 % (26978)Termination phase: Saturation
% 21.83/4.59
% 21.83/4.59 % (26978)Memory used [KB]: 2302
% 21.83/4.59 % (26978)Time elapsed: 0.273 s
% 21.83/4.59 % (26978)Instructions burned: 715 (million)
% 21.83/4.59 % (26978)------------------------------
% 21.83/4.59 % (26978)------------------------------
% 22.50/4.60 % (26983)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_26726 for (2969ds/783Mi)
% 22.50/4.60 % (26984)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_26726 for (2969ds/432Mi)
% 22.50/4.62 % (26983)Refutation not found, incomplete strategy
% 22.50/4.62 % (26983)------------------------------
% 22.50/4.62 % (26983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.50/4.62 % (26983)Termination reason: Refutation not found, incomplete strategy
% 22.50/4.62
% 22.50/4.62
% 22.50/4.62 % (26983)Memory used [KB]: 5756
% 22.50/4.62 % (26983)Time elapsed: 0.024 s
% 22.50/4.62 % (26983)Instructions burned: 57 (million)
% 22.50/4.62 % (26983)------------------------------
% 22.50/4.62 % (26983)------------------------------
% 22.50/4.62 % (26984)Refutation not found, incomplete strategy
% 22.50/4.62 % (26984)------------------------------
% 22.50/4.62 % (26984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.50/4.62 % (26984)Termination reason: Refutation not found, incomplete strategy
% 22.50/4.62
% 22.50/4.62
% 22.50/4.62 % (26984)Memory used [KB]: 5756
% 22.50/4.62 % (26984)Time elapsed: 0.023 s
% 22.50/4.62 % (26984)Instructions burned: 56 (million)
% 22.50/4.62 % (26984)------------------------------
% 22.50/4.62 % (26984)------------------------------
% 22.50/4.64 % (26985)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_26726 for (2969ds/1670Mi)
% 22.50/4.64 % (26986)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_26726 for (2969ds/90Mi)
% 22.50/4.68 % (26986)Instruction limit reached!
% 22.50/4.68 % (26986)------------------------------
% 22.50/4.68 % (26986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.50/4.68 % (26986)Termination reason: Unknown
% 22.50/4.68 % (26986)Termination phase: Property scanning
% 22.50/4.68
% 22.50/4.68 % (26986)Memory used [KB]: 1407
% 22.50/4.68 % (26986)Time elapsed: 0.037 s
% 22.50/4.68 % (26986)Instructions burned: 91 (million)
% 22.50/4.68 % (26986)------------------------------
% 22.50/4.68 % (26986)------------------------------
% 22.50/4.69 % (26987)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_26726 for (2969ds/346Mi)
% 22.73/4.74 % (26982)Instruction limit reached!
% 22.73/4.74 % (26982)------------------------------
% 22.73/4.74 % (26982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.73/4.74 % (26982)Termination reason: Unknown
% 22.73/4.74 % (26982)Termination phase: Saturation
% 22.73/4.74
% 22.73/4.74 % (26982)Memory used [KB]: 7675
% 22.73/4.74 % (26982)Time elapsed: 0.178 s
% 22.73/4.74 % (26982)Instructions burned: 481 (million)
% 22.73/4.74 % (26982)------------------------------
% 22.73/4.74 % (26982)------------------------------
% 22.73/4.76 % (26988)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_26726 for (2968ds/401Mi)
% 23.03/4.82 % (26987)Instruction limit reached!
% 23.03/4.82 % (26987)------------------------------
% 23.03/4.82 % (26987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.03/4.82 % (26987)Termination reason: Unknown
% 23.03/4.82 % (26987)Termination phase: Saturation
% 23.03/4.82
% 23.03/4.82 % (26987)Memory used [KB]: 6780
% 23.03/4.82 % (26987)Time elapsed: 0.129 s
% 23.03/4.82 % (26987)Instructions burned: 346 (million)
% 23.03/4.82 % (26987)------------------------------
% 23.03/4.82 % (26987)------------------------------
% 23.03/4.84 % (26989)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_26726 for (2967ds/6454Mi)
% 23.28/4.91 % (26988)Instruction limit reached!
% 23.28/4.91 % (26988)------------------------------
% 23.28/4.91 % (26988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.28/4.91 % (26988)Termination reason: Unknown
% 23.28/4.91 % (26988)Termination phase: Saturation
% 23.28/4.91
% 23.28/4.91 % (26988)Memory used [KB]: 7419
% 23.28/4.91 % (26988)Time elapsed: 0.150 s
% 23.28/4.91 % (26988)Instructions burned: 402 (million)
% 23.28/4.91 % (26988)------------------------------
% 23.28/4.91 % (26988)------------------------------
% 23.28/4.92 % (26990)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_26726 for (2966ds/283Mi)
% 23.28/4.96 % (26980)Instruction limit reached!
% 23.28/4.96 % (26980)------------------------------
% 23.28/4.96 % (26980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.28/4.96 % (26980)Termination reason: Unknown
% 23.28/4.96 % (26980)Termination phase: Saturation
% 23.28/4.96
% 23.28/4.96 % (26980)Memory used [KB]: 7675
% 23.28/4.96 % (26980)Time elapsed: 0.590 s
% 23.28/4.96 % (26980)Instructions burned: 1214 (million)
% 23.28/4.96 % (26980)------------------------------
% 23.28/4.96 % (26980)------------------------------
% 23.28/4.98 % (26991)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_26726 for (2966ds/865Mi)
% 26.51/5.05 % (26990)Instruction limit reached!
% 26.51/5.05 % (26990)------------------------------
% 26.51/5.05 % (26990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.51/5.05 % (26990)Termination reason: Unknown
% 26.51/5.05 % (26990)Termination phase: Saturation
% 26.51/5.05
% 26.51/5.05 % (26990)Memory used [KB]: 6268
% 26.51/5.05 % (26990)Time elapsed: 0.116 s
% 26.51/5.05 % (26990)Instructions burned: 285 (million)
% 26.51/5.05 % (26990)------------------------------
% 26.51/5.05 % (26990)------------------------------
% 26.51/5.07 % (26992)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_26726 for (2965ds/4528Mi)
% 26.51/5.09 % (26992)Refutation not found, incomplete strategy
% 26.51/5.09 % (26992)------------------------------
% 26.51/5.09 % (26992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.51/5.09 % (26992)Termination reason: Refutation not found, incomplete strategy
% 26.51/5.09
% 26.51/5.09
% 26.51/5.09 % (26992)Memory used [KB]: 1279
% 26.51/5.09 % (26992)Time elapsed: 0.024 s
% 26.51/5.09 % (26992)Instructions burned: 56 (million)
% 26.51/5.09 % (26992)------------------------------
% 26.51/5.09 % (26992)------------------------------
% 26.51/5.10 % (26993)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_26726 for (2964ds/1001Mi)
% 27.19/5.15 % (26991)Refutation not found, incomplete strategy
% 27.19/5.15 % (26991)------------------------------
% 27.19/5.15 % (26991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.19/5.15 % (26991)Termination reason: Refutation not found, incomplete strategy
% 27.19/5.15
% 27.19/5.15
% 27.19/5.15 % (26991)Memory used [KB]: 7547
% 27.19/5.15 % (26991)Time elapsed: 0.173 s
% 27.19/5.15 % (26991)Instructions burned: 473 (million)
% 27.19/5.15 % (26991)------------------------------
% 27.19/5.15 % (26991)------------------------------
% 27.19/5.17 % (26994)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_26726 for (2964ds/102Mi)
% 27.19/5.19 % (26981)Instruction limit reached!
% 27.19/5.19 % (26981)------------------------------
% 27.19/5.19 % (26981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.19/5.19 % (26981)Termination reason: Unknown
% 27.19/5.19 % (26981)Termination phase: Saturation
% 27.19/5.19
% 27.19/5.19 % (26981)Memory used [KB]: 8699
% 27.19/5.19 % (26981)Time elapsed: 0.760 s
% 27.19/5.19 % (26981)Instructions burned: 1980 (million)
% 27.19/5.19 % (26981)------------------------------
% 27.19/5.19 % (26981)------------------------------
% 27.53/5.21 % (26994)Instruction limit reached!
% 27.53/5.21 % (26994)------------------------------
% 27.53/5.21 % (26994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.53/5.21 % (26994)Termination reason: Unknown
% 27.53/5.21 % (26994)Termination phase: Property scanning
% 27.53/5.21
% 27.53/5.21 % (26994)Memory used [KB]: 1407
% 27.53/5.21 % (26994)Time elapsed: 0.045 s
% 27.53/5.21 % (26994)Instructions burned: 103 (million)
% 27.53/5.21 % (26994)------------------------------
% 27.53/5.21 % (26994)------------------------------
% 27.53/5.21 % (26995)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_26726 for (2963ds/952Mi)
% 27.53/5.23 % (26996)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_26726 for (2963ds/578Mi)
% 27.53/5.28 % (26985)Instruction limit reached!
% 27.53/5.28 % (26985)------------------------------
% 27.53/5.28 % (26985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.53/5.28 % (26985)Termination reason: Unknown
% 27.53/5.28 % (26985)Termination phase: Saturation
% 27.53/5.28
% 27.53/5.28 % (26985)Memory used [KB]: 8059
% 27.53/5.28 % (26985)Time elapsed: 0.646 s
% 27.53/5.28 % (26985)Instructions burned: 1670 (million)
% 27.53/5.28 % (26985)------------------------------
% 27.53/5.28 % (26985)------------------------------
% 27.99/5.30 % (26997)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_26726 for (2963ds/643Mi)
% 27.99/5.32 % (26972)Instruction limit reached!
% 27.99/5.32 % (26972)------------------------------
% 27.99/5.32 % (26972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.99/5.32 % (26972)Termination reason: Unknown
% 27.99/5.32 % (26972)Termination phase: Saturation
% 27.99/5.32
% 27.99/5.32 % (26972)Memory used [KB]: 9722
% 27.99/5.32 % (26972)Time elapsed: 1.252 s
% 27.99/5.32 % (26972)Instructions burned: 3374 (million)
% 27.99/5.32 % (26972)------------------------------
% 27.99/5.32 % (26972)------------------------------
% 27.99/5.34 % (26998)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_26726 for (2962ds/865Mi)
% 28.22/5.49 % (26993)Instruction limit reached!
% 28.22/5.49 % (26993)------------------------------
% 28.22/5.49 % (26993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.22/5.49 % (26993)Termination reason: Unknown
% 28.22/5.49 % (26993)Termination phase: Saturation
% 28.22/5.49
% 28.22/5.49 % (26993)Memory used [KB]: 7164
% 28.22/5.49 % (26993)Time elapsed: 0.384 s
% 28.22/5.49 % (26993)Instructions burned: 1002 (million)
% 28.22/5.49 % (26993)------------------------------
% 28.22/5.49 % (26993)------------------------------
% 28.22/5.50 % (26996)Instruction limit reached!
% 28.22/5.50 % (26996)------------------------------
% 28.22/5.50 % (26996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.22/5.50 % (26996)Termination reason: Unknown
% 28.22/5.50 % (26996)Termination phase: Saturation
% 28.22/5.50
% 28.22/5.50 % (26996)Memory used [KB]: 7419
% 28.22/5.50 % (26996)Time elapsed: 0.273 s
% 28.22/5.50 % (26996)Instructions burned: 578 (million)
% 28.22/5.50 % (26996)------------------------------
% 28.22/5.50 % (26996)------------------------------
% 28.83/5.50 % (26999)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_26726 for (2960ds/1174Mi)
% 28.83/5.51 % (27000)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_26726 for (2960ds/644Mi)
% 28.83/5.53 % (26997)Instruction limit reached!
% 28.83/5.53 % (26997)------------------------------
% 28.83/5.53 % (26997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.53 % (26997)Termination reason: Unknown
% 28.83/5.53 % (26997)Termination phase: Saturation
% 28.83/5.53
% 28.83/5.53 % (26997)Memory used [KB]: 7675
% 28.83/5.53 % (26997)Time elapsed: 0.240 s
% 28.83/5.53 % (26997)Instructions burned: 645 (million)
% 28.83/5.53 % (26997)------------------------------
% 28.83/5.53 % (26997)------------------------------
% 28.83/5.55 % (27001)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_26726 for (2960ds/1201Mi)
% 28.83/5.57 % (26995)Instruction limit reached!
% 28.83/5.57 % (26995)------------------------------
% 28.83/5.57 % (26995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.57 % (26995)Termination reason: Unknown
% 28.83/5.57 % (26995)Termination phase: Saturation
% 28.83/5.57
% 28.83/5.57 % (26995)Memory used [KB]: 7164
% 28.83/5.57 % (26995)Time elapsed: 0.363 s
% 28.83/5.57 % (26995)Instructions burned: 952 (million)
% 28.83/5.57 % (26995)------------------------------
% 28.83/5.57 % (26995)------------------------------
% 28.83/5.59 % (27002)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_26726 for (2960ds/1046Mi)
% 29.94/5.68 % (26998)Instruction limit reached!
% 29.94/5.68 % (26998)------------------------------
% 29.94/5.68 % (26998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.94/5.68 % (26998)Termination reason: Unknown
% 29.94/5.68 % (26998)Termination phase: Saturation
% 29.94/5.68
% 29.94/5.68 % (26998)Memory used [KB]: 7675
% 29.94/5.68 % (26998)Time elapsed: 0.340 s
% 29.94/5.68 % (26998)Instructions burned: 865 (million)
% 29.94/5.68 % (26998)------------------------------
% 29.94/5.68 % (26998)------------------------------
% 29.94/5.69 % (27000)Refutation not found, incomplete strategy
% 29.94/5.69 % (27000)------------------------------
% 29.94/5.69 % (27000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.94/5.69 % (27000)Termination reason: Refutation not found, incomplete strategy
% 29.94/5.69
% 29.94/5.69
% 29.94/5.69 % (27000)Memory used [KB]: 7675
% 29.94/5.69 % (27000)Time elapsed: 0.174 s
% 29.94/5.69 % (27000)Instructions burned: 475 (million)
% 29.94/5.69 % (27000)------------------------------
% 29.94/5.69 % (27000)------------------------------
% 29.94/5.69 % (26999)Refutation not found, incomplete strategy
% 29.94/5.69 % (26999)------------------------------
% 29.94/5.69 % (26999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.94/5.69 % (26999)Termination reason: Refutation not found, incomplete strategy
% 29.94/5.69
% 29.94/5.69
% 29.94/5.69 % (26999)Memory used [KB]: 7675
% 29.94/5.69 % (26999)Time elapsed: 0.186 s
% 29.94/5.69 % (26999)Instructions burned: 508 (million)
% 29.94/5.69 % (26999)------------------------------
% 29.94/5.69 % (26999)------------------------------
% 29.94/5.69 % (27003)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_26726 for (2959ds/222Mi)
% 30.89/5.70 % (27004)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_26726 for (2959ds/68Mi)
% 30.89/5.71 % (27005)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_26726 for (2958ds/454Mi)
% 30.89/5.73 % (27004)Instruction limit reached!
% 30.89/5.73 % (27004)------------------------------
% 30.89/5.73 % (27004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.89/5.73 % (27004)Termination reason: Unknown
% 30.89/5.73 % (27004)Termination phase: Property scanning
% 30.89/5.73
% 30.89/5.73 % (27004)Memory used [KB]: 1279
% 30.89/5.73 % (27004)Time elapsed: 0.028 s
% 30.89/5.73 % (27004)Instructions burned: 68 (million)
% 30.89/5.73 % (27004)------------------------------
% 30.89/5.73 % (27004)------------------------------
% 30.89/5.75 % (27006)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_26726 for (2958ds/360Mi)
% 30.89/5.78 % (27003)Instruction limit reached!
% 30.89/5.78 % (27003)------------------------------
% 30.89/5.78 % (27003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.89/5.78 % (27003)Termination reason: Unknown
% 30.89/5.78 % (27003)Termination phase: Saturation
% 30.89/5.78
% 30.89/5.78 % (27003)Memory used [KB]: 6524
% 30.89/5.78 % (27003)Time elapsed: 0.088 s
% 30.89/5.78 % (27003)Instructions burned: 223 (million)
% 30.89/5.78 % (27003)------------------------------
% 30.89/5.78 % (27003)------------------------------
% 31.24/5.80 % (27007)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_26726 for (2958ds/157Mi)
% 31.24/5.86 % (27007)Instruction limit reached!
% 31.24/5.86 % (27007)------------------------------
% 31.24/5.86 % (27007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.24/5.86 % (27007)Termination reason: Unknown
% 31.24/5.86 % (27007)Termination phase: Saturation
% 31.24/5.86
% 31.24/5.86 % (27007)Memory used [KB]: 6140
% 31.24/5.86 % (27007)Time elapsed: 0.064 s
% 31.24/5.86 % (27007)Instructions burned: 158 (million)
% 31.24/5.86 % (27007)------------------------------
% 31.24/5.86 % (27007)------------------------------
% 31.24/5.87 % (27005)Instruction limit reached!
% 31.24/5.87 % (27005)------------------------------
% 31.24/5.87 % (27005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.24/5.87 % (27005)Termination reason: Unknown
% 31.24/5.87 % (27005)Termination phase: Saturation
% 31.24/5.87
% 31.24/5.87 % (27005)Memory used [KB]: 12025
% 31.24/5.87 % (27005)Time elapsed: 0.166 s
% 31.24/5.87 % (27005)Instructions burned: 455 (million)
% 31.24/5.87 % (27005)------------------------------
% 31.24/5.87 % (27005)------------------------------
% 31.24/5.88 % (27008)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_26726 for (2957ds/5061Mi)
% 31.24/5.88 % (27006)Instruction limit reached!
% 31.24/5.88 % (27006)------------------------------
% 31.24/5.88 % (27006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.24/5.88 % (27006)Termination reason: Unknown
% 31.24/5.88 % (27006)Termination phase: Saturation
% 31.24/5.88
% 31.24/5.88 % (27006)Memory used [KB]: 6780
% 31.24/5.88 % (27006)Time elapsed: 0.134 s
% 31.24/5.88 % (27006)Instructions burned: 361 (million)
% 31.24/5.88 % (27006)------------------------------
% 31.24/5.88 % (27006)------------------------------
% 31.24/5.89 % (27009)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_26726 for (2957ds/2401Mi)
% 31.24/5.89 % (27010)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_26726 for (2957ds/5798Mi)
% 31.86/5.99 % (27002)Instruction limit reached!
% 31.86/5.99 % (27002)------------------------------
% 31.86/5.99 % (27002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.86/5.99 % (27002)Termination reason: Unknown
% 31.86/5.99 % (27002)Termination phase: Saturation
% 31.86/5.99
% 31.86/5.99 % (27002)Memory used [KB]: 7931
% 31.86/5.99 % (27002)Time elapsed: 0.403 s
% 31.86/5.99 % (27002)Instructions burned: 1046 (million)
% 31.86/5.99 % (27002)------------------------------
% 31.86/5.99 % (27002)------------------------------
% 31.86/6.01 % (27011)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_26726 for (2956ds/346Mi)
% 33.50/6.11 % (27001)Instruction limit reached!
% 33.50/6.11 % (27001)------------------------------
% 33.50/6.11 % (27001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.50/6.11 % (27001)Termination reason: Unknown
% 33.50/6.11 % (27001)Termination phase: Saturation
% 33.50/6.11
% 33.50/6.11 % (27001)Memory used [KB]: 7931
% 33.50/6.11 % (27001)Time elapsed: 0.556 s
% 33.50/6.11 % (27001)Instructions burned: 1202 (million)
% 33.50/6.11 % (27001)------------------------------
% 33.50/6.11 % (27001)------------------------------
% 33.50/6.12 % (27012)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_26726 for (2954ds/1321Mi)
% 34.18/6.14 % (27011)Instruction limit reached!
% 34.18/6.14 % (27011)------------------------------
% 34.18/6.14 % (27011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.18/6.14 % (27011)Termination reason: Unknown
% 34.18/6.14 % (27011)Termination phase: Saturation
% 34.18/6.14
% 34.18/6.14 % (27011)Memory used [KB]: 6780
% 34.18/6.14 % (27011)Time elapsed: 0.130 s
% 34.18/6.14 % (27011)Instructions burned: 348 (million)
% 34.18/6.14 % (27011)------------------------------
% 34.18/6.14 % (27011)------------------------------
% 34.18/6.15 % (27013)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_26726 for (2954ds/1312Mi)
% 34.18/6.18 % (27012)Refutation not found, incomplete strategy
% 34.18/6.18 % (27012)------------------------------
% 34.18/6.18 % (27012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.18/6.18 % (27012)Termination reason: Refutation not found, incomplete strategy
% 34.18/6.18
% 34.18/6.18
% 34.18/6.18 % (27012)Memory used [KB]: 2174
% 34.18/6.18 % (27012)Time elapsed: 0.062 s
% 34.18/6.18 % (27012)Instructions burned: 140 (million)
% 34.18/6.18 % (27012)------------------------------
% 34.18/6.18 % (27012)------------------------------
% 34.63/6.20 % (27014)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_26726 for (2953ds/672Mi)
% 34.63/6.22 % (27014)Refutation not found, incomplete strategy
% 34.63/6.22 % (27014)------------------------------
% 34.63/6.22 % (27014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.63/6.22 % (27014)Termination reason: Refutation not found, incomplete strategy
% 34.63/6.22
% 34.63/6.22
% 34.63/6.22 % (27014)Memory used [KB]: 5756
% 34.63/6.22 % (27014)Time elapsed: 0.024 s
% 34.63/6.22 % (27014)Instructions burned: 56 (million)
% 34.63/6.22 % (27014)------------------------------
% 34.63/6.22 % (27014)------------------------------
% 34.63/6.24 % (27015)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_26726 for (2953ds/1897Mi)
% 34.63/6.26 % (27015)Refutation not found, incomplete strategy
% 34.63/6.26 % (27015)------------------------------
% 34.63/6.26 % (27015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.63/6.26 % (27015)Termination reason: Refutation not found, incomplete strategy
% 34.63/6.26
% 34.63/6.26
% 34.63/6.26 % (27015)Memory used [KB]: 5756
% 34.63/6.26 % (27015)Time elapsed: 0.024 s
% 34.63/6.26 % (27015)Instructions burned: 56 (million)
% 34.63/6.26 % (27015)------------------------------
% 34.63/6.26 % (27015)------------------------------
% 34.63/6.28 % (27016)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_26726 for (2953ds/1202Mi)
% 36.70/6.64 % (26945)Instruction limit reached!
% 36.70/6.64 % (26945)------------------------------
% 36.70/6.64 % (26945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.70/6.64 % (26945)Termination reason: Unknown
% 36.70/6.64 % (26945)Termination phase: Saturation
% 36.70/6.64
% 36.70/6.64 % (26945)Memory used [KB]: 11129
% 36.70/6.64 % (26945)Time elapsed: 3.605 s
% 36.70/6.64 % (26945)Instructions burned: 8251 (million)
% 36.70/6.64 % (26945)------------------------------
% 36.70/6.64 % (26945)------------------------------
% 36.70/6.66 % (27017)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_26726 for (2949ds/1493Mi)
% 36.70/6.66 % (27013)Instruction limit reached!
% 36.70/6.66 % (27013)------------------------------
% 36.70/6.66 % (27013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.70/6.66 % (27013)Termination reason: Unknown
% 36.70/6.66 % (27013)Termination phase: Saturation
% 36.70/6.66
% 36.70/6.66 % (27013)Memory used [KB]: 7803
% 36.70/6.66 % (27013)Time elapsed: 0.534 s
% 36.70/6.66 % (27013)Instructions burned: 1312 (million)
% 36.70/6.66 % (27013)------------------------------
% 36.70/6.66 % (27013)------------------------------
% 36.70/6.66 % (27017)Refutation not found, incomplete strategy
% 36.70/6.66 % (27017)------------------------------
% 36.70/6.66 % (27017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.70/6.66 % (27017)Termination reason: Refutation not found, incomplete strategy
% 36.70/6.66
% 36.70/6.66
% 36.70/6.66 % (27017)Memory used [KB]: 5756
% 36.70/6.66 % (27017)Time elapsed: 0.007 s
% 36.70/6.66 % (27017)Instructions burned: 23 (million)
% 36.70/6.66 % (27017)------------------------------
% 36.70/6.66 % (27017)------------------------------
% 36.70/6.67 % (27018)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_26726 for (2949ds/7679Mi)
% 36.70/6.67 % (27019)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_26726 for (2949ds/340Mi)
% 36.70/6.69 % (27018)Refutation not found, incomplete strategy
% 36.70/6.69 % (27018)------------------------------
% 36.70/6.69 % (27018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.70/6.69 % (27018)Termination reason: Refutation not found, incomplete strategy
% 36.70/6.69
% 36.70/6.69
% 36.70/6.69 % (27018)Memory used [KB]: 1279
% 36.70/6.69 % (27018)Time elapsed: 0.016 s
% 36.70/6.69 % (27018)Instructions burned: 60 (million)
% 36.70/6.69 % (27018)------------------------------
% 36.70/6.69 % (27018)------------------------------
% 37.74/6.70 % (27020)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_26726 for (2948ds/3672Mi)
% 37.74/6.71 % (27020)Refutation not found, incomplete strategy
% 37.74/6.71 % (27020)------------------------------
% 37.74/6.71 % (27020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.74/6.71 % (27020)Termination reason: Refutation not found, incomplete strategy
% 37.74/6.71
% 37.74/6.71
% 37.74/6.71 % (27020)Memory used [KB]: 5756
% 37.74/6.71 % (27020)Time elapsed: 0.016 s
% 37.74/6.71 % (27020)Instructions burned: 58 (million)
% 37.74/6.71 % (27020)------------------------------
% 37.74/6.71 % (27020)------------------------------
% 37.74/6.72 % (27021)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_26726 for (2948ds/1535Mi)
% 37.74/6.75 % (27009)Instruction limit reached!
% 37.74/6.75 % (27009)------------------------------
% 37.74/6.75 % (27009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.74/6.75 % (27009)Termination reason: Unknown
% 37.74/6.75 % (27009)Termination phase: Saturation
% 37.74/6.75
% 37.74/6.75 % (27009)Memory used [KB]: 4733
% 37.74/6.75 % (27009)Time elapsed: 0.863 s
% 37.74/6.75 % (27009)Instructions burned: 2404 (million)
% 37.74/6.75 % (27009)------------------------------
% 37.74/6.75 % (27009)------------------------------
% 37.74/6.75 % (27019)Instruction limit reached!
% 37.74/6.75 % (27019)------------------------------
% 37.74/6.75 % (27019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.74/6.75 % (27019)Termination reason: Unknown
% 37.74/6.75 % (27019)Termination phase: Saturation
% 37.74/6.75
% 37.74/6.75 % (27019)Memory used [KB]: 6652
% 37.74/6.75 % (27019)Time elapsed: 0.080 s
% 37.74/6.75 % (27019)Instructions burned: 342 (million)
% 37.74/6.75 % (27019)------------------------------
% 37.74/6.75 % (27019)------------------------------
% 37.74/6.76 % (27022)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_26726 for (2948ds/4637Mi)
% 37.74/6.76 % (27023)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_26726 for (2948ds/3174Mi)
% 37.74/6.78 % (27016)Instruction limit reached!
% 37.74/6.78 % (27016)------------------------------
% 37.74/6.78 % (27016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.74/6.78 % (27016)Termination reason: Unknown
% 37.74/6.78 % (27016)Termination phase: Saturation
% 37.74/6.78
% 37.74/6.78 % (27016)Memory used [KB]: 3965
% 37.74/6.78 % (27016)Time elapsed: 0.503 s
% 37.74/6.78 % (27016)Instructions burned: 1202 (million)
% 37.74/6.78 % (27016)------------------------------
% 37.74/6.78 % (27016)------------------------------
% 37.74/6.79 % (27024)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_26726 for (2947ds/307Mi)
% 38.72/6.86 % (27024)Instruction limit reached!
% 38.72/6.86 % (27024)------------------------------
% 38.72/6.86 % (27024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.72/6.86 % (27024)Termination reason: Unknown
% 38.72/6.86 % (27024)Termination phase: Saturation
% 38.72/6.86
% 38.72/6.86 % (27024)Memory used [KB]: 6652
% 38.72/6.86 % (27024)Time elapsed: 0.069 s
% 38.72/6.86 % (27024)Instructions burned: 307 (million)
% 38.72/6.86 % (27024)------------------------------
% 38.72/6.86 % (27024)------------------------------
% 38.72/6.87 % (27025)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_26726 for (2947ds/3619Mi)
% 38.72/6.89 % (27025)Refutation not found, incomplete strategy
% 38.72/6.89 % (27025)------------------------------
% 38.72/6.89 % (27025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.72/6.89 % (27025)Termination reason: Refutation not found, incomplete strategy
% 38.72/6.89
% 38.72/6.89
% 38.72/6.89 % (27025)Memory used [KB]: 5884
% 38.72/6.89 % (27025)Time elapsed: 0.022 s
% 38.72/6.89 % (27025)Instructions burned: 78 (million)
% 38.72/6.89 % (27025)------------------------------
% 38.72/6.89 % (27025)------------------------------
% 39.14/6.90 % (27027)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_26726 for (2946ds/2325Mi)
% 40.39/7.09 % (27021)Instruction limit reached!
% 40.39/7.09 % (27021)------------------------------
% 40.39/7.09 % (27021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.39/7.09 % (27021)Termination reason: Unknown
% 40.39/7.09 % (27021)Termination phase: Saturation
% 40.39/7.09
% 40.39/7.09 % (27021)Memory used [KB]: 8443
% 40.39/7.09 % (27021)Time elapsed: 0.369 s
% 40.39/7.09 % (27021)Instructions burned: 1535 (million)
% 40.39/7.09 % (27021)------------------------------
% 40.39/7.09 % (27021)------------------------------
% 40.39/7.10 % (27112)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_26726 for (2944ds/2341Mi)
% 41.07/7.12 % (27112)Refutation not found, incomplete strategy
% 41.07/7.12 % (27112)------------------------------
% 41.07/7.12 % (27112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.07/7.12 % (27112)Termination reason: Refutation not found, incomplete strategy
% 41.07/7.12
% 41.07/7.12
% 41.07/7.12 % (27112)Memory used [KB]: 5756
% 41.07/7.12 % (27112)Time elapsed: 0.016 s
% 41.07/7.12 % (27112)Instructions burned: 60 (million)
% 41.07/7.12 % (27112)------------------------------
% 41.07/7.12 % (27112)------------------------------
% 41.07/7.13 % (27123)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_26726 for (2944ds/7257Mi)
% 41.07/7.14 % (27123)Refutation not found, incomplete strategy
% 41.07/7.14 % (27123)------------------------------
% 41.07/7.14 % (27123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.07/7.14 % (27123)Termination reason: Refutation not found, incomplete strategy
% 41.07/7.14
% 41.07/7.14
% 41.07/7.14 % (27123)Memory used [KB]: 5756
% 41.07/7.14 % (27123)Time elapsed: 0.015 s
% 41.07/7.14 % (27123)Instructions burned: 57 (million)
% 41.07/7.14 % (27123)------------------------------
% 41.07/7.14 % (27123)------------------------------
% 41.07/7.15 % (27139)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_26726 for (2944ds/3710Mi)
% 41.07/7.18 % (26989)Refutation not found, non-redundant clauses discarded% (26989)------------------------------
% 41.07/7.18 % (26989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.07/7.18 % (26989)Termination reason: Refutation not found, non-redundant clauses discarded
% 41.07/7.18
% 41.07/7.18 % (26989)Memory used [KB]: 9210
% 41.07/7.18 % (26989)Time elapsed: 2.345 s
% 41.07/7.18 % (26989)Instructions burned: 6415 (million)
% 41.07/7.18 % (26989)------------------------------
% 41.07/7.18 % (26989)------------------------------
% 41.07/7.19 % (27156)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_26726 for (2944ds/326Mi)
% 41.61/7.20 % (27156)Refutation not found, incomplete strategy
% 41.61/7.20 % (27156)------------------------------
% 41.61/7.20 % (27156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.61/7.20 % (27156)Termination reason: Refutation not found, incomplete strategy
% 41.61/7.20
% 41.61/7.20
% 41.61/7.20 % (27156)Memory used [KB]: 5756
% 41.61/7.20 % (27156)Time elapsed: 0.015 s
% 41.61/7.20 % (27156)Instructions burned: 54 (million)
% 41.61/7.20 % (27156)------------------------------
% 41.61/7.20 % (27156)------------------------------
% 41.61/7.21 % (27170)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_26726 for (2943ds/1100Mi)
% 42.64/7.47 % (27170)Instruction limit reached!
% 42.64/7.47 % (27170)------------------------------
% 42.64/7.47 % (27170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.64/7.47 % (27170)Termination reason: Unknown
% 42.64/7.47 % (27170)Termination phase: Saturation
% 42.64/7.47
% 42.64/7.47 % (27170)Memory used [KB]: 7291
% 42.64/7.47 % (27170)Time elapsed: 0.259 s
% 42.64/7.47 % (27170)Instructions burned: 1103 (million)
% 42.64/7.47 % (27170)------------------------------
% 42.64/7.47 % (27170)------------------------------
% 42.64/7.48 % (27263)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_26726 for (2941ds/406Mi)
% 42.64/7.48 % (27008)Instruction limit reached!
% 42.64/7.48 % (27008)------------------------------
% 42.64/7.48 % (27008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.64/7.48 % (27008)Termination reason: Unknown
% 42.64/7.48 % (27008)Termination phase: Saturation
% 42.64/7.48
% 42.64/7.48 % (27008)Memory used [KB]: 8571
% 42.64/7.48 % (27008)Time elapsed: 1.608 s
% 42.64/7.48 % (27008)Instructions burned: 5061 (million)
% 42.64/7.48 % (27008)------------------------------
% 42.64/7.48 % (27008)------------------------------
% 42.64/7.49 % (27264)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_26726 for (2941ds/1871Mi)
% 43.41/7.51 % (27010)Instruction limit reached!
% 43.41/7.51 % (27010)------------------------------
% 43.41/7.51 % (27010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.41/7.51 % (27010)Termination reason: Unknown
% 43.41/7.51 % (27010)Termination phase: Saturation
% 43.41/7.51
% 43.41/7.51 % (27010)Memory used [KB]: 5884
% 43.41/7.51 % (27010)Time elapsed: 1.618 s
% 43.41/7.51 % (27010)Instructions burned: 5800 (million)
% 43.41/7.51 % (27010)------------------------------
% 43.41/7.51 % (27010)------------------------------
% 43.41/7.52 % (27265)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_26726 for (2940ds/1194Mi)
% 43.41/7.54 % (27027)Instruction limit reached!
% 43.41/7.54 % (27027)------------------------------
% 43.41/7.54 % (27027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.41/7.54 % (27027)Termination reason: Unknown
% 43.41/7.54 % (27027)Termination phase: Saturation
% 43.41/7.54
% 43.41/7.54 % (27027)Memory used [KB]: 8827
% 43.41/7.54 % (27027)Time elapsed: 0.642 s
% 43.41/7.54 % (27027)Instructions burned: 2326 (million)
% 43.41/7.54 % (27027)------------------------------
% 43.41/7.54 % (27027)------------------------------
% 43.41/7.55 % (27266)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_26726 for (2940ds/474Mi)
% 43.41/7.60 % (27263)Instruction limit reached!
% 43.41/7.60 % (27263)------------------------------
% 43.41/7.60 % (27263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.41/7.60 % (27263)Termination reason: Unknown
% 43.41/7.60 % (27263)Termination phase: Saturation
% 43.41/7.60
% 43.41/7.60 % (27263)Memory used [KB]: 7419
% 43.41/7.60 % (27263)Time elapsed: 0.114 s
% 43.41/7.60 % (27263)Instructions burned: 407 (million)
% 43.41/7.60 % (27263)------------------------------
% 43.41/7.60 % (27263)------------------------------
% 43.81/7.60 % (27267)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_26726 for (2939ds/3115Mi)
% 43.81/7.64 % (27023)Instruction limit reached!
% 43.81/7.64 % (27023)------------------------------
% 43.81/7.64 % (27023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.81/7.64 % (27023)Termination reason: Unknown
% 43.81/7.64 % (27023)Termination phase: Saturation
% 43.81/7.64
% 43.81/7.64 % (27023)Memory used [KB]: 10234
% 43.81/7.64 % (27023)Time elapsed: 0.875 s
% 43.81/7.64 % (27023)Instructions burned: 3174 (million)
% 43.81/7.64 % (27023)------------------------------
% 43.81/7.64 % (27023)------------------------------
% 43.81/7.65 % (27268)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_26726 for (2939ds/831Mi)
% 43.81/7.65 % (27266)Instruction limit reached!
% 43.81/7.65 % (27266)------------------------------
% 43.81/7.65 % (27266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.81/7.65 % (27266)Termination reason: Unknown
% 43.81/7.65 % (27266)Termination phase: Saturation
% 43.81/7.65
% 43.81/7.65 % (27266)Memory used [KB]: 7675
% 43.81/7.65 % (27266)Time elapsed: 0.106 s
% 43.81/7.65 % (27266)Instructions burned: 474 (million)
% 43.81/7.65 % (27266)------------------------------
% 43.81/7.65 % (27266)------------------------------
% 43.81/7.66 % (27269)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_26726 for (2939ds/1188Mi)
% 44.08/7.76 % (27268)Refutation not found, incomplete strategy
% 44.08/7.76 % (27268)------------------------------
% 44.08/7.76 % (27268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.08/7.76 % (27268)Termination reason: Refutation not found, incomplete strategy
% 44.08/7.76
% 44.08/7.76
% 44.08/7.76 % (27268)Memory used [KB]: 7675
% 44.08/7.76 % (27268)Time elapsed: 0.111 s
% 44.08/7.76 % (27268)Instructions burned: 496 (million)
% 44.08/7.76 % (27268)------------------------------
% 44.08/7.76 % (27268)------------------------------
% 44.08/7.77 % (27270)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_26726 for (2938ds/2868Mi)
% 44.31/7.80 % (27265)Instruction limit reached!
% 44.31/7.80 % (27265)------------------------------
% 44.31/7.80 % (27265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.31/7.80 % (27265)Termination reason: Unknown
% 44.31/7.80 % (27265)Termination phase: Saturation
% 44.31/7.80
% 44.31/7.80 % (27265)Memory used [KB]: 7291
% 44.31/7.80 % (27265)Time elapsed: 0.278 s
% 44.31/7.80 % (27265)Instructions burned: 1196 (million)
% 44.31/7.80 % (27265)------------------------------
% 44.31/7.80 % (27265)------------------------------
% 44.31/7.81 % (27022)Instruction limit reached!
% 44.31/7.81 % (27022)------------------------------
% 44.31/7.81 % (27022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.31/7.81 % (27022)Termination reason: Unknown
% 44.31/7.81 % (27022)Termination phase: Saturation
% 44.31/7.81
% 44.31/7.81 % (27022)Memory used [KB]: 10106
% 44.31/7.81 % (27022)Time elapsed: 1.049 s
% 44.31/7.81 % (27022)Instructions burned: 4639 (million)
% 44.31/7.81 % (27022)------------------------------
% 44.31/7.81 % (27022)------------------------------
% 44.31/7.81 % (27271)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_26726 for (2937ds/1516Mi)
% 44.31/7.82 % (27272)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_26726 for (2937ds/2321Mi)
% 44.31/7.82 % (27271)Refutation not found, incomplete strategy
% 44.31/7.82 % (27271)------------------------------
% 44.31/7.82 % (27271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.31/7.82 % (27271)Termination reason: Refutation not found, incomplete strategy
% 44.31/7.82
% 44.31/7.82
% 44.31/7.82 % (27271)Memory used [KB]: 5756
% 44.31/7.82 % (27271)Time elapsed: 0.015 s
% 44.31/7.82 % (27271)Instructions burned: 56 (million)
% 44.31/7.82 % (27271)------------------------------
% 44.31/7.82 % (27271)------------------------------
% 44.31/7.83 % (27273)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_26726 for (2937ds/2812Mi)
% 44.31/7.87 % (27270)Refutation not found, incomplete strategy
% 44.31/7.87 % (27270)------------------------------
% 44.31/7.87 % (27270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.31/7.87 % (27270)Termination reason: Refutation not found, incomplete strategy
% 44.31/7.87
% 44.31/7.87
% 44.31/7.87 % (27270)Memory used [KB]: 7547
% 44.31/7.87 % (27270)Time elapsed: 0.104 s
% 44.31/7.87 % (27270)Instructions burned: 464 (million)
% 44.31/7.87 % (27270)------------------------------
% 44.31/7.87 % (27270)------------------------------
% 44.31/7.88 % (27274)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_26726 for (2937ds/4604Mi)
% 44.75/7.92 % (27272)Refutation not found, incomplete strategy
% 44.75/7.92 % (27272)------------------------------
% 44.75/7.92 % (27272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.75/7.92 % (27272)Termination reason: Refutation not found, incomplete strategy
% 44.75/7.92
% 44.75/7.92
% 44.75/7.92 % (27272)Memory used [KB]: 7547
% 44.75/7.92 % (27272)Time elapsed: 0.104 s
% 44.75/7.92 % (27272)Instructions burned: 463 (million)
% 44.75/7.92 % (27272)------------------------------
% 44.75/7.92 % (27272)------------------------------
% 44.75/7.93 % (27275)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_26726 for (2936ds/2678Mi)
% 44.75/7.96 % (27269)Instruction limit reached!
% 44.75/7.96 % (27269)------------------------------
% 44.75/7.96 % (27269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.75/7.96 % (27269)Termination reason: Unknown
% 44.75/7.96 % (27269)Termination phase: Saturation
% 44.75/7.96
% 44.75/7.96 % (27269)Memory used [KB]: 7931
% 44.75/7.96 % (27269)Time elapsed: 0.296 s
% 44.75/7.96 % (27269)Instructions burned: 1189 (million)
% 44.75/7.96 % (27269)------------------------------
% 44.75/7.96 % (27269)------------------------------
% 44.75/7.97 % (27276)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_26726 for (2936ds/643Mi)
% 44.75/8.02 % (27264)Instruction limit reached!
% 44.75/8.02 % (27264)------------------------------
% 44.75/8.02 % (27264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.75/8.02 % (27264)Termination reason: Unknown
% 44.75/8.02 % (27264)Termination phase: Saturation
% 44.75/8.02
% 44.75/8.02 % (27264)Memory used [KB]: 9083
% 44.75/8.02 % (27264)Time elapsed: 0.524 s
% 44.75/8.02 % (27264)Instructions burned: 1873 (million)
% 44.75/8.02 % (27264)------------------------------
% 44.75/8.02 % (27264)------------------------------
% 47.48/8.03 % (27277)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_26726 for (2935ds/458Mi)
% 47.48/8.11 % (27139)Instruction limit reached!
% 47.48/8.11 % (27139)------------------------------
% 47.48/8.11 % (27139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.48/8.11 % (27139)Termination reason: Unknown
% 47.48/8.11 % (27139)Termination phase: Saturation
% 47.48/8.11
% 47.48/8.11 % (27139)Memory used [KB]: 8443
% 47.48/8.11 % (27139)Time elapsed: 0.959 s
% 47.48/8.11 % (27139)Instructions burned: 3710 (million)
% 47.48/8.11 % (27139)------------------------------
% 47.48/8.11 % (27139)------------------------------
% 47.48/8.11 % (27276)Instruction limit reached!
% 47.48/8.11 % (27276)------------------------------
% 47.48/8.11 % (27276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.48/8.11 % (27276)Termination reason: Unknown
% 47.48/8.11 % (27276)Termination phase: Saturation
% 47.48/8.11
% 47.48/8.11 % (27276)Memory used [KB]: 7675
% 47.48/8.11 % (27276)Time elapsed: 0.145 s
% 47.48/8.11 % (27276)Instructions burned: 643 (million)
% 47.48/8.11 % (27276)------------------------------
% 47.48/8.11 % (27276)------------------------------
% 47.48/8.12 % (27278)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_26726 for (2934ds/2546Mi)
% 47.48/8.12 % (27279)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_26726 for (2934ds/1432Mi)
% 48.08/8.13 % (27277)Instruction limit reached!
% 48.08/8.13 % (27277)------------------------------
% 48.08/8.13 % (27277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.08/8.13 % (27277)Termination reason: Unknown
% 48.08/8.13 % (27277)Termination phase: Saturation
% 48.08/8.13
% 48.08/8.13 % (27277)Memory used [KB]: 7547
% 48.08/8.13 % (27277)Time elapsed: 0.102 s
% 48.08/8.13 % (27277)Instructions burned: 460 (million)
% 48.08/8.13 % (27277)------------------------------
% 48.08/8.13 % (27277)------------------------------
% 48.08/8.14 % (27280)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_26726 for (2934ds/386Mi)
% 48.49/8.22 % (27280)Instruction limit reached!
% 48.49/8.22 % (27280)------------------------------
% 48.49/8.22 % (27280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.49/8.22 % (27280)Termination reason: Unknown
% 48.49/8.22 % (27280)Termination phase: Saturation
% 48.49/8.22
% 48.49/8.22 % (27280)Memory used [KB]: 6908
% 48.49/8.22 % (27280)Time elapsed: 0.086 s
% 48.49/8.22 % (27280)Instructions burned: 388 (million)
% 48.49/8.22 % (27280)------------------------------
% 48.49/8.22 % (27280)------------------------------
% 48.49/8.23 % (27281)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_26726 for (2933ds/360Mi)
% 48.98/8.31 % (27281)Instruction limit reached!
% 48.98/8.31 % (27281)------------------------------
% 48.98/8.31 % (27281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.98/8.31 % (27281)Termination reason: Unknown
% 48.98/8.31 % (27281)Termination phase: Saturation
% 48.98/8.31
% 48.98/8.31 % (27281)Memory used [KB]: 6780
% 48.98/8.31 % (27281)Time elapsed: 0.080 s
% 48.98/8.31 % (27281)Instructions burned: 360 (million)
% 48.98/8.31 % (27281)------------------------------
% 48.98/8.31 % (27281)------------------------------
% 48.98/8.32 % (27282)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_26726 for (2932ds/5446Mi)
% 48.98/8.38 % (27267)Instruction limit reached!
% 48.98/8.38 % (27267)------------------------------
% 48.98/8.38 % (27267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.98/8.38 % (27267)Termination reason: Unknown
% 48.98/8.38 % (27267)Termination phase: Saturation
% 48.98/8.38
% 48.98/8.38 % (27267)Memory used [KB]: 8571
% 48.98/8.38 % (27267)Time elapsed: 0.774 s
% 48.98/8.38 % (27267)Instructions burned: 3116 (million)
% 48.98/8.38 % (27267)------------------------------
% 48.98/8.38 % (27267)------------------------------
% 48.98/8.39 % (27283)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_26726 for (2932ds/2573Mi)
% 49.47/8.41 % (27279)Instruction limit reached!
% 49.47/8.41 % (27279)------------------------------
% 49.47/8.41 % (27279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.47/8.41 % (27279)Termination reason: Unknown
% 49.47/8.41 % (27279)Termination phase: Saturation
% 49.47/8.41
% 49.47/8.41 % (27279)Memory used [KB]: 11513
% 49.47/8.41 % (27279)Time elapsed: 0.293 s
% 49.47/8.41 % (27279)Instructions burned: 1436 (million)
% 49.47/8.41 % (27279)------------------------------
% 49.47/8.41 % (27279)------------------------------
% 49.47/8.42 % (27284)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_26726 for (2931ds/2655Mi)
% 49.47/8.49 % (27273)Instruction limit reached!
% 49.47/8.49 % (27273)------------------------------
% 49.47/8.49 % (27273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.47/8.49 % (27273)Termination reason: Unknown
% 49.47/8.49 % (27273)Termination phase: Saturation
% 49.47/8.49
% 49.47/8.49 % (27273)Memory used [KB]: 9594
% 49.47/8.49 % (27273)Time elapsed: 0.665 s
% 49.47/8.49 % (27273)Instructions burned: 2814 (million)
% 49.47/8.49 % (27273)------------------------------
% 49.47/8.49 % (27273)------------------------------
% 50.07/8.50 % (27285)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_26726 for (2930ds/2781Mi)
% 50.27/8.60 % (27275)Instruction limit reached!
% 50.27/8.60 % (27275)------------------------------
% 50.27/8.60 % (27275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.27/8.60 % (27275)Termination reason: Unknown
% 50.27/8.60 % (27275)Termination phase: Saturation
% 50.27/8.60
% 50.27/8.60 % (27275)Memory used [KB]: 8315
% 50.27/8.60 % (27275)Time elapsed: 0.672 s
% 50.27/8.60 % (27275)Instructions burned: 2681 (million)
% 50.27/8.60 % (27275)------------------------------
% 50.27/8.60 % (27275)------------------------------
% 50.27/8.61 % (27286)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_26726 for (2929ds/307Mi)
% 50.27/8.68 % (27286)Instruction limit reached!
% 50.27/8.68 % (27286)------------------------------
% 50.27/8.68 % (27286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.27/8.68 % (27286)Termination reason: Unknown
% 50.27/8.68 % (27286)Termination phase: Saturation
% 50.27/8.68
% 50.27/8.68 % (27286)Memory used [KB]: 6652
% 50.27/8.68 % (27286)Time elapsed: 0.069 s
% 50.27/8.68 % (27286)Instructions burned: 307 (million)
% 50.27/8.68 % (27286)------------------------------
% 50.27/8.68 % (27286)------------------------------
% 50.27/8.69 % (27287)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_26726 for (2929ds/1548Mi)
% 50.45/8.70 % (27287)Refutation not found, incomplete strategy
% 50.45/8.70 % (27287)------------------------------
% 50.45/8.70 % (27287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.45/8.70 % (27287)Termination reason: Refutation not found, incomplete strategy
% 50.45/8.70
% 50.45/8.70
% 50.45/8.70 % (27287)Memory used [KB]: 5756
% 50.45/8.70 % (27287)Time elapsed: 0.014 s
% 50.45/8.70 % (27287)Instructions burned: 54 (million)
% 50.45/8.70 % (27287)------------------------------
% 50.45/8.70 % (27287)------------------------------
% 50.45/8.71 % (27288)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_26726 for (2928ds/5214Mi)
% 50.45/8.76 % (27278)Instruction limit reached!
% 50.45/8.76 % (27278)------------------------------
% 50.45/8.76 % (27278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.45/8.76 % (27278)Termination reason: Unknown
% 50.45/8.76 % (27278)Termination phase: Saturation
% 50.45/8.76
% 50.45/8.76 % (27278)Memory used [KB]: 8827
% 50.45/8.76 % (27278)Time elapsed: 0.641 s
% 50.45/8.76 % (27278)Instructions burned: 2547 (million)
% 50.45/8.76 % (27278)------------------------------
% 50.45/8.76 % (27278)------------------------------
% 50.45/8.77 % (27289)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_26726 for (2928ds/3201Mi)
% 54.52/9.05 % (27283)Instruction limit reached!
% 54.52/9.05 % (27283)------------------------------
% 54.52/9.05 % (27283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.52/9.05 % (27283)Termination reason: Unknown
% 54.52/9.05 % (27283)Termination phase: Saturation
% 54.52/9.05
% 54.52/9.05 % (27283)Memory used [KB]: 8187
% 54.52/9.05 % (27283)Time elapsed: 0.659 s
% 54.52/9.05 % (27283)Instructions burned: 2576 (million)
% 54.52/9.05 % (27283)------------------------------
% 54.52/9.05 % (27283)------------------------------
% 54.52/9.06 % (27290)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_26726 for (2925ds/454Mi)
% 54.52/9.10 % (27284)Instruction limit reached!
% 54.52/9.10 % (27284)------------------------------
% 54.52/9.10 % (27284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.52/9.10 % (27284)Termination reason: Unknown
% 54.52/9.10 % (27284)Termination phase: Saturation
% 54.52/9.10
% 54.52/9.10 % (27284)Memory used [KB]: 3837
% 54.52/9.10 % (27284)Time elapsed: 0.679 s
% 54.52/9.10 % (27284)Instructions burned: 2655 (million)
% 54.52/9.10 % (27284)------------------------------
% 54.52/9.10 % (27284)------------------------------
% 54.52/9.11 % (27291)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_26726 for (2924ds/3049Mi)
% 55.15/9.16 % (27290)Instruction limit reached!
% 55.15/9.16 % (27290)------------------------------
% 55.15/9.16 % (27290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.15/9.16 % (27290)Termination reason: Unknown
% 55.15/9.16 % (27290)Termination phase: Saturation
% 55.15/9.16
% 55.15/9.16 % (27290)Memory used [KB]: 12025
% 55.15/9.16 % (27290)Time elapsed: 0.105 s
% 55.15/9.16 % (27290)Instructions burned: 457 (million)
% 55.15/9.16 % (27290)------------------------------
% 55.15/9.16 % (27290)------------------------------
% 55.15/9.17 % (27292)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_26726 for (2924ds/7311Mi)
% 55.15/9.17 % (27274)Instruction limit reached!
% 55.15/9.17 % (27274)------------------------------
% 55.15/9.17 % (27274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.15/9.17 % (27274)Termination reason: Unknown
% 55.15/9.17 % (27274)Termination phase: Saturation
% 55.15/9.17
% 55.15/9.17 % (27274)Memory used [KB]: 9594
% 55.15/9.17 % (27274)Time elapsed: 1.295 s
% 55.15/9.17 % (27274)Instructions burned: 4606 (million)
% 55.15/9.17 % (27274)------------------------------
% 55.15/9.17 % (27274)------------------------------
% 55.15/9.18 % (27292)Refutation not found, incomplete strategy
% 55.15/9.18 % (27292)------------------------------
% 55.15/9.18 % (27292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.15/9.18 % (27292)Termination reason: Refutation not found, incomplete strategy
% 55.15/9.18
% 55.15/9.18
% 55.15/9.18 % (27292)Memory used [KB]: 5756
% 55.15/9.18 % (27292)Time elapsed: 0.014 s
% 55.15/9.18 % (27292)Instructions burned: 53 (million)
% 55.15/9.18 % (27292)------------------------------
% 55.15/9.18 % (27292)------------------------------
% 55.15/9.18 % (27293)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_26726 for (2924ds/6804Mi)
% 55.15/9.19 % (27294)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_26726 for (2923ds/1683Mi)
% 55.15/9.19 % (27285)Instruction limit reached!
% 55.15/9.19 % (27285)------------------------------
% 55.15/9.19 % (27285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.15/9.19 % (27285)Termination reason: Unknown
% 55.15/9.19 % (27285)Termination phase: Saturation
% 55.15/9.19
% 55.15/9.19 % (27285)Memory used [KB]: 3709
% 55.15/9.19 % (27285)Time elapsed: 0.690 s
% 55.15/9.19 % (27285)Instructions burned: 2781 (million)
% 55.15/9.19 % (27285)------------------------------
% 55.15/9.19 % (27285)------------------------------
% 55.62/9.20 % (27295)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_26726 for (2923ds/4688Mi)
% 55.62/9.21 % (27293)Refutation not found, incomplete strategy
% 55.62/9.21 % (27293)------------------------------
% 55.62/9.21 % (27293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.62/9.21 % (27293)Termination reason: Refutation not found, incomplete strategy
% 55.62/9.21
% 55.62/9.21
% 55.62/9.21 % (27293)Memory used [KB]: 6012
% 55.62/9.21 % (27293)Time elapsed: 0.023 s
% 55.62/9.21 % (27293)Instructions burned: 89 (million)
% 55.62/9.21 % (27293)------------------------------
% 55.62/9.21 % (27293)------------------------------
% 55.62/9.22 % (27296)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_26726 for (2923ds/2207Mi)
% 56.26/9.46 % (27282)Instruction limit reached!
% 56.26/9.46 % (27282)------------------------------
% 56.26/9.46 % (27282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.26/9.46 % (27282)Termination reason: Unknown
% 56.26/9.46 % (27282)Termination phase: Saturation
% 56.26/9.46
% 56.26/9.46 % (27282)Memory used [KB]: 10106
% 56.26/9.46 % (27282)Time elapsed: 1.140 s
% 56.26/9.46 % (27282)Instructions burned: 5449 (million)
% 56.26/9.46 % (27282)------------------------------
% 56.26/9.46 % (27282)------------------------------
% 56.26/9.47 % (27297)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_26726 for (2921ds/8216Mi)
% 56.26/9.48 % (27297)Refutation not found, incomplete strategy
% 56.26/9.48 % (27297)------------------------------
% 56.26/9.48 % (27297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.26/9.48 % (27297)Termination reason: Refutation not found, incomplete strategy
% 56.26/9.48
% 56.26/9.48
% 56.26/9.48 % (27297)Memory used [KB]: 5756
% 56.26/9.48 % (27297)Time elapsed: 0.009 s
% 56.26/9.48 % (27297)Instructions burned: 32 (million)
% 56.26/9.48 % (27297)------------------------------
% 56.26/9.48 % (27297)------------------------------
% 56.26/9.49 % (27298)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_26726 for (2921ds/430Mi)
% 56.56/9.51 % (27289)Instruction limit reached!
% 56.56/9.51 % (27289)------------------------------
% 56.56/9.51 % (27289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.56/9.51 % (27289)Termination reason: Unknown
% 56.56/9.51 % (27289)Termination phase: Saturation
% 56.56/9.51
% 56.56/9.51 % (27289)Memory used [KB]: 9722
% 56.56/9.51 % (27289)Time elapsed: 0.740 s
% 56.56/9.51 % (27289)Instructions burned: 3203 (million)
% 56.56/9.51 % (27289)------------------------------
% 56.56/9.51 % (27289)------------------------------
% 56.56/9.52 % (27299)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_26726 for (2920ds/2012Mi)
% 56.56/9.58 % (27298)Instruction limit reached!
% 56.56/9.58 % (27298)------------------------------
% 56.56/9.58 % (27298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.56/9.58 % (27298)Termination reason: Unknown
% 56.56/9.58 % (27298)Termination phase: Saturation
% 56.56/9.58
% 56.56/9.58 % (27298)Memory used [KB]: 7547
% 56.56/9.58 % (27298)Time elapsed: 0.098 s
% 56.56/9.58 % (27298)Instructions burned: 432 (million)
% 56.56/9.58 % (27298)------------------------------
% 56.56/9.58 % (27298)------------------------------
% 56.56/9.59 % (27300)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_26726 for (2919ds/631Mi)
% 56.77/9.66 % (27294)Instruction limit reached!
% 56.77/9.66 % (27294)------------------------------
% 56.77/9.66 % (27294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.77/9.66 % (27294)Termination reason: Unknown
% 56.77/9.66 % (27294)Termination phase: Saturation
% 56.77/9.66
% 56.77/9.66 % (27294)Memory used [KB]: 8059
% 56.77/9.66 % (27294)Time elapsed: 0.465 s
% 56.77/9.66 % (27294)Instructions burned: 1685 (million)
% 56.77/9.66 % (27294)------------------------------
% 56.77/9.66 % (27294)------------------------------
% 56.77/9.67 % (27301)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_26726 for (2919ds/8785Mi)
% 57.35/9.70 % (27300)Refutation not found, incomplete strategy
% 57.35/9.70 % (27300)------------------------------
% 57.35/9.70 % (27300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.35/9.70 % (27300)Termination reason: Refutation not found, incomplete strategy
% 57.35/9.70
% 57.35/9.70
% 57.35/9.70 % (27300)Memory used [KB]: 7675
% 57.35/9.70 % (27300)Time elapsed: 0.106 s
% 57.35/9.70 % (27300)Instructions burned: 471 (million)
% 57.35/9.70 % (27300)------------------------------
% 57.35/9.70 % (27300)------------------------------
% 57.35/9.71 % (27302)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_26726 for (2918ds/739Mi)
% 57.35/9.73 % (27296)Instruction limit reached!
% 57.35/9.73 % (27296)------------------------------
% 57.35/9.73 % (27296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.35/9.73 % (27296)Termination reason: Unknown
% 57.35/9.73 % (27296)Termination phase: Saturation
% 57.35/9.73
% 57.35/9.73 % (27296)Memory used [KB]: 8955
% 57.35/9.73 % (27296)Time elapsed: 0.514 s
% 57.35/9.73 % (27296)Instructions burned: 2207 (million)
% 57.35/9.73 % (27296)------------------------------
% 57.35/9.73 % (27296)------------------------------
% 57.35/9.74 % (27303)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_26726 for (2918ds/5473Mi)
% 58.10/9.83 % (27291)Instruction limit reached!
% 58.10/9.83 % (27291)------------------------------
% 58.10/9.83 % (27291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.10/9.83 % (27291)Termination reason: Unknown
% 58.10/9.83 % (27291)Termination phase: Saturation
% 58.10/9.83
% 58.10/9.83 % (27291)Memory used [KB]: 9594
% 58.10/9.83 % (27291)Time elapsed: 0.725 s
% 58.10/9.83 % (27291)Instructions burned: 3050 (million)
% 58.10/9.83 % (27291)------------------------------
% 58.10/9.83 % (27291)------------------------------
% 58.10/9.84 % (27304)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_26726 for (2917ds/43570Mi)
% 58.10/9.86 % (27304)Refutation not found, incomplete strategy
% 58.10/9.86 % (27304)------------------------------
% 58.10/9.86 % (27304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.10/9.86 % (27304)Termination reason: Refutation not found, incomplete strategy
% 58.10/9.86
% 58.10/9.86
% 58.10/9.86 % (27304)Memory used [KB]: 5756
% 58.10/9.86 % (27304)Time elapsed: 0.015 s
% 58.10/9.86 % (27304)Instructions burned: 53 (million)
% 58.10/9.86 % (27304)------------------------------
% 58.10/9.86 % (27304)------------------------------
% 58.10/9.87 % (27305)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_26726 for (2917ds/8382Mi)
% 58.96/9.93 % (27302)Instruction limit reached!
% 58.96/9.93 % (27302)------------------------------
% 58.96/9.93 % (27302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.96/9.93 % (27302)Termination reason: Unknown
% 58.96/9.93 % (27302)Termination phase: Saturation
% 58.96/9.93
% 58.96/9.93 % (27302)Memory used [KB]: 7419
% 58.96/9.93 % (27302)Time elapsed: 0.221 s
% 58.96/9.93 % (27302)Instructions burned: 741 (million)
% 58.96/9.93 % (27302)------------------------------
% 58.96/9.93 % (27302)------------------------------
% 58.96/9.94 % (27306)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_26726 for (2916ds/407Mi)
% 58.96/9.97 % (27288)Instruction limit reached!
% 58.96/9.97 % (27288)------------------------------
% 58.96/9.97 % (27288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.96/9.97 % (27288)Termination reason: Unknown
% 58.96/9.97 % (27288)Termination phase: Saturation
% 58.96/9.97
% 58.96/9.97 % (27288)Memory used [KB]: 10618
% 58.96/9.97 % (27288)Time elapsed: 1.264 s
% 58.96/9.97 % (27288)Instructions burned: 5217 (million)
% 58.96/9.97 % (27288)------------------------------
% 58.96/9.97 % (27288)------------------------------
% 58.96/9.98 % (27307)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_26726 for (2916ds/2971Mi)
% 61.54/10.03 % (27299)Instruction limit reached!
% 61.54/10.03 % (27299)------------------------------
% 61.54/10.03 % (27299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.54/10.03 % (27299)Termination reason: Unknown
% 61.54/10.03 % (27299)Termination phase: Saturation
% 61.54/10.03
% 61.54/10.03 % (27299)Memory used [KB]: 12792
% 61.54/10.03 % (27299)Time elapsed: 0.516 s
% 61.54/10.03 % (27299)Instructions burned: 2014 (million)
% 61.54/10.03 % (27299)------------------------------
% 61.54/10.03 % (27299)------------------------------
% 61.54/10.03 % (27306)Instruction limit reached!
% 61.54/10.03 % (27306)------------------------------
% 61.54/10.03 % (27306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.54/10.03 % (27306)Termination reason: Unknown
% 61.54/10.03 % (27306)Termination phase: Saturation
% 61.54/10.03
% 61.54/10.03 % (27306)Memory used [KB]: 6396
% 61.54/10.03 % (27306)Time elapsed: 0.098 s
% 61.54/10.03 % (27306)Instructions burned: 410 (million)
% 61.54/10.03 % (27306)------------------------------
% 61.54/10.03 % (27306)------------------------------
% 61.54/10.04 % (27308)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_26726 for (2915ds/9822Mi)
% 61.54/10.04 % (27309)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_26726 for (2915ds/8425Mi)
% 61.54/10.07 % (27308)Refutation not found, incomplete strategy
% 61.54/10.07 % (27308)------------------------------
% 61.54/10.07 % (27308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.54/10.07 % (27308)Termination reason: Refutation not found, incomplete strategy
% 61.54/10.07
% 61.54/10.07
% 61.54/10.07 % (27308)Memory used [KB]: 6652
% 61.54/10.07 % (27308)Time elapsed: 0.035 s
% 61.54/10.07 % (27308)Instructions burned: 128 (million)
% 61.54/10.07 % (27308)------------------------------
% 61.54/10.07 % (27308)------------------------------
% 61.54/10.08 % (27310)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_26726 for (2915ds/3107Mi)
% 61.54/10.09 % (27307)Refutation not found, incomplete strategy
% 61.54/10.09 % (27307)------------------------------
% 61.54/10.09 % (27307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.54/10.09 % (27307)Termination reason: Refutation not found, incomplete strategy
% 61.54/10.09
% 61.54/10.09
% 61.54/10.09 % (27307)Memory used [KB]: 7547
% 61.54/10.09 % (27307)Time elapsed: 0.103 s
% 61.54/10.09 % (27307)Instructions burned: 466 (million)
% 61.54/10.09 % (27307)------------------------------
% 61.54/10.09 % (27307)------------------------------
% 61.54/10.10 % (27311)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_26726 for (2914ds/7967Mi)
% 62.39/10.20 % (27310)Refutation not found, incomplete strategy
% 62.39/10.20 % (27310)------------------------------
% 62.39/10.20 % (27310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.39/10.20 % (27310)Termination reason: Refutation not found, incomplete strategy
% 62.39/10.20
% 62.39/10.20
% 62.39/10.20 % (27310)Memory used [KB]: 7675
% 62.39/10.20 % (27310)Time elapsed: 0.113 s
% 62.39/10.20 % (27310)Instructions burned: 495 (million)
% 62.39/10.20 % (27310)------------------------------
% 62.39/10.20 % (27310)------------------------------
% 62.39/10.20 % (27311)Refutation not found, incomplete strategy
% 62.39/10.20 % (27311)------------------------------
% 62.39/10.20 % (27311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.39/10.20 % (27311)Termination reason: Refutation not found, incomplete strategy
% 62.39/10.20
% 62.39/10.20
% 62.39/10.20 % (27311)Memory used [KB]: 7547
% 62.39/10.20 % (27311)Time elapsed: 0.105 s
% 62.39/10.20 % (27311)Instructions burned: 465 (million)
% 62.39/10.20 % (27311)------------------------------
% 62.39/10.20 % (27311)------------------------------
% 62.39/10.21 % (27312)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_26726 for (2913ds/3629Mi)
% 62.39/10.21 % (27313)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_26726 for (2913ds/939Mi)
% 63.42/10.44 % (27313)Instruction limit reached!
% 63.42/10.44 % (27313)------------------------------
% 63.42/10.44 % (27313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.42/10.44 % (27313)Termination reason: Unknown
% 63.42/10.44 % (27313)Termination phase: Saturation
% 63.42/10.44
% 63.42/10.44 % (27313)Memory used [KB]: 7036
% 63.42/10.44 % (27313)Time elapsed: 0.228 s
% 63.42/10.44 % (27313)Instructions burned: 941 (million)
% 63.42/10.44 % (27313)------------------------------
% 63.42/10.44 % (27313)------------------------------
% 63.42/10.45 % (27314)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_26726 for (2911ds/1188Mi)
% 64.44/10.62 % (27295)Instruction limit reached!
% 64.44/10.62 % (27295)------------------------------
% 64.44/10.62 % (27295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.44/10.62 % (27295)Termination reason: Unknown
% 64.44/10.62 % (27295)Termination phase: Saturation
% 64.44/10.62
% 64.44/10.62 % (27295)Memory used [KB]: 9850
% 64.44/10.62 % (27295)Time elapsed: 1.415 s
% 64.44/10.62 % (27295)Instructions burned: 4688 (million)
% 64.44/10.62 % (27295)------------------------------
% 64.44/10.62 % (27295)------------------------------
% 64.44/10.63 % (27315)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_26726 for (2909ds/3205Mi)
% 64.78/10.74 % (27314)Instruction limit reached!
% 64.78/10.74 % (27314)------------------------------
% 64.78/10.74 % (27314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.78/10.74 % (27314)Termination reason: Unknown
% 64.78/10.74 % (27314)Termination phase: Saturation
% 64.78/10.74
% 64.78/10.74 % (27314)Memory used [KB]: 7931
% 64.78/10.74 % (27314)Time elapsed: 0.294 s
% 64.78/10.74 % (27314)Instructions burned: 1189 (million)
% 64.78/10.74 % (27314)------------------------------
% 64.78/10.74 % (27314)------------------------------
% 64.78/10.75 % (27316)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_26726 for (2908ds/865Mi)
% 65.69/10.96 % (27316)Instruction limit reached!
% 65.69/10.96 % (27316)------------------------------
% 65.69/10.96 % (27316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.69/10.96 % (27316)Termination reason: Unknown
% 65.69/10.96 % (27316)Termination phase: Saturation
% 65.69/10.96
% 65.69/10.96 % (27316)Memory used [KB]: 7547
% 65.69/10.96 % (27316)Time elapsed: 0.210 s
% 65.69/10.96 % (27316)Instructions burned: 866 (million)
% 65.69/10.96 % (27316)------------------------------
% 65.69/10.96 % (27316)------------------------------
% 65.69/10.97 % (27317)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_26726 for (2906ds/7469Mi)
% 65.69/10.99 % (27303)Instruction limit reached!
% 65.69/10.99 % (27303)------------------------------
% 65.69/10.99 % (27303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.69/10.99 % (27303)Termination reason: Unknown
% 65.69/10.99 % (27303)Termination phase: Saturation
% 65.69/10.99
% 65.69/10.99 % (27303)Memory used [KB]: 10746
% 65.69/10.99 % (27303)Time elapsed: 1.256 s
% 65.69/10.99 % (27303)Instructions burned: 5473 (million)
% 65.69/10.99 % (27303)------------------------------
% 65.69/10.99 % (27303)------------------------------
% 65.69/11.00 % (27318)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_26726 for (2905ds/4165Mi)
% 69.77/11.28 % (27312)Instruction limit reached!
% 69.77/11.28 % (27312)------------------------------
% 69.77/11.28 % (27312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.77/11.28 % (27312)Termination reason: Unknown
% 69.77/11.28 % (27312)Termination phase: Saturation
% 69.77/11.28
% 69.77/11.28 % (27312)Memory used [KB]: 16247
% 69.77/11.28 % (27312)Time elapsed: 1.075 s
% 69.77/11.28 % (27312)Instructions burned: 3631 (million)
% 69.77/11.28 % (27312)------------------------------
% 69.77/11.28 % (27312)------------------------------
% 69.77/11.29 % (27319)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_26726 for (2903ds/13468Mi)
% 70.46/11.30 % (27319)Refutation not found, incomplete strategy
% 70.46/11.30 % (27319)------------------------------
% 70.46/11.30 % (27319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.46/11.30 % (27319)Termination reason: Refutation not found, incomplete strategy
% 70.46/11.30
% 70.46/11.30
% 70.46/11.30 % (27319)Memory used [KB]: 5756
% 70.46/11.30 % (27319)Time elapsed: 0.030 s
% 70.46/11.30 % (27319)Instructions burned: 26 (million)
% 70.46/11.30 % (27319)------------------------------
% 70.46/11.30 % (27319)------------------------------
% 70.46/11.31 % (27320)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_26726 for (2902ds/2635Mi)
% 70.46/11.34 % (27315)Instruction limit reached!
% 70.46/11.34 % (27315)------------------------------
% 70.46/11.34 % (27315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.46/11.34 % (27315)Termination reason: Unknown
% 70.46/11.34 % (27315)Termination phase: Saturation
% 70.46/11.34
% 70.46/11.34 % (27315)Memory used [KB]: 9466
% 70.46/11.34 % (27315)Time elapsed: 0.714 s
% 70.46/11.34 % (27315)Instructions burned: 3211 (million)
% 70.46/11.34 % (27315)------------------------------
% 70.46/11.34 % (27315)------------------------------
% 70.46/11.35 % (27321)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_26726 for (2902ds/631Mi)
% 71.06/11.42 % (27320)Refutation not found, incomplete strategy
% 71.06/11.42 % (27320)------------------------------
% 71.06/11.42 % (27320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.06/11.42 % (27320)Termination reason: Refutation not found, incomplete strategy
% 71.06/11.42
% 71.06/11.42
% 71.06/11.42 % (27320)Memory used [KB]: 7675
% 71.06/11.42 % (27320)Time elapsed: 0.111 s
% 71.06/11.42 % (27320)Instructions burned: 500 (million)
% 71.06/11.42 % (27320)------------------------------
% 71.06/11.42 % (27320)------------------------------
% 71.06/11.43 % (27322)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_26726 for (2901ds/15557Mi)
% 71.06/11.49 % (27321)Instruction limit reached!
% 71.06/11.49 % (27321)------------------------------
% 71.06/11.49 % (27321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.06/11.49 % (27321)Termination reason: Unknown
% 71.06/11.49 % (27321)Termination phase: Saturation
% 71.06/11.49
% 71.06/11.49 % (27321)Memory used [KB]: 7675
% 71.06/11.49 % (27321)Time elapsed: 0.142 s
% 71.06/11.49 % (27321)Instructions burned: 633 (million)
% 71.06/11.49 % (27321)------------------------------
% 71.06/11.49 % (27321)------------------------------
% 71.82/11.50 % (27323)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_26726 for (2900ds/2142Mi)
% 71.82/11.52 % (27323)Refutation not found, incomplete strategy
% 71.82/11.52 % (27323)------------------------------
% 71.82/11.52 % (27323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.82/11.52 % (27323)Termination reason: Refutation not found, incomplete strategy
% 71.82/11.52
% 71.82/11.52
% 71.82/11.52 % (27323)Memory used [KB]: 5756
% 71.82/11.52 % (27323)Time elapsed: 0.016 s
% 71.82/11.52 % (27323)Instructions burned: 59 (million)
% 71.82/11.52 % (27323)------------------------------
% 71.82/11.52 % (27323)------------------------------
% 71.82/11.53 % (27324)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_26726 for (2900ds/5624Mi)
% 71.82/11.53 % (27305)Instruction limit reached!
% 71.82/11.53 % (27305)------------------------------
% 71.82/11.53 % (27305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.82/11.53 % (27305)Termination reason: Unknown
% 71.82/11.53 % (27305)Termination phase: Saturation
% 71.82/11.53
% 71.82/11.53 % (27305)Memory used [KB]: 10106
% 71.82/11.53 % (27305)Time elapsed: 1.660 s
% 71.82/11.53 % (27305)Instructions burned: 8382 (million)
% 71.82/11.53 % (27305)------------------------------
% 71.82/11.53 % (27305)------------------------------
% 71.82/11.53 % (27324)Refutation not found, incomplete strategy
% 71.82/11.53 % (27324)------------------------------
% 71.82/11.53 % (27324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.82/11.53 % (27324)Termination reason: Refutation not found, incomplete strategy
% 71.82/11.53
% 71.82/11.53
% 71.82/11.53 % (27324)Memory used [KB]: 5756
% 71.82/11.53 % (27324)Time elapsed: 0.006 s
% 71.82/11.53 % (27324)Instructions burned: 22 (million)
% 71.82/11.53 % (27324)------------------------------
% 71.82/11.53 % (27324)------------------------------
% 71.82/11.54 % (27325)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_26726 for (2900ds/1665Mi)
% 71.82/11.54 % (27326)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_26726 for (2900ds/64912Mi)
% 71.82/11.56 % (27326)Refutation not found, incomplete strategy
% 71.82/11.56 % (27326)------------------------------
% 71.82/11.56 % (27326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.82/11.56 % (27326)Termination reason: Refutation not found, incomplete strategy
% 71.82/11.56
% 71.82/11.56
% 71.82/11.56 % (27326)Memory used [KB]: 1279
% 71.82/11.56 % (27326)Time elapsed: 0.015 s
% 71.82/11.56 % (27326)Instructions burned: 54 (million)
% 71.82/11.56 % (27326)------------------------------
% 71.82/11.56 % (27326)------------------------------
% 71.82/11.57 % (27327)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_26726 for (2900ds/7801Mi)
% 73.13/11.87 % (27301)Instruction limit reached!
% 73.13/11.87 % (27301)------------------------------
% 73.13/11.87 % (27301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.13/11.87 % (27301)Termination reason: Unknown
% 73.13/11.87 % (27301)Termination phase: Saturation
% 73.13/11.87
% 73.13/11.87 % (27301)Memory used [KB]: 12025
% 73.13/11.87 % (27301)Time elapsed: 2.210 s
% 73.13/11.87 % (27301)Instructions burned: 8785 (million)
% 73.13/11.87 % (27301)------------------------------
% 73.13/11.87 % (27301)------------------------------
% 73.13/11.88 % (27328)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_26726 for (2897ds/15194Mi)
% 73.53/11.95 % (27325)Instruction limit reached!
% 73.53/11.95 % (27325)------------------------------
% 73.53/11.95 % (27325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.53/11.95 % (27325)Termination reason: Unknown
% 73.53/11.95 % (27325)Termination phase: Saturation
% 73.53/11.95
% 73.53/11.95 % (27325)Memory used [KB]: 8059
% 73.53/11.95 % (27325)Time elapsed: 0.411 s
% 73.53/11.95 % (27325)Instructions burned: 1665 (million)
% 73.53/11.95 % (27325)------------------------------
% 73.53/11.95 % (27325)------------------------------
% 73.53/11.96 % (27329)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_26726 for (2896ds/6753Mi)
% 73.53/11.98 % (27309)Instruction limit reached!
% 73.53/11.98 % (27309)------------------------------
% 73.53/11.98 % (27309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.53/11.98 % (27309)Termination reason: Unknown
% 73.53/11.98 % (27309)Termination phase: Saturation
% 73.53/11.98
% 73.53/11.98 % (27309)Memory used [KB]: 6268
% 73.53/11.98 % (27309)Time elapsed: 1.934 s
% 73.53/11.98 % (27309)Instructions burned: 8426 (million)
% 73.53/11.98 % (27309)------------------------------
% 73.53/11.98 % (27309)------------------------------
% 73.53/11.98 % (27329)Refutation not found, incomplete strategy
% 73.53/11.98 % (27329)------------------------------
% 73.53/11.98 % (27329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.53/11.98 % (27329)Termination reason: Refutation not found, incomplete strategy
% 73.53/11.98
% 73.53/11.98
% 73.53/11.98 % (27329)Memory used [KB]: 6012
% 73.53/11.98 % (27329)Time elapsed: 0.024 s
% 73.53/11.98 % (27329)Instructions burned: 93 (million)
% 73.53/11.98 % (27329)------------------------------
% 73.53/11.98 % (27329)------------------------------
% 73.53/11.99 % (27330)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_26726 for (2896ds/1003Mi)
% 73.53/11.99 % (27331)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_26726 for (2896ds/13018Mi)
% 73.53/12.01 % (27328)Refutation not found, incomplete strategy
% 73.53/12.01 % (27328)------------------------------
% 73.53/12.01 % (27328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.53/12.01 % (27328)Termination reason: Refutation not found, incomplete strategy
% 73.53/12.01
% 73.53/12.01
% 73.53/12.01 % (27328)Memory used [KB]: 7675
% 73.53/12.01 % (27328)Time elapsed: 0.123 s
% 73.53/12.01 % (27328)Instructions burned: 534 (million)
% 73.53/12.01 % (27328)------------------------------
% 73.53/12.01 % (27328)------------------------------
% 73.53/12.02 % (27332)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_26726 for (2895ds/1267Mi)
% 75.58/12.03 % (27332)Refutation not found, incomplete strategy
% 75.58/12.03 % (27332)------------------------------
% 75.58/12.03 % (27332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.58/12.03 % (27332)Termination reason: Refutation not found, incomplete strategy
% 75.58/12.03
% 75.58/12.03
% 75.58/12.03 % (27332)Memory used [KB]: 5756
% 75.58/12.03 % (27332)Time elapsed: 0.015 s
% 75.58/12.03 % (27332)Instructions burned: 56 (million)
% 75.58/12.03 % (27332)------------------------------
% 75.58/12.03 % (27332)------------------------------
% 75.58/12.04 % (27333)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_26726 for (2895ds/2570Mi)
% 76.64/12.23 % (27330)Instruction limit reached!
% 76.64/12.23 % (27330)------------------------------
% 76.64/12.23 % (27330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.64/12.23 % (27330)Termination reason: Unknown
% 76.64/12.23 % (27330)Termination phase: Saturation
% 76.64/12.23
% 76.64/12.23 % (27330)Memory used [KB]: 7803
% 76.64/12.23 % (27330)Time elapsed: 0.246 s
% 76.64/12.23 % (27330)Instructions burned: 1005 (million)
% 76.64/12.23 % (27330)------------------------------
% 76.64/12.23 % (27330)------------------------------
% 76.64/12.24 % (27318)Instruction limit reached!
% 76.64/12.24 % (27318)------------------------------
% 76.64/12.24 % (27318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.64/12.24 % (27318)Termination reason: Unknown
% 76.64/12.24 % (27318)Termination phase: Saturation
% 76.64/12.24
% 76.64/12.24 % (27318)Memory used [KB]: 9338
% 76.64/12.24 % (27318)Time elapsed: 1.233 s
% 76.64/12.24 % (27318)Instructions burned: 4165 (million)
% 76.64/12.24 % (27318)------------------------------
% 76.64/12.24 % (27318)------------------------------
% 76.64/12.24 % (27334)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_26726 for (2893ds/13163Mi)
% 76.64/12.25 % (27335)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_26726 for (2893ds/5087Mi)
% 77.12/12.31 % (27335)Refutation not found, incomplete strategy
% 77.12/12.31 % (27335)------------------------------
% 77.12/12.31 % (27335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.12/12.31 % (27335)Termination reason: Refutation not found, incomplete strategy
% 77.12/12.31
% 77.12/12.31
% 77.12/12.31 % (27335)Memory used [KB]: 6908
% 77.12/12.31 % (27335)Time elapsed: 0.065 s
% 77.12/12.31 % (27335)Instructions burned: 257 (million)
% 77.12/12.31 % (27335)------------------------------
% 77.12/12.31 % (27335)------------------------------
% 77.12/12.32 % (27336)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_26726 for (2892ds/10380Mi)
% 77.59/12.41 % (27336)Refutation not found, incomplete strategy
% 77.59/12.41 % (27336)------------------------------
% 77.59/12.41 % (27336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.59/12.41 % (27336)Termination reason: Refutation not found, incomplete strategy
% 77.59/12.41
% 77.59/12.41
% 77.59/12.41 % (27336)Memory used [KB]: 6396
% 77.59/12.41 % (27336)Time elapsed: 0.092 s
% 77.59/12.41 % (27336)Instructions burned: 372 (million)
% 77.59/12.41 % (27336)------------------------------
% 77.59/12.41 % (27336)------------------------------
% 77.59/12.42 % (27337)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_26726 for (2891ds/4218Mi)
% 77.59/12.45 % (27337)Refutation not found, incomplete strategy
% 77.59/12.45 % (27337)------------------------------
% 77.59/12.45 % (27337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.59/12.45 % (27337)Termination reason: Refutation not found, incomplete strategy
% 77.59/12.45
% 77.59/12.45
% 77.59/12.45 % (27337)Memory used [KB]: 5884
% 77.59/12.45 % (27337)Time elapsed: 0.027 s
% 77.59/12.45 % (27337)Instructions burned: 114 (million)
% 77.59/12.45 % (27337)------------------------------
% 77.59/12.45 % (27337)------------------------------
% 77.59/12.46 % (27338)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_26726 for (2891ds/3971Mi)
% 78.54/12.68 % (27317)Instruction limit reached!
% 78.54/12.68 % (27317)------------------------------
% 78.54/12.68 % (27317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.54/12.68 % (27317)Termination reason: Unknown
% 78.54/12.68 % (27317)Termination phase: Saturation
% 78.54/12.68
% 78.54/12.68 % (27317)Memory used [KB]: 9210
% 78.54/12.68 % (27317)Time elapsed: 1.712 s
% 78.54/12.68 % (27317)Instructions burned: 7470 (million)
% 78.54/12.68 % (27317)------------------------------
% 78.54/12.68 % (27317)------------------------------
% 78.54/12.68 % (27333)Instruction limit reached!
% 78.54/12.68 % (27333)------------------------------
% 78.54/12.68 % (27333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.54/12.68 % (27333)Termination reason: Unknown
% 78.54/12.68 % (27333)Termination phase: Saturation
% 78.54/12.68
% 78.54/12.68 % (27333)Memory used [KB]: 8571
% 78.54/12.68 % (27333)Time elapsed: 0.664 s
% 78.54/12.68 % (27333)Instructions burned: 2570 (million)
% 78.54/12.68 % (27333)------------------------------
% 78.54/12.68 % (27333)------------------------------
% 78.54/12.69 % (27339)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_26726 for (2889ds/14014Mi)
% 78.54/12.69 % (27340)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_26726 for (2888ds/8517Mi)
% 79.59/12.70 % (27339)Refutation not found, incomplete strategy
% 79.59/12.70 % (27339)------------------------------
% 79.59/12.70 % (27339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.59/12.70 % (27339)Termination reason: Refutation not found, incomplete strategy
% 79.59/12.70
% 79.59/12.70
% 79.59/12.70 % (27339)Memory used [KB]: 5756
% 79.59/12.70 % (27339)Time elapsed: 0.015 s
% 79.59/12.70 % (27339)Instructions burned: 57 (million)
% 79.59/12.70 % (27339)------------------------------
% 79.59/12.70 % (27339)------------------------------
% 79.59/12.71 % (27340)Refutation not found, incomplete strategy
% 79.59/12.71 % (27340)------------------------------
% 79.59/12.71 % (27340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.59/12.71 % (27340)Termination reason: Refutation not found, incomplete strategy
% 79.59/12.71
% 79.59/12.71
% 79.59/12.71 % (27340)Memory used [KB]: 5756
% 79.59/12.71 % (27340)Time elapsed: 0.015 s
% 79.59/12.71 % (27340)Instructions burned: 56 (million)
% 79.59/12.71 % (27340)------------------------------
% 79.59/12.71 % (27340)------------------------------
% 79.59/12.71 % (27341)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_26726 for (2888ds/10148Mi)
% 79.59/12.72 % (27342)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_26726 for (2888ds/9078Mi)
% 79.59/12.73 % (27342)Refutation not found, incomplete strategy
% 79.59/12.73 % (27342)------------------------------
% 79.59/12.73 % (27342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.59/12.73 % (27342)Termination reason: Refutation not found, incomplete strategy
% 79.59/12.73
% 79.59/12.73
% 79.59/12.73 % (27342)Memory used [KB]: 5756
% 79.59/12.73 % (27342)Time elapsed: 0.015 s
% 79.59/12.73 % (27342)Instructions burned: 56 (million)
% 79.59/12.73 % (27342)------------------------------
% 79.59/12.73 % (27342)------------------------------
% 79.59/12.74 % (27343)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_26726 for (2888ds/16164Mi)
% 79.59/12.75 % (27343)Refutation not found, incomplete strategy
% 79.59/12.75 % (27343)------------------------------
% 79.59/12.75 % (27343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.59/12.75 % (27343)Termination reason: Refutation not found, incomplete strategy
% 79.59/12.75
% 79.59/12.75
% 79.59/12.75 % (27343)Memory used [KB]: 5756
% 79.59/12.75 % (27343)Time elapsed: 0.006 s
% 79.59/12.75 % (27343)Instructions burned: 22 (million)
% 79.59/12.75 % (27343)------------------------------
% 79.59/12.75 % (27343)------------------------------
% 79.59/12.76 % (27344)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_26726 for (2888ds/6102Mi)
% 85.22/13.44 % (27338)Instruction limit reached!
% 85.22/13.44 % (27338)------------------------------
% 85.22/13.44 % (27338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.22/13.44 % (27338)Termination reason: Unknown
% 85.22/13.44 % (27338)Termination phase: Saturation
% 85.22/13.44
% 85.22/13.44 % (27338)Memory used [KB]: 10234
% 85.22/13.44 % (27338)Time elapsed: 0.980 s
% 85.22/13.44 % (27338)Instructions burned: 3974 (million)
% 85.22/13.44 % (27338)------------------------------
% 85.22/13.44 % (27338)------------------------------
% 85.22/13.45 % (27345)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_26726 for (2881ds/10308Mi)
% 85.22/13.47 % (27345)Refutation not found, incomplete strategy
% 85.22/13.47 % (27345)------------------------------
% 85.22/13.47 % (27345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.22/13.47 % (27345)Termination reason: Refutation not found, incomplete strategy
% 85.22/13.47
% 85.22/13.47
% 85.22/13.47 % (27345)Memory used [KB]: 6012
% 85.22/13.47 % (27345)Time elapsed: 0.024 s
% 85.22/13.47 % (27345)Instructions burned: 93 (million)
% 85.22/13.47 % (27345)------------------------------
% 85.22/13.47 % (27345)------------------------------
% 85.22/13.48 % (27346)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_26726 for (2881ds/4041Mi)
% 85.22/13.49 % (27346)Refutation not found, incomplete strategy
% 85.22/13.49 % (27346)------------------------------
% 85.22/13.49 % (27346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.22/13.49 % (27346)Termination reason: Refutation not found, incomplete strategy
% 85.22/13.49
% 85.22/13.49
% 85.22/13.49 % (27346)Memory used [KB]: 5756
% 85.22/13.49 % (27346)Time elapsed: 0.015 s
% 85.22/13.49 % (27346)Instructions burned: 56 (million)
% 85.22/13.49 % (27346)------------------------------
% 85.22/13.49 % (27346)------------------------------
% 85.93/13.50 % (27347)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_26726 for (2880ds/6901Mi)
% 85.93/13.52 % (27347)Refutation not found, incomplete strategy
% 85.93/13.52 % (27347)------------------------------
% 85.93/13.52 % (27347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.93/13.52 % (27347)Termination reason: Refutation not found, incomplete strategy
% 85.93/13.52
% 85.93/13.52
% 85.93/13.52 % (27347)Memory used [KB]: 5756
% 85.93/13.52 % (27347)Time elapsed: 0.015 s
% 85.93/13.52 % (27347)Instructions burned: 58 (million)
% 85.93/13.52 % (27347)------------------------------
% 85.93/13.52 % (27347)------------------------------
% 85.93/13.53 % (27348)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on DTF2THF_26726 for (2880ds/5576Mi)
% 88.36/13.93 % (27327)Instruction limit reached!
% 88.36/13.93 % (27327)------------------------------
% 88.36/13.93 % (27327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.36/13.93 % (27327)Termination reason: Unknown
% 88.36/13.93 % (27327)Termination phase: Saturation
% 88.36/13.93
% 88.36/13.93 % (27327)Memory used [KB]: 13432
% 88.36/13.93 % (27327)Time elapsed: 2.365 s
% 88.36/13.93 % (27327)Instructions burned: 7804 (million)
% 88.36/13.93 % (27327)------------------------------
% 88.36/13.93 % (27327)------------------------------
% 88.36/13.94 % (27349)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on DTF2THF_26726 for (2876ds/2014Mi)
% 88.36/13.95 % (27322)First to succeed.
% 89.60/14.05 % (27322)Refutation found. Thanks to Tanya!
% 89.60/14.05 % SZS status Theorem for DTF2THF_26726
% 89.60/14.05 % SZS output start Proof for DTF2THF_26726
% 89.60/14.05 thf(type_def_5, type, mworld: $tType).
% 89.60/14.05 thf(func_def_0, type, mworld: $tType).
% 89.60/14.05 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 89.60/14.05 thf(func_def_2, type, mactual: mworld).
% 89.60/14.05 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 89.60/14.05 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 89.60/14.05 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 89.60/14.05 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 89.60/14.05 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 89.60/14.05 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 89.60/14.05 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 89.60/14.05 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 89.60/14.05 thf(func_def_12, type, v1: mworld > $o).
% 89.60/14.05 thf(func_def_13, type, v2: mworld > $o).
% 89.60/14.05 thf(func_def_14, type, v3: mworld > $o).
% 89.60/14.05 thf(func_def_15, type, v4: mworld > $o).
% 89.60/14.05 thf(func_def_16, type, v5: mworld > $o).
% 89.60/14.05 thf(func_def_17, type, v6: mworld > $o).
% 89.60/14.05 thf(func_def_18, type, v7: mworld > $o).
% 89.60/14.05 thf(func_def_19, type, v8: mworld > $o).
% 89.60/14.05 thf(func_def_20, type, v9: mworld > $o).
% 89.60/14.05 thf(func_def_21, type, v10: mworld > $o).
% 89.60/14.05 thf(func_def_22, type, v12: mworld > $o).
% 89.60/14.05 thf(func_def_23, type, v11: mworld > $o).
% 89.60/14.05 thf(func_def_24, type, v14: mworld > $o).
% 89.60/14.05 thf(func_def_25, type, v13: mworld > $o).
% 89.60/14.05 thf(func_def_26, type, v16: mworld > $o).
% 89.60/14.05 thf(func_def_27, type, v15: mworld > $o).
% 89.60/14.05 thf(func_def_28, type, v18: mworld > $o).
% 89.60/14.05 thf(func_def_29, type, v17: mworld > $o).
% 89.60/14.05 thf(func_def_30, type, v19: mworld > $o).
% 89.60/14.05 thf(func_def_31, type, v21: mworld > $o).
% 89.60/14.05 thf(func_def_32, type, v20: mworld > $o).
% 89.60/14.05 thf(func_def_33, type, v23: mworld > $o).
% 89.60/14.05 thf(func_def_34, type, v22: mworld > $o).
% 89.60/14.05 thf(func_def_35, type, v25: mworld > $o).
% 89.60/14.05 thf(func_def_36, type, v24: mworld > $o).
% 89.60/14.05 thf(func_def_37, type, v27: mworld > $o).
% 89.60/14.05 thf(func_def_38, type, v26: mworld > $o).
% 89.60/14.05 thf(func_def_39, type, v28: mworld > $o).
% 89.60/14.05 thf(func_def_54, type, ph1: !>[X0: $tType]:(X0)).
% 89.60/14.05 thf(func_def_55, type, sK2: mworld).
% 89.60/14.05 thf(func_def_56, type, sK3: mworld > mworld).
% 89.60/14.05 thf(func_def_57, type, sK4: mworld > mworld).
% 89.60/14.05 thf(func_def_58, type, sK5: mworld > mworld).
% 89.60/14.05 thf(func_def_59, type, sK6: mworld > mworld).
% 89.60/14.05 thf(func_def_60, type, sK7: mworld > mworld).
% 89.60/14.05 thf(func_def_61, type, sK8: mworld > mworld).
% 89.60/14.05 thf(func_def_62, type, sK9: mworld > mworld).
% 89.60/14.05 thf(func_def_63, type, sK10: mworld > mworld).
% 89.60/14.05 thf(func_def_64, type, sK11: mworld > mworld).
% 89.60/14.05 thf(func_def_65, type, sK12: mworld > mworld).
% 89.60/14.05 thf(func_def_66, type, sK13: mworld > mworld).
% 89.60/14.05 thf(func_def_67, type, sK14: mworld > mworld).
% 89.60/14.05 thf(func_def_68, type, sK15: mworld > mworld).
% 89.60/14.05 thf(func_def_69, type, sK16: mworld > mworld).
% 89.60/14.05 thf(func_def_70, type, sK17: mworld > mworld).
% 89.60/14.05 thf(func_def_71, type, sK18: mworld > mworld).
% 89.60/14.05 thf(func_def_72, type, sK19: mworld > mworld).
% 89.60/14.05 thf(func_def_73, type, sK20: mworld > mworld).
% 89.60/14.05 thf(func_def_74, type, sK21: mworld > mworld).
% 89.60/14.05 thf(func_def_75, type, sK22: mworld > mworld).
% 89.60/14.05 thf(func_def_76, type, sK23: mworld > mworld).
% 89.60/14.05 thf(func_def_77, type, sK24: mworld > mworld).
% 89.60/14.05 thf(func_def_78, type, sK25: mworld > mworld).
% 89.60/14.05 thf(func_def_79, type, sK26: mworld > mworld).
% 89.60/14.05 thf(func_def_80, type, sK27: mworld > mworld).
% 89.60/14.05 thf(f3742,plain,(
% 89.60/14.05 $false),
% 89.60/14.05 inference(avatar_sat_refutation,[status(thm)],[f2141,f2415,f2680,f2964,f2967,f2968,f2969,f3305,f3354,f3476,f3550,f3570,f3741])).
% 89.60/14.05 thf(f3741,plain,(
% 89.60/14.05 ~spl0_17 | ~spl0_22),
% 89.60/14.05 inference(avatar_contradiction_clause,[status(thm)],[f3740])).
% 89.60/14.05 thf(f3740,plain,(
% 89.60/14.05 $false | (~spl0_17 | ~spl0_22)),
% 89.60/14.05 inference(trivial_inequality_removal,[status(thm)],[f3739])).
% 89.60/14.05 thf(f3739,plain,(
% 89.60/14.05 ($false = $true) | (~spl0_17 | ~spl0_22)),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3738,f3612])).
% 89.60/14.05 thf(f3612,plain,(
% 89.60/14.05 ( ! [X26 : mworld] : (($false = (v3 @ X26))) ) | ~spl0_17),
% 89.60/14.05 inference(not_proxy_clausification,[status(thm)],[f3605])).
% 89.60/14.05 thf(f3605,plain,(
% 89.60/14.05 ( ! [X26 : mworld] : (((~ (v3 @ X26)) = $true)) ) | ~spl0_17),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3604])).
% 89.60/14.05 thf(f3604,plain,(
% 89.60/14.05 ( ! [X26 : mworld] : (($true = ($true => (~ (v3 @ X26))))) ) | ~spl0_17),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3603,f358])).
% 89.60/14.05 thf(f358,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ X1 @ X2) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f357])).
% 89.60/14.05 thf(f357,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (((!! @ mworld @ (mrel @ X1)) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f356])).
% 89.60/14.05 thf(f356,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: (!! @ mworld @ (mrel @ Y0))) @ X1))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f349])).
% 89.60/14.05 thf(f349,plain,(
% 89.60/14.05 ($true = (!! @ mworld @ (^[Y0 : mworld]: (!! @ mworld @ (mrel @ Y0)))))),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f211])).
% 89.60/14.05 thf(f211,plain,(
% 89.60/14.05 ((!! @ mworld @ (^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (mrel @ Y0 @ Y1))))) = $true)),
% 89.60/14.05 inference(cnf_transformation,[status(thm)],[f101])).
% 89.60/14.05 thf(f101,plain,(
% 89.60/14.05 ((!! @ mworld @ (^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (mrel @ Y0 @ Y1))))) = $true)),
% 89.60/14.05 inference(fool_elimination,[status(thm)],[f100])).
% 89.60/14.05 thf(f100,plain,(
% 89.60/14.05 ! [X0 : mworld,X1 : mworld] : (mrel @ X1 @ X0)),
% 89.60/14.05 inference(rectify,[status(thm)],[f9])).
% 89.60/14.05 thf(f9,axiom,(
% 89.60/14.05 ! [X4 : mworld,X2 : mworld] : (mrel @ X2 @ X4)),
% 89.60/14.05 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mrel_universal)).
% 89.60/14.05 thf(f3603,plain,(
% 89.60/14.05 ( ! [X26 : mworld,X25 : mworld] : (($true = ((mrel @ X25 @ X26) => (~ (v3 @ X26))))) ) | ~spl0_17),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3602])).
% 89.60/14.05 thf(f3602,plain,(
% 89.60/14.05 ( ! [X26 : mworld,X25 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X25 @ Y0) => (~ (v3 @ Y0)))) @ X26))) ) | ~spl0_17),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3601])).
% 89.60/14.05 thf(f3601,plain,(
% 89.60/14.05 ( ! [X25 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X25 @ Y0) => (~ (v3 @ Y0))))))) ) | ~spl0_17),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3600])).
% 89.60/14.05 thf(f3600,plain,(
% 89.60/14.05 ( ! [X25 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X25 @ Y0) => (~ (v3 @ Y0)))))) = $true)) ) | ~spl0_17),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3599,f358])).
% 89.60/14.05 thf(f3599,plain,(
% 89.60/14.05 ( ! [X24 : mworld,X25 : mworld] : ((((mrel @ X24 @ X25) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X25 @ Y0) => (~ (v3 @ Y0)))))) = $true)) ) | ~spl0_17),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3598])).
% 89.60/14.05 thf(f3598,plain,(
% 89.60/14.05 ( ! [X24 : mworld,X25 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))) @ X25) = $true)) ) | ~spl0_17),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2963])).
% 89.60/14.05 thf(f2963,plain,(
% 89.60/14.05 ( ! [X24 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))))) ) | ~spl0_17),
% 89.60/14.05 inference(avatar_component_clause,[status(thm)],[f2962])).
% 89.60/14.05 thf(f2962,definition,(
% 89.60/14.05 spl0_17 <=> ! [X24 : mworld] : ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))))),
% 89.60/14.05 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 89.60/14.05 thf(f3738,plain,(
% 89.60/14.05 ( ! [X10 : mworld] : (((v3 @ X10) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3737])).
% 89.60/14.05 thf(f3737,plain,(
% 89.60/14.05 ( ! [X10 : mworld] : ((($true => (v3 @ X10)) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3736,f358])).
% 89.60/14.05 thf(f3736,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X9 : mworld] : ((((mrel @ X9 @ X10) => (v3 @ X10)) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3735])).
% 89.60/14.05 thf(f3735,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (v3 @ Y0))) @ X10))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3734])).
% 89.60/14.05 thf(f3734,plain,(
% 89.60/14.05 ( ! [X9 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (v3 @ Y0)))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3733])).
% 89.60/14.05 thf(f3733,plain,(
% 89.60/14.05 ( ! [X9 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (v3 @ Y0))))))) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3732,f358])).
% 89.60/14.05 thf(f3732,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X9 : mworld] : ((((mrel @ X8 @ X9) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (v3 @ Y0))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3731])).
% 89.60/14.05 thf(f3731,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))) @ X9))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3730])).
% 89.60/14.05 thf(f3730,plain,(
% 89.60/14.05 ( ! [X8 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3729])).
% 89.60/14.05 thf(f3729,plain,(
% 89.60/14.05 ( ! [X8 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3728,f358])).
% 89.60/14.05 thf(f3728,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X7 : mworld] : (($true = ((mrel @ X7 @ X8) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3727])).
% 89.60/14.05 thf(f3727,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X7 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v3 @ Y2))))))))) @ X8))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3726])).
% 89.60/14.05 thf(f3726,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v3 @ Y2)))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3725])).
% 89.60/14.05 thf(f3725,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v3 @ Y2))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3724,f358])).
% 89.60/14.05 thf(f3724,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y2))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3723])).
% 89.60/14.05 thf(f3723,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y3)))))))))))) @ X7) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3722])).
% 89.60/14.05 thf(f3722,plain,(
% 89.60/14.05 ( ! [X6 : mworld] : (($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) => (v3 @ Y3))))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3721])).
% 89.60/14.05 thf(f3721,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y3)))))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3720,f358])).
% 89.60/14.05 thf(f3720,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y3)))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3719])).
% 89.60/14.05 thf(f3719,plain,(
% 89.60/14.05 ( ! [X6 : mworld,X5 : mworld] : (($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) => (v3 @ Y4))))))))))))))) @ X6))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3718])).
% 89.60/14.05 thf(f3718,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v3 @ Y4)))))))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3717])).
% 89.60/14.05 thf(f3717,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : ((($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) => (v3 @ Y4))))))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3716,f358])).
% 89.60/14.05 thf(f3716,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($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) => (v3 @ Y4))))))))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3715])).
% 89.60/14.05 thf(f3715,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v3 @ Y5)))))))))))))))))) @ X5))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3714])).
% 89.60/14.05 thf(f3714,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($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) => (v3 @ Y5))))))))))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3713])).
% 89.60/14.05 thf(f3713,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y5)))))))))))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3712,f358])).
% 89.60/14.05 thf(f3712,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($true = ((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v3 @ Y5)))))))))))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3711])).
% 89.60/14.05 thf(f3711,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($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) => (v3 @ Y6))))))))))))))))))))) @ X4))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3710])).
% 89.60/14.05 thf(f3710,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v3 @ Y6)))))))))))))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(trivial_inequality_removal,[status(thm)],[f3706])).
% 89.60/14.05 thf(f3706,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($false = $true) | ($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) => (v3 @ Y6)))))))))))))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f2754,f3704])).
% 89.60/14.05 thf(f3704,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($false = (v10 @ X5))) ) | ~spl0_22),
% 89.60/14.05 inference(not_proxy_clausification,[status(thm)],[f3703])).
% 89.60/14.05 thf(f3703,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (((~ (v10 @ X5)) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3702])).
% 89.60/14.05 thf(f3702,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = ($true => (~ (v10 @ X5))))) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3701,f358])).
% 89.60/14.05 thf(f3701,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : ((((mrel @ X4 @ X5) => (~ (v10 @ X5))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3700])).
% 89.60/14.05 thf(f3700,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (~ (v10 @ Y0)))) @ X5))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3699])).
% 89.60/14.05 thf(f3699,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (~ (v10 @ Y0))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3698])).
% 89.60/14.05 thf(f3698,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (~ (v10 @ Y0)))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3697,f358])).
% 89.60/14.05 thf(f3697,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($true = ((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (~ (v10 @ Y0)))))))) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3696])).
% 89.60/14.05 thf(f3696,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v10 @ Y1))))))) @ X4))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3695])).
% 89.60/14.05 thf(f3695,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v10 @ Y1)))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3694])).
% 89.60/14.05 thf(f3694,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v10 @ Y1))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3693,f358])).
% 89.60/14.05 thf(f3693,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X3 : mworld] : (($true = ((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v10 @ Y1))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3692])).
% 89.60/14.05 thf(f3692,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X3 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v10 @ Y2)))))))))) @ X3) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3691])).
% 89.60/14.05 thf(f3691,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v10 @ Y2))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3690])).
% 89.60/14.05 thf(f3690,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v10 @ Y2)))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3689,f358])).
% 89.60/14.05 thf(f3689,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v10 @ Y2)))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3688])).
% 89.60/14.05 thf(f3688,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y3))))))))))))) @ X2))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3687])).
% 89.60/14.05 thf(f3687,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y3)))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3686])).
% 89.60/14.05 thf(f3686,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : ((($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) => (~ (v10 @ Y3))))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3685,f358])).
% 89.60/14.05 thf(f3685,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ (sK15 @ 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) => (~ (v10 @ Y3))))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3682])).
% 89.60/14.05 thf(f3682,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK15 @ 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) => (~ (v10 @ Y4)))))))))))))))) @ X1))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3675])).
% 89.60/14.05 thf(f3675,plain,(
% 89.60/14.05 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK15 @ 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) => (~ (v10 @ Y4))))))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3674])).
% 89.60/14.05 thf(f3674,plain,(
% 89.60/14.05 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK15 @ 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) => (~ (v10 @ Y4))))))))))))))))) | $false) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3673])).
% 89.60/14.05 thf(f3673,plain,(
% 89.60/14.05 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK15 @ 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) => (~ (v10 @ Y4))))))))))))))))) | (~ $true)) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(superposition,[status(thm)],[f3670,f2336])).
% 89.60/14.05 thf(f2336,plain,(
% 89.60/14.05 ( ! [X13 : mworld] : (((v15 @ (sK15 @ X13)) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2335])).
% 89.60/14.05 thf(f2335,plain,(
% 89.60/14.05 ( ! [X13 : mworld] : ((((v15 @ (sK15 @ X13)) & $true) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2334,f358])).
% 89.60/14.05 thf(f2334,plain,(
% 89.60/14.05 ( ! [X13 : mworld] : ((((v15 @ (sK15 @ X13)) & (mrel @ X13 @ (sK15 @ X13))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2333])).
% 89.60/14.05 thf(f2333,plain,(
% 89.60/14.05 ( ! [X13 : mworld] : (($true = ((^[Y0 : mworld]: ((v15 @ Y0) & (mrel @ X13 @ Y0))) @ (sK15 @ X13)))) )),
% 89.60/14.05 inference(sigma_clausification,[status(thm)],[f2316])).
% 89.60/14.05 thf(f2316,plain,(
% 89.60/14.05 ( ! [X13 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((v15 @ Y0) & (mrel @ X13 @ Y0)))))) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2314])).
% 89.60/14.05 thf(f2314,plain,(
% 89.60/14.05 ( ! [X13 : mworld] : (($true = ((?? @ mworld @ (^[Y0 : mworld]: ((v15 @ Y0) & (mrel @ X13 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v15 @ Y0)) & (mrel @ X13 @ Y0))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2313])).
% 89.60/14.05 thf(f2313,plain,(
% 89.60/14.05 ( ! [X13 : mworld] : ((($true & ((?? @ mworld @ (^[Y0 : mworld]: ((v15 @ Y0) & (mrel @ X13 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v15 @ Y0)) & (mrel @ X13 @ Y0)))))) = $true)) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f2306,f2312])).
% 89.60/14.05 thf(f2312,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2306])).
% 89.60/14.05 thf(f2306,plain,(
% 89.60/14.05 ( ! [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)))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2305])).
% 89.60/14.05 thf(f2305,plain,(
% 89.60/14.05 ( ! [X13 : mworld] : ((($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) => ((!! @ 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)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2304,f358])).
% 89.60/14.05 thf(f2304,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ 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)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2303])).
% 89.60/14.05 thf(f2303,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ 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) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2102])).
% 89.60/14.05 thf(f2102,plain,(
% 89.60/14.05 ( ! [X12 : mworld] : (($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))))))))))) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2096])).
% 89.60/14.05 thf(f2096,plain,(
% 89.60/14.05 ( ! [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)))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2095])).
% 89.60/14.05 thf(f2095,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2094,f358])).
% 89.60/14.05 thf(f2094,plain,(
% 89.60/14.05 ( ! [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))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2093])).
% 89.60/14.05 thf(f2093,plain,(
% 89.60/14.05 ( ! [X11 : mworld,X12 : mworld] : (($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) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[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))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2088])).
% 89.60/14.05 thf(f2088,plain,(
% 89.60/14.05 ( ! [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))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2087])).
% 89.60/14.05 thf(f2087,plain,(
% 89.60/14.05 ( ! [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))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2086,f1785])).
% 89.60/14.05 thf(f1785,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (((?? @ mworld @ (mrel @ X1)) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1784])).
% 89.60/14.05 thf(f1784,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($true = ($true & (?? @ mworld @ (mrel @ X1))))) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f1778,f1781])).
% 89.60/14.05 thf(f1781,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ 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)))))) = $true)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f1778])).
% 89.60/14.05 thf(f1778,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($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))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1777])).
% 89.60/14.05 thf(f1777,plain,(
% 89.60/14.05 ( ! [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)))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1776,f358])).
% 89.60/14.05 thf(f1776,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($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) => ((!! @ 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)))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f1775])).
% 89.60/14.05 thf(f1775,plain,(
% 89.60/14.05 ( ! [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) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f1774])).
% 89.60/14.05 thf(f1774,plain,(
% 89.60/14.05 ($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)))))))),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1773])).
% 89.60/14.05 thf(f1773,plain,(
% 89.60/14.05 (((!! @ 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)),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f339,f1771])).
% 89.60/14.05 thf(f1771,plain,(
% 89.60/14.05 ((?? @ mworld @ (mrel @ mactual)) = $true)),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f339])).
% 89.60/14.05 thf(f339,plain,(
% 89.60/14.05 (((!! @ 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))) = $true)),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f338])).
% 89.60/14.05 thf(f338,plain,(
% 89.60/14.05 ($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]: (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))))),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f337])).
% 89.60/14.05 thf(f337,plain,(
% 89.60/14.05 (((!! @ 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))) = $true)),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f336])).
% 89.60/14.05 thf(f336,plain,(
% 89.60/14.05 ($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]: ($true & (mrel @ Y0 @ Y1)))))))) & (?? @ mworld @ (^[Y0 : mworld]: (mrel @ mactual @ Y0)))))),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f335])).
% 89.60/14.05 thf(f335,plain,(
% 89.60/14.05 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => ((!! @ mworld @ (^[Y26 : mworld]: ((mrel @ Y25 @ Y26) => (?? @ mworld @ (^[Y27 : mworld]: ($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))))) = $true)),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f251])).
% 89.60/14.05 thf(f251,plain,(
% 89.60/14.05 ($true = ((^[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))))))),
% 89.60/14.05 inference(definition_unfolding,[status(thm)],[f191,f226,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f227,f239,f188,f188,f188,f188,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f188,f188,f188,f188,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f188,f188,f188,f188,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f227,f188,f188,f213,f188,f188,f188,f188])).
% 89.60/14.05 thf(f213,plain,(
% 89.60/14.05 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 89.60/14.05 inference(cnf_transformation,[status(thm)],[f71])).
% 89.60/14.05 thf(f71,plain,(
% 89.60/14.05 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 89.60/14.05 inference(fool_elimination,[status(thm)],[f70])).
% 89.60/14.05 thf(f70,plain,(
% 89.60/14.05 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 89.60/14.05 inference(rectify,[status(thm)],[f2])).
% 89.60/14.05 thf(f2,axiom,(
% 89.60/14.05 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 89.60/14.05 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mnot_def)).
% 89.60/14.05 thf(f188,plain,(
% 89.60/14.05 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 89.60/14.05 inference(cnf_transformation,[status(thm)],[f157])).
% 89.60/14.05 thf(f157,plain,(
% 89.60/14.05 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 89.60/14.05 inference(fool_elimination,[status(thm)],[f156])).
% 89.60/14.05 thf(f156,plain,(
% 89.60/14.05 ((^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((mrel @ X1 @ X2) & (X0 @ X2)))) = mdia)),
% 89.60/14.05 inference(rectify,[status(thm)],[f8])).
% 89.60/14.05 thf(f8,axiom,(
% 89.60/14.05 ((^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((mrel @ X2 @ X4) & (X0 @ X4)))) = mdia)),
% 89.60/14.05 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mdia_def)).
% 89.60/14.05 thf(f239,plain,(
% 89.60/14.05 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 89.60/14.05 inference(cnf_transformation,[status(thm)],[f135])).
% 89.60/14.05 thf(f135,plain,(
% 89.60/14.05 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 89.60/14.05 inference(fool_elimination,[status(thm)],[f134])).
% 89.60/14.05 thf(f134,plain,(
% 89.60/14.05 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 89.60/14.05 inference(rectify,[status(thm)],[f7])).
% 89.60/14.05 thf(f7,axiom,(
% 89.60/14.05 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 89.60/14.05 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mbox_def)).
% 89.60/14.05 thf(f227,plain,(
% 89.60/14.05 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 89.60/14.05 inference(cnf_transformation,[status(thm)],[f77])).
% 89.60/14.05 thf(f77,plain,(
% 89.60/14.05 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 89.60/14.05 inference(fool_elimination,[status(thm)],[f76])).
% 89.60/14.05 thf(f76,plain,(
% 89.60/14.05 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))) = mand)),
% 89.60/14.05 inference(rectify,[status(thm)],[f3])).
% 89.60/14.05 thf(f3,axiom,(
% 89.60/14.05 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))) = mand)),
% 89.60/14.05 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mand_def)).
% 89.60/14.05 thf(f226,plain,(
% 89.60/14.05 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 89.60/14.05 inference(cnf_transformation,[status(thm)],[f158])).
% 89.60/14.05 thf(f158,plain,(
% 89.60/14.05 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 89.60/14.05 inference(fool_elimination,[status(thm)],[f1])).
% 89.60/14.05 thf(f1,axiom,(
% 89.60/14.05 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 89.60/14.05 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mlocal_def)).
% 89.60/14.05 thf(f191,plain,(
% 89.60/14.05 ((mlocal @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mdia @ (^[Y0 : mworld]: ($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))))) = $true)),
% 89.60/14.05 inference(cnf_transformation,[status(thm)],[f73])).
% 89.60/14.05 thf(f73,plain,(
% 89.60/14.05 ((mlocal @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mdia @ (^[Y0 : mworld]: ($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))))) = $true)),
% 89.60/14.05 inference(fool_elimination,[status(thm)],[f72])).
% 89.60/14.05 thf(f72,plain,(
% 89.60/14.05 (mlocal @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mdia @ (^[X0 : mworld] : ($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] : ($true)))))),
% 89.60/14.05 inference(rectify,[status(thm)],[f60])).
% 89.60/14.05 thf(f60,axiom,(
% 89.60/14.05 (mlocal @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mdia @ (^[X2 : mworld] : ($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] : ($true)))))),
% 89.60/14.05 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',alt1)).
% 89.60/14.05 thf(f2086,plain,(
% 89.60/14.05 ( ! [X11 : mworld] : (($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))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2085])).
% 89.60/14.05 thf(f2085,plain,(
% 89.60/14.05 ( ! [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)))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2084,f358])).
% 89.60/14.05 thf(f2084,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2083])).
% 89.60/14.05 thf(f2083,plain,(
% 89.60/14.05 ( ! [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) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2078])).
% 89.60/14.05 thf(f2078,plain,(
% 89.60/14.05 ( ! [X10 : mworld] : (($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)))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2077])).
% 89.60/14.05 thf(f2077,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2076,f1785])).
% 89.60/14.05 thf(f2076,plain,(
% 89.60/14.05 ( ! [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))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2075])).
% 89.60/14.05 thf(f2075,plain,(
% 89.60/14.05 ( ! [X10 : mworld] : ((($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)))))) & (?? @ mworld @ (mrel @ X10)))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2074,f358])).
% 89.60/14.05 thf(f2074,plain,(
% 89.60/14.05 ( ! [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)))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2073])).
% 89.60/14.05 thf(f2073,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X9 : mworld] : (($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) => ((!! @ mworld @ (^[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))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2066])).
% 89.60/14.05 thf(f2066,plain,(
% 89.60/14.05 ( ! [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)))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2065])).
% 89.60/14.05 thf(f2065,plain,(
% 89.60/14.05 ( ! [X9 : mworld] : (($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))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2064,f1785])).
% 89.60/14.05 thf(f2064,plain,(
% 89.60/14.05 ( ! [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))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2063])).
% 89.60/14.05 thf(f2063,plain,(
% 89.60/14.05 ( ! [X9 : mworld] : (($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)))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2062,f358])).
% 89.60/14.05 thf(f2062,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[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)))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2061])).
% 89.60/14.05 thf(f2061,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2055])).
% 89.60/14.05 thf(f2055,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2054])).
% 89.60/14.05 thf(f2054,plain,(
% 89.60/14.05 ( ! [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) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2053,f1785])).
% 89.60/14.05 thf(f2053,plain,(
% 89.60/14.05 ( ! [X8 : mworld] : (($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) => ((!! @ 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))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2052])).
% 89.60/14.05 thf(f2052,plain,(
% 89.60/14.05 ( ! [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)))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2051,f358])).
% 89.60/14.05 thf(f2051,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ mworld @ (^[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)))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2050])).
% 89.60/14.05 thf(f2050,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f1892])).
% 89.60/14.05 thf(f1892,plain,(
% 89.60/14.05 ( ! [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)))))) = $true)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f1878])).
% 89.60/14.05 thf(f1878,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($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)))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1877])).
% 89.60/14.05 thf(f1877,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1876,f358])).
% 89.60/14.05 thf(f1876,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ 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))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f1875])).
% 89.60/14.05 thf(f1875,plain,(
% 89.60/14.05 ( ! [X6 : mworld,X7 : mworld] : (($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) => ((!! @ 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))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f1863])).
% 89.60/14.05 thf(f1863,plain,(
% 89.60/14.05 ( ! [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))))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1862])).
% 89.60/14.05 thf(f1862,plain,(
% 89.60/14.05 ( ! [X6 : mworld] : (($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))))))))) & $true))) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f1855,f1860])).
% 89.60/14.05 thf(f1860,plain,(
% 89.60/14.05 ( ! [X6 : mworld] : (($true = ((?? @ mworld @ (^[Y0 : mworld]: ((v22 @ Y0) & (mrel @ X6 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v22 @ Y0)) & (mrel @ X6 @ Y0))))))) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f1855])).
% 89.60/14.05 thf(f1855,plain,(
% 89.60/14.05 ( ! [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)))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1854])).
% 89.60/14.05 thf(f1854,plain,(
% 89.60/14.05 ( ! [X6 : mworld] : (($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) => ((!! @ 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))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1853,f358])).
% 89.60/14.05 thf(f1853,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ 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))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f1852])).
% 89.60/14.05 thf(f1852,plain,(
% 89.60/14.05 ( ! [X6 : mworld,X5 : mworld] : (($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) => ((!! @ 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))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f1818])).
% 89.60/14.05 thf(f1818,plain,(
% 89.60/14.05 ( ! [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))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1817])).
% 89.60/14.05 thf(f1817,plain,(
% 89.60/14.05 ( ! [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))))))))) & $true))) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f1810,f1815])).
% 89.60/14.05 thf(f1815,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = ((?? @ mworld @ (^[Y0 : mworld]: ((v23 @ Y0) & (mrel @ X5 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v23 @ Y0)) & (mrel @ X5 @ Y0))))))) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f1810])).
% 89.60/14.05 thf(f1810,plain,(
% 89.60/14.05 ( ! [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)))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1809])).
% 89.60/14.05 thf(f1809,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : ((($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)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1808,f358])).
% 89.60/14.05 thf(f1808,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ 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))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f1807])).
% 89.60/14.05 thf(f1807,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($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) => ((!! @ 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))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f1806])).
% 89.60/14.05 thf(f1806,plain,(
% 89.60/14.05 ( ! [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))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1805])).
% 89.60/14.05 thf(f1805,plain,(
% 89.60/14.05 ( ! [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))))))))) & $true))) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f1802,f1803])).
% 89.60/14.05 thf(f1803,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v24 @ Y0) & (mrel @ X4 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v24 @ Y0)) & (mrel @ X4 @ Y0))))) = $true)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f1802])).
% 89.60/14.05 thf(f1802,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ 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)))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1801])).
% 89.60/14.05 thf(f1801,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($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) => ((!! @ 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))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1800,f358])).
% 89.60/14.05 thf(f1800,plain,(
% 89.60/14.05 ( ! [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))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f1799])).
% 89.60/14.05 thf(f1799,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($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) => ((!! @ 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))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f1798])).
% 89.60/14.05 thf(f1798,plain,(
% 89.60/14.05 ( ! [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))))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1797])).
% 89.60/14.05 thf(f1797,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($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))))))))) & $true))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1796,f1785])).
% 89.60/14.05 thf(f1796,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($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))))))))) & (?? @ mworld @ (mrel @ X3))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1795])).
% 89.60/14.05 thf(f1795,plain,(
% 89.60/14.05 ( ! [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)))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1794,f358])).
% 89.60/14.05 thf(f1794,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ 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)))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f1793])).
% 89.60/14.05 thf(f1793,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ 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) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f1792])).
% 89.60/14.05 thf(f1792,plain,(
% 89.60/14.05 ( ! [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)))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1791])).
% 89.60/14.05 thf(f1791,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($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))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1790,f1785])).
% 89.60/14.05 thf(f1790,plain,(
% 89.60/14.05 ( ! [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))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1789])).
% 89.60/14.05 thf(f1789,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($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)))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1788,f358])).
% 89.60/14.05 thf(f1788,plain,(
% 89.60/14.05 ( ! [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)))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f1787])).
% 89.60/14.05 thf(f1787,plain,(
% 89.60/14.05 ( ! [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))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f1781])).
% 89.60/14.05 thf(f3670,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y4))))))))))))))))) | (~ (v15 @ X6))))) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3669])).
% 89.60/14.05 thf(f3669,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y4))))))))))))))))) | (~ (v15 @ X6)))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3668,f358])).
% 89.60/14.05 thf(f3668,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y4))))))))))))))))) | (~ (v15 @ X6)))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3667])).
% 89.60/14.05 thf(f3667,plain,(
% 89.60/14.05 ( ! [X6 : mworld,X5 : mworld] : (($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) => (~ (v10 @ Y5))))))))))))))))) | (~ (v15 @ Y0))))) @ X6))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3666])).
% 89.60/14.05 thf(f3666,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v10 @ Y5))))))))))))))))) | (~ (v15 @ Y0)))))))) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3665])).
% 89.60/14.05 thf(f3665,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($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) => (~ (v10 @ Y5))))))))))))))))) | (~ (v15 @ Y0))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3664,f358])).
% 89.60/14.05 thf(f3664,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y5))))))))))))))))) | (~ (v15 @ Y0))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3663])).
% 89.60/14.05 thf(f3663,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($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) => (~ (v10 @ Y6))))))))))))))))) | (~ (v15 @ Y1)))))))) @ X5))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3662])).
% 89.60/14.05 thf(f3662,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v10 @ Y6))))))))))))))))) | (~ (v15 @ Y1))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3661])).
% 89.60/14.05 thf(f3661,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : ((($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) => (~ (v10 @ Y6))))))))))))))))) | (~ (v15 @ Y1)))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3660,f358])).
% 89.60/14.05 thf(f3660,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y6))))))))))))))))) | (~ (v15 @ Y1)))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3659])).
% 89.60/14.05 thf(f3659,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y7))))))))))))))))) | (~ (v15 @ Y2))))))))))) @ X4) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3658])).
% 89.60/14.05 thf(f3658,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($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) => (~ (v10 @ Y7))))))))))))))))) | (~ (v15 @ Y2)))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3657])).
% 89.60/14.05 thf(f3657,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y7))))))))))))))))) | (~ (v15 @ Y2))))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3656,f358])).
% 89.60/14.05 thf(f3656,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y7))))))))))))))))) | (~ (v15 @ Y2))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3655])).
% 89.60/14.05 thf(f3655,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X3 : mworld] : (($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) => (~ (v10 @ Y8))))))))))))))))) | (~ (v15 @ Y3)))))))))))))) @ X3))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3301])).
% 89.60/14.05 thf(f3301,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v10 @ Y8))))))))))))))))) | (~ (v15 @ Y3))))))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(avatar_component_clause,[status(thm)],[f3300])).
% 89.60/14.05 thf(f3300,definition,(
% 89.60/14.05 spl0_22 <=> ! [X2 : mworld] : ($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) => (~ (v10 @ Y8))))))))))))))))) | (~ (v15 @ Y3))))))))))))))))),
% 89.60/14.05 introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition])).
% 89.60/14.05 thf(f2754,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y6))))))))))))))))))))))) | ((v10 @ X3) = $true)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2753])).
% 89.60/14.05 thf(f2753,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y6)))))))))))))))))))))) | (v10 @ X3)) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2752])).
% 89.60/14.05 thf(f2752,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($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) => (v3 @ Y6)))))))))))))))))))))) | (v10 @ X3))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2751,f358])).
% 89.60/14.05 thf(f2751,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y6)))))))))))))))))))))) | (v10 @ X3))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2750])).
% 89.60/14.05 thf(f2750,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y7)))))))))))))))))))))) | (v10 @ Y0)))) @ X3) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2742])).
% 89.60/14.05 thf(f2742,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($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) => (v3 @ Y7)))))))))))))))))))))) | (v10 @ Y0))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2741])).
% 89.60/14.05 thf(f2741,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y7)))))))))))))))))))))) | (v10 @ Y0)))))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2740,f358])).
% 89.60/14.05 thf(f2740,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($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) => (v3 @ Y7)))))))))))))))))))))) | (v10 @ Y0)))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2739])).
% 89.60/14.05 thf(f2739,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v3 @ Y8)))))))))))))))))))))) | (v10 @ Y1))))))) @ X2))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2733])).
% 89.60/14.05 thf(f2733,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($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) => (v3 @ Y8)))))))))))))))))))))) | (v10 @ Y1)))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2732])).
% 89.60/14.05 thf(f2732,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y8)))))))))))))))))))))) | (v10 @ Y1))))))))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2730,f358])).
% 89.60/14.05 thf(f2730,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : (($true = ((mrel @ (sK18 @ 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) => (v3 @ Y8)))))))))))))))))))))) | (v10 @ Y1))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2728])).
% 89.60/14.05 thf(f2728,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK18 @ 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) => (v3 @ Y9)))))))))))))))))))))) | (v10 @ Y2)))))))))) @ X1))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2722])).
% 89.60/14.05 thf(f2722,plain,(
% 89.60/14.05 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK18 @ 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) => (v3 @ Y9)))))))))))))))))))))) | (v10 @ Y2))))))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2721])).
% 89.60/14.05 thf(f2721,plain,(
% 89.60/14.05 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK18 @ 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) => (v3 @ Y9)))))))))))))))))))))) | (v10 @ Y2))))))))))) | $false) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2717])).
% 89.60/14.05 thf(f2717,plain,(
% 89.60/14.05 ( ! [X0 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK18 @ 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) => (v3 @ Y9)))))))))))))))))))))) | (v10 @ Y2))))))))))) | (~ $true)))) )),
% 89.60/14.05 inference(superposition,[status(thm)],[f2234,f2657])).
% 89.60/14.05 thf(f2657,plain,(
% 89.60/14.05 ( ! [X15 : mworld] : (($true = (v13 @ (sK18 @ X15)))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2656])).
% 89.60/14.05 thf(f2656,plain,(
% 89.60/14.05 ( ! [X15 : mworld] : (($true = ((v13 @ (sK18 @ X15)) & $true))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2646,f358])).
% 89.60/14.05 thf(f2646,plain,(
% 89.60/14.05 ( ! [X15 : mworld] : (($true = ((v13 @ (sK18 @ X15)) & (mrel @ X15 @ (sK18 @ X15))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2645])).
% 89.60/14.05 thf(f2645,plain,(
% 89.60/14.05 ( ! [X15 : mworld] : ((((^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0))) @ (sK18 @ X15)) = $true)) )),
% 89.60/14.05 inference(sigma_clausification,[status(thm)],[f2644])).
% 89.60/14.05 thf(f2644,plain,(
% 89.60/14.05 ( ! [X15 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0)))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2643])).
% 89.60/14.05 thf(f2643,plain,(
% 89.60/14.05 ( ! [X15 : mworld] : (($true = ((?? @ mworld @ (^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0)))) & $true))) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f2640,f2641])).
% 89.60/14.05 thf(f2641,plain,(
% 89.60/14.05 ( ! [X15 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((~ (v13 @ Y0)) & (mrel @ X15 @ Y0)))))) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2640])).
% 89.60/14.05 thf(f2640,plain,(
% 89.60/14.05 ( ! [X15 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v13 @ Y0)) & (mrel @ X15 @ Y0))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2639])).
% 89.60/14.05 thf(f2639,plain,(
% 89.60/14.05 ( ! [X15 : mworld] : (($true = ($true & ((?? @ mworld @ (^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v13 @ Y0)) & (mrel @ X15 @ Y0)))))))) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f2636,f2638])).
% 89.60/14.05 thf(f2638,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2636])).
% 89.60/14.05 thf(f2636,plain,(
% 89.60/14.05 ( ! [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)))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2635])).
% 89.60/14.05 thf(f2635,plain,(
% 89.60/14.05 ( ! [X15 : mworld] : ((($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))))))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2634,f358])).
% 89.60/14.05 thf(f2634,plain,(
% 89.60/14.05 ( ! [X14 : mworld,X15 : mworld] : (($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))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2633])).
% 89.60/14.05 thf(f2633,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2541])).
% 89.60/14.05 thf(f2541,plain,(
% 89.60/14.05 ( ! [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))))))))) = $true)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2533])).
% 89.60/14.05 thf(f2533,plain,(
% 89.60/14.05 ( ! [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)))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2532])).
% 89.60/14.05 thf(f2532,plain,(
% 89.60/14.05 ( ! [X14 : mworld] : ((($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))))))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2531,f358])).
% 89.60/14.05 thf(f2531,plain,(
% 89.60/14.05 ( ! [X14 : mworld,X13 : mworld] : (($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))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2530])).
% 89.60/14.05 thf(f2530,plain,(
% 89.60/14.05 ( ! [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) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2312])).
% 89.60/14.05 thf(f2234,plain,(
% 89.60/14.05 ( ! [X10 : mworld] : (($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) => (v3 @ Y9)))))))))))))))))))))) | (v10 @ Y2))))))))))) | (~ (v13 @ X10))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2233])).
% 89.60/14.05 thf(f2233,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y9)))))))))))))))))))))) | (v10 @ Y2))))))))))) | (~ (v13 @ X10)))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2232,f358])).
% 89.60/14.05 thf(f2232,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X9 : mworld] : (($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) => (v3 @ Y9)))))))))))))))))))))) | (v10 @ Y2))))))))))) | (~ (v13 @ X10)))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2231])).
% 89.60/14.05 thf(f2231,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y10)))))))))))))))))))))) | (v10 @ Y3))))))))))) | (~ (v13 @ Y0))))) @ X10) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2230])).
% 89.60/14.05 thf(f2230,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y10)))))))))))))))))))))) | (v10 @ Y3))))))))))) | (~ (v13 @ Y0)))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2229])).
% 89.60/14.05 thf(f2229,plain,(
% 89.60/14.05 ( ! [X9 : mworld] : ((($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) => (v3 @ Y10)))))))))))))))))))))) | (v10 @ Y3))))))))))) | (~ (v13 @ Y0))))))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2228,f358])).
% 89.60/14.05 thf(f2228,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y10)))))))))))))))))))))) | (v10 @ Y3))))))))))) | (~ (v13 @ Y0))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2227])).
% 89.60/14.05 thf(f2227,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X9 : mworld] : (($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) => (v3 @ Y11)))))))))))))))))))))) | (v10 @ Y4))))))))))) | (~ (v13 @ Y1)))))))) @ X9))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2226])).
% 89.60/14.05 thf(f2226,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y11)))))))))))))))))))))) | (v10 @ Y4))))))))))) | (~ (v13 @ Y1))))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2225])).
% 89.60/14.05 thf(f2225,plain,(
% 89.60/14.05 ( ! [X8 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v3 @ Y11)))))))))))))))))))))) | (v10 @ Y4))))))))))) | (~ (v13 @ Y1)))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2224,f358])).
% 89.60/14.05 thf(f2224,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X7 : mworld] : (($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) => (v3 @ Y11)))))))))))))))))))))) | (v10 @ Y4))))))))))) | (~ (v13 @ Y1)))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2223])).
% 89.60/14.05 thf(f2223,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y12)))))))))))))))))))))) | (v10 @ Y5))))))))))) | (~ (v13 @ Y2))))))))))) @ X8) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2222])).
% 89.60/14.05 thf(f2222,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($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) => (v3 @ Y12)))))))))))))))))))))) | (v10 @ Y5))))))))))) | (~ (v13 @ Y2)))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2221])).
% 89.60/14.05 thf(f2221,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y12)))))))))))))))))))))) | (v10 @ Y5))))))))))) | (~ (v13 @ Y2))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2220,f358])).
% 89.60/14.05 thf(f2220,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y12)))))))))))))))))))))) | (v10 @ Y5))))))))))) | (~ (v13 @ Y2))))))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2219])).
% 89.60/14.05 thf(f2219,plain,(
% 89.60/14.05 ( ! [X6 : mworld,X7 : mworld] : (($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) => (v3 @ Y13)))))))))))))))))))))) | (v10 @ Y6))))))))))) | (~ (v13 @ Y3)))))))))))))) @ X7))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2218])).
% 89.60/14.05 thf(f2218,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y13)))))))))))))))))))))) | (v10 @ Y6))))))))))) | (~ (v13 @ Y3))))))))))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2217])).
% 89.60/14.05 thf(f2217,plain,(
% 89.60/14.05 ( ! [X6 : mworld] : (($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) => (v3 @ Y13)))))))))))))))))))))) | (v10 @ Y6))))))))))) | (~ (v13 @ Y3)))))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2216,f358])).
% 89.60/14.05 thf(f2216,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y13)))))))))))))))))))))) | (v10 @ Y6))))))))))) | (~ (v13 @ Y3)))))))))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2215])).
% 89.60/14.05 thf(f2215,plain,(
% 89.60/14.05 ( ! [X6 : mworld,X5 : mworld] : (($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) => (v3 @ Y14)))))))))))))))))))))) | (v10 @ Y7))))))))))) | (~ (v13 @ Y4))))))))))))))))) @ X6))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2213])).
% 89.60/14.05 thf(f2213,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y14)))))))))))))))))))))) | (v10 @ Y7))))))))))) | (~ (v13 @ Y4)))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2212])).
% 89.60/14.05 thf(f2212,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v3 @ Y14)))))))))))))))))))))) | (v10 @ Y7))))))))))) | (~ (v13 @ Y4))))))))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2211,f358])).
% 89.60/14.05 thf(f2211,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($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) => (v3 @ Y14)))))))))))))))))))))) | (v10 @ Y7))))))))))) | (~ (v13 @ Y4))))))))))))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2210])).
% 89.60/14.05 thf(f2210,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v3 @ Y15)))))))))))))))))))))) | (v10 @ Y8))))))))))) | (~ (v13 @ Y5)))))))))))))))))))) @ X5))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2205])).
% 89.60/14.05 thf(f2205,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($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) => (v3 @ Y15)))))))))))))))))))))) | (v10 @ Y8))))))))))) | (~ (v13 @ Y5))))))))))))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2204])).
% 89.60/14.05 thf(f2204,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y15)))))))))))))))))))))) | (v10 @ Y8))))))))))) | (~ (v13 @ Y5)))))))))))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2203,f358])).
% 89.60/14.05 thf(f2203,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y15)))))))))))))))))))))) | (v10 @ Y8))))))))))) | (~ (v13 @ Y5)))))))))))))))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2202])).
% 89.60/14.05 thf(f2202,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y16)))))))))))))))))))))) | (v10 @ Y9))))))))))) | (~ (v13 @ Y6))))))))))))))))))))))) @ X4) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2197])).
% 89.60/14.05 thf(f2197,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($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) => (v3 @ Y16)))))))))))))))))))))) | (v10 @ Y9))))))))))) | (~ (v13 @ Y6)))))))))))))))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2196])).
% 89.60/14.05 thf(f2196,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y16)))))))))))))))))))))) | (v10 @ Y9))))))))))) | (~ (v13 @ Y6))))))))))))))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2195,f358])).
% 89.60/14.05 thf(f2195,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y16)))))))))))))))))))))) | (v10 @ Y9))))))))))) | (~ (v13 @ Y6))))))))))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2194])).
% 89.60/14.05 thf(f2194,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y17)))))))))))))))))))))) | (v10 @ Y10))))))))))) | (~ (v13 @ Y7)))))))))))))))))))))))))) @ X3) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2189])).
% 89.60/14.05 thf(f2189,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($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) => (v3 @ Y17)))))))))))))))))))))) | (v10 @ Y10))))))))))) | (~ (v13 @ Y7))))))))))))))))))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2188])).
% 89.60/14.05 thf(f2188,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y17)))))))))))))))))))))) | (v10 @ Y10))))))))))) | (~ (v13 @ Y7)))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2187,f358])).
% 89.60/14.05 thf(f2187,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y17)))))))))))))))))))))) | (v10 @ Y10))))))))))) | (~ (v13 @ Y7)))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2186])).
% 89.60/14.05 thf(f2186,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y18)))))))))))))))))))))) | (v10 @ Y11))))))))))) | (~ (v13 @ Y8))))))))))))))))))))))))))))) @ X2) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2181])).
% 89.60/14.05 thf(f2181,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($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) => (v3 @ Y18)))))))))))))))))))))) | (v10 @ Y11))))))))))) | (~ (v13 @ Y8)))))))))))))))))))))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2180])).
% 89.60/14.05 thf(f2180,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y18)))))))))))))))))))))) | (v10 @ Y11))))))))))) | (~ (v13 @ Y8))))))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2178,f358])).
% 89.60/14.05 thf(f2178,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v3 @ Y18)))))))))))))))))))))) | (v10 @ Y11))))))))))) | (~ (v13 @ Y8))))))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2176])).
% 89.60/14.05 thf(f2176,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : (($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) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v3 @ Y19)))))))))))))))))))))) | (v10 @ Y12))))))))))) | (~ (v13 @ Y9)))))))))))))))))))))))))))))))) @ X1))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f1975])).
% 89.60/14.05 thf(f1975,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v3 @ Y19)))))))))))))))))))))) | (v10 @ Y12))))))))))) | (~ (v13 @ Y9))))))))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1973])).
% 89.60/14.05 thf(f1973,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v3 @ Y19)))))))))))))))))))))) | (v10 @ Y12))))))))))) | (~ (v13 @ Y9))))))))))))))))))))))))))))))))) | $false) = $true)) )),
% 89.60/14.05 inference(superposition,[status(thm)],[f989,f1964])).
% 89.60/14.05 thf(f1964,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (((v23 @ (sK9 @ X5)) = $false)) )),
% 89.60/14.05 inference(not_proxy_clausification,[status(thm)],[f1953])).
% 89.60/14.05 thf(f1953,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = (~ (v23 @ (sK9 @ X5))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1952])).
% 89.60/14.05 thf(f1952,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : ((((~ (v23 @ (sK9 @ X5))) & $true) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1951,f358])).
% 89.60/14.05 thf(f1951,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : ((((~ (v23 @ (sK9 @ X5))) & (mrel @ X5 @ (sK9 @ X5))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f1950])).
% 89.60/14.05 thf(f1950,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = ((^[Y0 : mworld]: ((~ (v23 @ Y0)) & (mrel @ X5 @ Y0))) @ (sK9 @ X5)))) )),
% 89.60/14.05 inference(sigma_clausification,[status(thm)],[f1938])).
% 89.60/14.05 thf(f1938,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((~ (v23 @ Y0)) & (mrel @ X5 @ Y0)))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1937])).
% 89.60/14.05 thf(f1937,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = ($true & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v23 @ Y0)) & (mrel @ X5 @ Y0))))))) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f1815,f1936])).
% 89.60/14.05 thf(f1936,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((v23 @ Y0) & (mrel @ X5 @ Y0)))))) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f1815])).
% 89.60/14.05 thf(f989,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y19)))))))))))))))))))))) | (v10 @ Y12))))))))))) | (~ (v13 @ Y9))))))))))))))))))))))))))))))))) | (v23 @ X6)) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f988])).
% 89.60/14.05 thf(f988,plain,(
% 89.60/14.05 ( ! [X6 : mworld] : (($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) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v3 @ Y19)))))))))))))))))))))) | (v10 @ Y12))))))))))) | (~ (v13 @ Y9))))))))))))))))))))))))))))))))) | (v23 @ X6))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f987,f358])).
% 89.60/14.05 thf(f987,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v3 @ Y19)))))))))))))))))))))) | (v10 @ Y12))))))))))) | (~ (v13 @ Y9))))))))))))))))))))))))))))))))) | (v23 @ X6))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f986])).
% 89.60/14.05 thf(f986,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y20)))))))))))))))))))))) | (v10 @ Y13))))))))))) | (~ (v13 @ Y10))))))))))))))))))))))))))))))))) | (v23 @ Y0)))) @ X6) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f985])).
% 89.60/14.05 thf(f985,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y20)))))))))))))))))))))) | (v10 @ Y13))))))))))) | (~ (v13 @ Y10))))))))))))))))))))))))))))))))) | (v23 @ Y0))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f984])).
% 89.60/14.05 thf(f984,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($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) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ 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) => (v3 @ Y20)))))))))))))))))))))) | (v10 @ Y13))))))))))) | (~ (v13 @ Y10))))))))))))))))))))))))))))))))) | (v23 @ Y0)))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f983,f358])).
% 89.60/14.05 thf(f983,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (v3 @ Y20)))))))))))))))))))))) | (v10 @ Y13))))))))))) | (~ (v13 @ Y10))))))))))))))))))))))))))))))))) | (v23 @ Y0)))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f982])).
% 89.60/14.05 thf(f982,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($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) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v3 @ Y21)))))))))))))))))))))) | (v10 @ Y14))))))))))) | (~ (v13 @ Y11))))))))))))))))))))))))))))))))) | (v23 @ Y1))))))) @ X5))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f981])).
% 89.60/14.05 thf(f981,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v3 @ Y21)))))))))))))))))))))) | (v10 @ Y14))))))))))) | (~ (v13 @ Y11))))))))))))))))))))))))))))))))) | (v23 @ Y1)))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f980])).
% 89.60/14.05 thf(f980,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($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) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v3 @ Y21)))))))))))))))))))))) | (v10 @ Y14))))))))))) | (~ (v13 @ Y11))))))))))))))))))))))))))))))))) | (v23 @ Y1))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f979,f358])).
% 89.60/14.05 thf(f979,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y21)))))))))))))))))))))) | (v10 @ Y14))))))))))) | (~ (v13 @ Y11))))))))))))))))))))))))))))))))) | (v23 @ Y1))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f978])).
% 89.60/14.05 thf(f978,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($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) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (v3 @ Y22)))))))))))))))))))))) | (v10 @ Y15))))))))))) | (~ (v13 @ Y12))))))))))))))))))))))))))))))))) | (v23 @ Y2)))))))))) @ X4))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f977])).
% 89.60/14.05 thf(f977,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (v3 @ Y22)))))))))))))))))))))) | (v10 @ Y15))))))))))) | (~ (v13 @ Y12))))))))))))))))))))))))))))))))) | (v23 @ Y2))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f976])).
% 89.60/14.05 thf(f976,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($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) => (v3 @ Y22)))))))))))))))))))))) | (v10 @ Y15))))))))))) | (~ (v13 @ Y12))))))))))))))))))))))))))))))))) | (v23 @ Y2)))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f975,f358])).
% 89.60/14.05 thf(f975,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y22)))))))))))))))))))))) | (v10 @ Y15))))))))))) | (~ (v13 @ Y12))))))))))))))))))))))))))))))))) | (v23 @ Y2)))))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f974])).
% 89.60/14.05 thf(f974,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X3 : mworld] : (($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) => (v3 @ Y23)))))))))))))))))))))) | (v10 @ Y16))))))))))) | (~ (v13 @ Y13))))))))))))))))))))))))))))))))) | (v23 @ Y3))))))))))))) @ X3))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f973])).
% 89.60/14.05 thf(f973,plain,(
% 89.60/14.05 ( ! [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) => (v3 @ Y23)))))))))))))))))))))) | (v10 @ Y16))))))))))) | (~ (v13 @ Y13))))))))))))))))))))))))))))))))) | (v23 @ Y3)))))))))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f972])).
% 89.60/14.05 thf(f972,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (v3 @ Y23)))))))))))))))))))))) | (v10 @ Y16))))))))))) | (~ (v13 @ Y13))))))))))))))))))))))))))))))))) | (v23 @ Y3))))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f971,f358])).
% 89.60/14.05 thf(f971,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($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) => (v3 @ Y23)))))))))))))))))))))) | (v10 @ Y16))))))))))) | (~ (v13 @ Y13))))))))))))))))))))))))))))))))) | (v23 @ Y3))))))))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f970])).
% 89.60/14.05 thf(f970,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (v3 @ Y24)))))))))))))))))))))) | (v10 @ Y17))))))))))) | (~ (v13 @ Y14))))))))))))))))))))))))))))))))) | (v23 @ Y4)))))))))))))))) @ X2) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f969])).
% 89.60/14.05 thf(f969,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (v3 @ Y24)))))))))))))))))))))) | (v10 @ Y17))))))))))) | (~ (v13 @ Y14))))))))))))))))))))))))))))))))) | (v23 @ Y4))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f968])).
% 89.60/14.05 thf(f968,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : ((($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) => (v3 @ Y24)))))))))))))))))))))) | (v10 @ Y17))))))))))) | (~ (v13 @ Y14))))))))))))))))))))))))))))))))) | (v23 @ Y4)))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f967,f358])).
% 89.60/14.05 thf(f967,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($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) => (!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (v3 @ Y24)))))))))))))))))))))) | (v10 @ Y17))))))))))) | (~ (v13 @ Y14))))))))))))))))))))))))))))))))) | (v23 @ Y4)))))))))))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f966])).
% 89.60/14.05 thf(f966,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => (v3 @ Y25)))))))))))))))))))))) | (v10 @ Y18))))))))))) | (~ (v13 @ Y15))))))))))))))))))))))))))))))))) | (v23 @ Y5))))))))))))))))))) @ X1))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f344])).
% 89.60/14.05 thf(f344,plain,(
% 89.60/14.05 ((!! @ 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) => (v3 @ Y25)))))))))))))))))))))) | (v10 @ Y18))))))))))) | (~ (v13 @ Y15))))))))))))))))))))))))))))))))) | (v23 @ Y5)))))))))))))))))))) = $true)),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f294])).
% 89.60/14.05 thf(f294,plain,(
% 89.60/14.05 (((^[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 > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v23 @ ((^[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))))) @ v13) @ ((^[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]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v3)))))))))))))))))))))))))))))) = $true)),
% 89.60/14.05 inference(definition_unfolding,[status(thm)],[f242,f226,f239,f239,f239,f239,f239,f239,f201,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f201,f213,f239,f239,f239,f201,f239,f239,f239,f239,f239,f239,f239])).
% 89.60/14.05 thf(f201,plain,(
% 89.60/14.05 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 89.60/14.05 inference(cnf_transformation,[status(thm)],[f117])).
% 89.60/14.05 thf(f117,plain,(
% 89.60/14.05 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 89.60/14.05 inference(fool_elimination,[status(thm)],[f116])).
% 89.60/14.05 thf(f116,plain,(
% 89.60/14.05 (mor = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) | (X1 @ X2))))),
% 89.60/14.05 inference(rectify,[status(thm)],[f4])).
% 89.60/14.05 thf(f4,axiom,(
% 89.60/14.05 (mor = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) | (X3 @ X2))))),
% 89.60/14.05 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mor_def)).
% 89.60/14.05 thf(f242,plain,(
% 89.60/14.05 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v23 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v13) @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v3)))))))))))))))))))))))))))))) = $true)),
% 89.60/14.05 inference(cnf_transformation,[status(thm)],[f91])).
% 89.60/14.05 thf(f91,plain,(
% 89.60/14.05 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v23 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v13) @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v3)))))))))))))))))))))))))))))) = $true)),
% 89.60/14.05 inference(fool_elimination,[status(thm)],[f90])).
% 89.60/14.05 thf(f90,plain,(
% 89.60/14.05 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v23 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v13) @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v3))))))))))))))))))))))))))))))),
% 89.60/14.05 inference(rectify,[status(thm)],[f42])).
% 89.60/14.05 thf(f42,axiom,(
% 89.60/14.05 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v23 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v13) @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v3))))))))))))))))))))))))))))))),
% 89.60/14.05 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod33)).
% 89.60/14.05 thf(f3570,plain,(
% 89.60/14.05 ~spl0_16),
% 89.60/14.05 inference(avatar_contradiction_clause,[status(thm)],[f3569])).
% 89.60/14.05 thf(f3569,plain,(
% 89.60/14.05 $false | ~spl0_16),
% 89.60/14.05 inference(trivial_inequality_removal,[status(thm)],[f3565])).
% 89.60/14.05 thf(f3565,plain,(
% 89.60/14.05 ($false = $true) | ~spl0_16),
% 89.60/14.05 inference(superposition,[status(thm)],[f2960,f2929])).
% 89.60/14.05 thf(f2929,plain,(
% 89.60/14.05 ( ! [X22 : mworld] : (((v6 @ (sK25 @ X22)) = $false)) )),
% 89.60/14.05 inference(not_proxy_clausification,[status(thm)],[f2922])).
% 89.60/14.05 thf(f2922,plain,(
% 89.60/14.05 ( ! [X22 : mworld] : (($true = (~ (v6 @ (sK25 @ X22))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2921])).
% 89.60/14.05 thf(f2921,plain,(
% 89.60/14.05 ( ! [X22 : mworld] : (($true = ((~ (v6 @ (sK25 @ X22))) & $true))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2920,f358])).
% 89.60/14.05 thf(f2920,plain,(
% 89.60/14.05 ( ! [X22 : mworld] : ((((~ (v6 @ (sK25 @ X22))) & (mrel @ X22 @ (sK25 @ X22))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2919])).
% 89.60/14.05 thf(f2919,plain,(
% 89.60/14.05 ( ! [X22 : mworld] : (($true = ((^[Y0 : mworld]: ((~ (v6 @ Y0)) & (mrel @ X22 @ Y0))) @ (sK25 @ X22)))) )),
% 89.60/14.05 inference(sigma_clausification,[status(thm)],[f2898])).
% 89.60/14.05 thf(f2898,plain,(
% 89.60/14.05 ( ! [X22 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((~ (v6 @ Y0)) & (mrel @ X22 @ Y0)))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2897])).
% 89.60/14.05 thf(f2897,plain,(
% 89.60/14.05 ( ! [X22 : mworld] : ((($true & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v6 @ Y0)) & (mrel @ X22 @ Y0))))) = $true)) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f2891,f2896])).
% 89.60/14.05 thf(f2896,plain,(
% 89.60/14.05 ( ! [X22 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((v6 @ Y0) & (mrel @ X22 @ Y0)))) = $true)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2891])).
% 89.60/14.05 thf(f2891,plain,(
% 89.60/14.05 ( ! [X22 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v6 @ Y0) & (mrel @ X22 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v6 @ Y0)) & (mrel @ X22 @ Y0))))) = $true)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2886])).
% 89.60/14.05 thf(f2886,plain,(
% 89.60/14.05 ( ! [X22 : mworld] : (($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)))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2885])).
% 89.60/14.05 thf(f2885,plain,(
% 89.60/14.05 ( ! [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))))))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2884,f358])).
% 89.60/14.05 thf(f2884,plain,(
% 89.60/14.05 ( ! [X21 : mworld,X22 : mworld] : (($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))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2883])).
% 89.60/14.05 thf(f2883,plain,(
% 89.60/14.05 ( ! [X21 : mworld,X22 : mworld] : (($true = ((^[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))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2840])).
% 89.60/14.05 thf(f2840,plain,(
% 89.60/14.05 ( ! [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))))))))) = $true)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2834])).
% 89.60/14.05 thf(f2834,plain,(
% 89.60/14.05 ( ! [X21 : mworld] : (($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)))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2833])).
% 89.60/14.05 thf(f2833,plain,(
% 89.60/14.05 ( ! [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))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2832,f358])).
% 89.60/14.05 thf(f2832,plain,(
% 89.60/14.05 ( ! [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))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2831])).
% 89.60/14.05 thf(f2831,plain,(
% 89.60/14.05 ( ! [X21 : mworld,X20 : mworld] : (($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))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2826])).
% 89.60/14.05 thf(f2826,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2825])).
% 89.60/14.05 thf(f2825,plain,(
% 89.60/14.05 ( ! [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) = $true)) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f2821,f2823])).
% 89.60/14.05 thf(f2823,plain,(
% 89.60/14.05 ( ! [X20 : mworld] : (($true = ((?? @ mworld @ (^[Y0 : mworld]: ((v8 @ Y0) & (mrel @ X20 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v8 @ Y0)) & (mrel @ X20 @ Y0))))))) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2821])).
% 89.60/14.05 thf(f2821,plain,(
% 89.60/14.05 ( ! [X20 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (?? @ mworld @ (mrel @ Y6))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v5 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v5 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v6 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v6 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v7 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v7 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v8 @ Y0) & (mrel @ X20 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v8 @ Y0)) & (mrel @ X20 @ Y0)))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2820])).
% 89.60/14.05 thf(f2820,plain,(
% 89.60/14.05 ( ! [X20 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (?? @ mworld @ (mrel @ Y6))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v5 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v5 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v6 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v6 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v7 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v7 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v8 @ Y0) & (mrel @ X20 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v8 @ Y0)) & (mrel @ X20 @ Y0))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2819,f358])).
% 89.60/14.05 thf(f2819,plain,(
% 89.60/14.05 ( ! [X19 : mworld,X20 : mworld] : (($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))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2818])).
% 89.60/14.05 thf(f2818,plain,(
% 89.60/14.05 ( ! [X19 : mworld,X20 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X19 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (?? @ mworld @ (mrel @ Y7))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v5 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v5 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v6 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v6 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v7 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v7 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v8 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v8 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X20))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2813])).
% 89.60/14.05 thf(f2813,plain,(
% 89.60/14.05 ( ! [X19 : mworld] : (($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))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2812])).
% 89.60/14.05 thf(f2812,plain,(
% 89.60/14.05 ( ! [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))))))))) & $true))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2811,f1785])).
% 89.60/14.05 thf(f2811,plain,(
% 89.60/14.05 ( ! [X19 : mworld] : (($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))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2810])).
% 89.60/14.05 thf(f2810,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ 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)))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2809,f358])).
% 89.60/14.05 thf(f2809,plain,(
% 89.60/14.05 ( ! [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)))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2808])).
% 89.60/14.05 thf(f2808,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2803])).
% 89.60/14.05 thf(f2803,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2802])).
% 89.60/14.05 thf(f2802,plain,(
% 89.60/14.05 ( ! [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) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2801,f1785])).
% 89.60/14.05 thf(f2801,plain,(
% 89.60/14.05 ( ! [X18 : mworld] : (($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))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2800])).
% 89.60/14.05 thf(f2800,plain,(
% 89.60/14.05 ( ! [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)))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2799,f358])).
% 89.60/14.05 thf(f2799,plain,(
% 89.60/14.05 ( ! [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)))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2798])).
% 89.60/14.05 thf(f2798,plain,(
% 89.60/14.05 ( ! [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) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2793])).
% 89.60/14.05 thf(f2793,plain,(
% 89.60/14.05 ( ! [X17 : mworld] : (($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)))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2792])).
% 89.60/14.05 thf(f2792,plain,(
% 89.60/14.05 ( ! [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))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2791,f1785])).
% 89.60/14.05 thf(f2791,plain,(
% 89.60/14.05 ( ! [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)))))) & (?? @ mworld @ (mrel @ X17))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2790])).
% 89.60/14.05 thf(f2790,plain,(
% 89.60/14.05 ( ! [X17 : mworld] : (($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)))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2789,f358])).
% 89.60/14.05 thf(f2789,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2788])).
% 89.60/14.05 thf(f2788,plain,(
% 89.60/14.05 ( ! [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) => ((!! @ 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) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2783])).
% 89.60/14.05 thf(f2783,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2782])).
% 89.60/14.05 thf(f2782,plain,(
% 89.60/14.05 ( ! [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) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2781,f1785])).
% 89.60/14.05 thf(f2781,plain,(
% 89.60/14.05 ( ! [X16 : mworld] : (($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))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2780])).
% 89.60/14.05 thf(f2780,plain,(
% 89.60/14.05 ( ! [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)))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2779,f358])).
% 89.60/14.05 thf(f2779,plain,(
% 89.60/14.05 ( ! [X16 : mworld,X15 : mworld] : (($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)))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2778])).
% 89.60/14.05 thf(f2778,plain,(
% 89.60/14.05 ( ! [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)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2638])).
% 89.60/14.05 thf(f2960,plain,(
% 89.60/14.05 ( ! [X23 : mworld] : (((v6 @ X23) = $true)) ) | ~spl0_16),
% 89.60/14.05 inference(avatar_component_clause,[status(thm)],[f2959])).
% 89.60/14.05 thf(f2959,definition,(
% 89.60/14.05 spl0_16 <=> ! [X23 : mworld] : ((v6 @ X23) = $true)),
% 89.60/14.05 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 89.60/14.05 thf(f3550,plain,(
% 89.60/14.05 spl0_16 | ~spl0_15 | ~spl0_23),
% 89.60/14.05 inference(avatar_split_clause,[status(thm)],[f3549,f3303,f2678,f2959])).
% 89.60/14.05 thf(f2678,definition,(
% 89.60/14.05 spl0_15 <=> ! [X11 : mworld] : ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (v10 @ Y0)))) = $true)),
% 89.60/14.05 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 89.60/14.05 thf(f3303,definition,(
% 89.60/14.05 spl0_23 <=> ! [X1 : mworld] : ($true = (v20 @ X1))),
% 89.60/14.05 introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition])).
% 89.60/14.05 thf(f3549,plain,(
% 89.60/14.05 ( ! [X8 : mworld] : (((v6 @ X8) = $true)) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3548])).
% 89.60/14.05 thf(f3548,plain,(
% 89.60/14.05 ( ! [X8 : mworld] : ((($true => (v6 @ X8)) = $true)) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3547,f358])).
% 89.60/14.05 thf(f3547,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X7 : mworld] : (($true = ((mrel @ X7 @ X8) => (v6 @ X8)))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3546])).
% 89.60/14.05 thf(f3546,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (v6 @ Y0))) @ X8) = $true)) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3541])).
% 89.60/14.05 thf(f3541,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (v6 @ Y0)))))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3540])).
% 89.60/14.05 thf(f3540,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (v6 @ Y0))))))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3539,f358])).
% 89.60/14.05 thf(f3539,plain,(
% 89.60/14.05 ( ! [X6 : mworld,X7 : mworld] : ((((mrel @ X6 @ X7) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (v6 @ Y0))))) = $true)) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3538])).
% 89.60/14.05 thf(f3538,plain,(
% 89.60/14.05 ( ! [X6 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v6 @ Y1)))))) @ X7) = $true)) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3533])).
% 89.60/14.05 thf(f3533,plain,(
% 89.60/14.05 ( ! [X6 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v6 @ Y1))))))))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3532])).
% 89.60/14.05 thf(f3532,plain,(
% 89.60/14.05 ( ! [X6 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v6 @ Y1)))))))))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3531,f358])).
% 89.60/14.05 thf(f3531,plain,(
% 89.60/14.05 ( ! [X6 : mworld,X5 : mworld] : (($true = ((mrel @ X5 @ X6) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v6 @ Y1)))))))))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3530])).
% 89.60/14.05 thf(f3530,plain,(
% 89.60/14.05 ( ! [X6 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v6 @ Y2))))))))) @ X6))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3525])).
% 89.60/14.05 thf(f3525,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v6 @ Y2)))))))))))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3524])).
% 89.60/14.05 thf(f3524,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v6 @ Y2))))))))))))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3523,f358])).
% 89.60/14.05 thf(f3523,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($true = ((mrel @ X4 @ X5) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v6 @ Y2))))))))))))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3522])).
% 89.60/14.05 thf(f3522,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v6 @ Y3)))))))))))) @ X5))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3517])).
% 89.60/14.05 thf(f3517,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($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) => (v6 @ Y3))))))))))))))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3516])).
% 89.60/14.05 thf(f3516,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y3))))))))))))) | $false) = $true)) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3515])).
% 89.60/14.05 thf(f3515,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($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) => (v6 @ Y3))))))))))))) | (~ $true)))) ) | (~spl0_15 | ~spl0_23)),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3514,f2986])).
% 89.60/14.05 thf(f2986,plain,(
% 89.60/14.05 ( ! [X12 : mworld] : (((v10 @ X12) = $true)) ) | ~spl0_15),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2985])).
% 89.60/14.05 thf(f2985,plain,(
% 89.60/14.05 ( ! [X12 : mworld] : (($true = ($true => (v10 @ X12)))) ) | ~spl0_15),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2984,f358])).
% 89.60/14.05 thf(f2984,plain,(
% 89.60/14.05 ( ! [X11 : mworld,X12 : mworld] : ((((mrel @ X11 @ X12) => (v10 @ X12)) = $true)) ) | ~spl0_15),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2983])).
% 89.60/14.05 thf(f2983,plain,(
% 89.60/14.05 ( ! [X11 : mworld,X12 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (v10 @ Y0))) @ X12))) ) | ~spl0_15),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2679])).
% 89.60/14.05 thf(f2679,plain,(
% 89.60/14.05 ( ! [X11 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (v10 @ Y0)))) = $true)) ) | ~spl0_15),
% 89.60/14.05 inference(avatar_component_clause,[status(thm)],[f2678])).
% 89.60/14.05 thf(f3514,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($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) => (v6 @ Y3))))))))))))) | (~ (v10 @ X4))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3513])).
% 89.60/14.05 thf(f3513,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y3))))))))))))) | (~ (v10 @ X4)))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3512,f358])).
% 89.60/14.05 thf(f3512,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y3))))))))))))) | (~ (v10 @ X4)))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3511])).
% 89.60/14.05 thf(f3511,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($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) => (v6 @ Y4))))))))))))) | (~ (v10 @ Y0))))) @ X4))) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3506])).
% 89.60/14.05 thf(f3506,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v6 @ Y4))))))))))))) | (~ (v10 @ Y0)))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3505])).
% 89.60/14.05 thf(f3505,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v6 @ Y4))))))))))))) | (~ (v10 @ Y0))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3504,f358])).
% 89.60/14.05 thf(f3504,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X3 : mworld] : (($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) => (v6 @ Y4))))))))))))) | (~ (v10 @ Y0))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3503])).
% 89.60/14.05 thf(f3503,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y5))))))))))))) | (~ (v10 @ Y1)))))))) @ X3) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3498])).
% 89.60/14.05 thf(f3498,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y5))))))))))))) | (~ (v10 @ Y1))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3497])).
% 89.60/14.05 thf(f3497,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v6 @ Y5))))))))))))) | (~ (v10 @ Y1)))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3496,f358])).
% 89.60/14.05 thf(f3496,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($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) => (v6 @ Y5))))))))))))) | (~ (v10 @ Y1)))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3495])).
% 89.60/14.05 thf(f3495,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y6))))))))))))) | (~ (v10 @ Y2))))))))))) @ X2) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3490])).
% 89.60/14.05 thf(f3490,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y6))))))))))))) | (~ (v10 @ Y2)))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3489])).
% 89.60/14.05 thf(f3489,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v6 @ Y6))))))))))))) | (~ (v10 @ Y2))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3488,f358])).
% 89.60/14.05 thf(f3488,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : (($true = ((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) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v6 @ Y6))))))))))))) | (~ (v10 @ Y2))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3485])).
% 89.60/14.05 thf(f3485,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v6 @ Y7))))))))))))) | (~ (v10 @ Y3)))))))))))))) @ X1) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3436])).
% 89.60/14.05 thf(f3436,plain,(
% 89.60/14.05 ( ! [X0 : mworld] : (($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) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v6 @ Y7))))))))))))) | (~ (v10 @ Y3))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3435])).
% 89.60/14.05 thf(f3435,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v6 @ Y7))))))))))))) | (~ (v10 @ Y3))))))))))))))) | $false))) ) | ~spl0_23),
% 89.60/14.05 inference(superposition,[status(thm)],[f3428,f2556])).
% 89.60/14.05 thf(f2556,plain,(
% 89.60/14.05 ( ! [X14 : mworld] : (((v14 @ (sK17 @ X14)) = $false)) )),
% 89.60/14.05 inference(not_proxy_clausification,[status(thm)],[f2555])).
% 89.60/14.05 thf(f2555,plain,(
% 89.60/14.05 ( ! [X14 : mworld] : (((~ (v14 @ (sK17 @ X14))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2554])).
% 89.60/14.05 thf(f2554,plain,(
% 89.60/14.05 ( ! [X14 : mworld] : (($true = ((~ (v14 @ (sK17 @ X14))) & $true))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2553,f358])).
% 89.60/14.05 thf(f2553,plain,(
% 89.60/14.05 ( ! [X14 : mworld] : (($true = ((~ (v14 @ (sK17 @ X14))) & (mrel @ X14 @ (sK17 @ X14))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2552])).
% 89.60/14.05 thf(f2552,plain,(
% 89.60/14.05 ( ! [X14 : mworld] : ((((^[Y0 : mworld]: ((~ (v14 @ Y0)) & (mrel @ X14 @ Y0))) @ (sK17 @ X14)) = $true)) )),
% 89.60/14.05 inference(sigma_clausification,[status(thm)],[f2544])).
% 89.60/14.05 thf(f2544,plain,(
% 89.60/14.05 ( ! [X14 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((~ (v14 @ Y0)) & (mrel @ X14 @ Y0)))))) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2543])).
% 89.60/14.05 thf(f2543,plain,(
% 89.60/14.05 ( ! [X14 : mworld] : (($true = ((?? @ mworld @ (^[Y0 : mworld]: ((v14 @ Y0) & (mrel @ X14 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v14 @ Y0)) & (mrel @ X14 @ Y0))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2542])).
% 89.60/14.05 thf(f2542,plain,(
% 89.60/14.05 ( ! [X14 : mworld] : (($true = ($true & ((?? @ mworld @ (^[Y0 : mworld]: ((v14 @ Y0) & (mrel @ X14 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v14 @ Y0)) & (mrel @ X14 @ Y0)))))))) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f2533,f2541])).
% 89.60/14.05 thf(f3428,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y7))))))))))))) | (~ (v10 @ Y3))))))))))))))) | (v14 @ X15)) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3427])).
% 89.60/14.05 thf(f3427,plain,(
% 89.60/14.05 ( ! [X15 : mworld] : (($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) => (v6 @ Y7))))))))))))) | (~ (v10 @ Y3))))))))))))))) | (v14 @ X15))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3426,f358])).
% 89.60/14.05 thf(f3426,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y3))))))))))))))) | (v14 @ X15))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3425])).
% 89.60/14.05 thf(f3425,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y4))))))))))))))) | (v14 @ Y0)))) @ X15) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3420])).
% 89.60/14.05 thf(f3420,plain,(
% 89.60/14.05 ( ! [X14 : mworld] : (($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))))))))))))) | (~ (v10 @ Y4))))))))))))))) | (v14 @ Y0))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3419])).
% 89.60/14.05 thf(f3419,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y4))))))))))))))) | (v14 @ Y0)))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3418,f358])).
% 89.60/14.05 thf(f3418,plain,(
% 89.60/14.05 ( ! [X14 : mworld,X13 : mworld] : (($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) => (v6 @ Y8))))))))))))) | (~ (v10 @ Y4))))))))))))))) | (v14 @ Y0)))))))) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3417])).
% 89.60/14.05 thf(f3417,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y5))))))))))))))) | (v14 @ Y1))))))) @ X14) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3412])).
% 89.60/14.05 thf(f3412,plain,(
% 89.60/14.05 ( ! [X13 : mworld] : (($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))))))))))))) | (~ (v10 @ Y5))))))))))))))) | (v14 @ Y1)))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3411])).
% 89.60/14.05 thf(f3411,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y5))))))))))))))) | (v14 @ Y1))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3410,f358])).
% 89.60/14.05 thf(f3410,plain,(
% 89.60/14.05 ( ! [X12 : mworld,X13 : mworld] : (($true = ((mrel @ X12 @ X13) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v6 @ Y9))))))))))))) | (~ (v10 @ Y5))))))))))))))) | (v14 @ Y1))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3409])).
% 89.60/14.05 thf(f3409,plain,(
% 89.60/14.05 ( ! [X12 : mworld,X13 : mworld] : (($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) => (v6 @ Y10))))))))))))) | (~ (v10 @ Y6))))))))))))))) | (v14 @ Y2)))))))))) @ X13))) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3404])).
% 89.60/14.05 thf(f3404,plain,(
% 89.60/14.05 ( ! [X12 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v6 @ Y10))))))))))))) | (~ (v10 @ Y6))))))))))))))) | (v14 @ Y2))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3403])).
% 89.60/14.05 thf(f3403,plain,(
% 89.60/14.05 ( ! [X12 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v6 @ Y10))))))))))))) | (~ (v10 @ Y6))))))))))))))) | (v14 @ Y2)))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3402,f358])).
% 89.60/14.05 thf(f3402,plain,(
% 89.60/14.05 ( ! [X11 : mworld,X12 : mworld] : (($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) => (v6 @ Y10))))))))))))) | (~ (v10 @ Y6))))))))))))))) | (v14 @ Y2)))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3401])).
% 89.60/14.05 thf(f3401,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y7))))))))))))))) | (v14 @ Y3))))))))))))) @ X12) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3396])).
% 89.60/14.05 thf(f3396,plain,(
% 89.60/14.05 ( ! [X11 : mworld] : (($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))))))))))))) | (~ (v10 @ Y7))))))))))))))) | (v14 @ Y3)))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3395])).
% 89.60/14.05 thf(f3395,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y7))))))))))))))) | (v14 @ Y3))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3394,f358])).
% 89.60/14.05 thf(f3394,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X11 : mworld] : (($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) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v6 @ Y11))))))))))))) | (~ (v10 @ Y7))))))))))))))) | (v14 @ Y3))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3393])).
% 89.60/14.05 thf(f3393,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X11 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v6 @ Y12))))))))))))) | (~ (v10 @ Y8))))))))))))))) | (v14 @ Y4)))))))))))))))) @ X11))) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3388])).
% 89.60/14.05 thf(f3388,plain,(
% 89.60/14.05 ( ! [X10 : mworld] : (($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))))))))))))) | (~ (v10 @ Y8))))))))))))))) | (v14 @ Y4))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3387])).
% 89.60/14.05 thf(f3387,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y8))))))))))))))) | (v14 @ Y4)))))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3386,f358])).
% 89.60/14.05 thf(f3386,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X9 : mworld] : (($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))))))))))))) | (~ (v10 @ Y8))))))))))))))) | (v14 @ Y4)))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3385])).
% 89.60/14.05 thf(f3385,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v6 @ Y13))))))))))))) | (~ (v10 @ Y9))))))))))))))) | (v14 @ Y5))))))))))))))))))) @ X10))) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3380])).
% 89.60/14.05 thf(f3380,plain,(
% 89.60/14.05 ( ! [X9 : mworld] : (($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))))))))))))) | (~ (v10 @ Y9))))))))))))))) | (v14 @ Y5)))))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3379])).
% 89.60/14.05 thf(f3379,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y9))))))))))))))) | (v14 @ Y5)))))))))))))))))))) | $false))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3356])).
% 89.60/14.05 thf(f3356,plain,(
% 89.60/14.05 ( ! [X9 : mworld] : (($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))))))))))))) | (~ (v10 @ Y9))))))))))))))) | (v14 @ Y5)))))))))))))))))))) | (~ $true)))) ) | ~spl0_23),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f800,f3304])).
% 89.60/14.05 thf(f3304,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($true = (v20 @ X1))) ) | ~spl0_23),
% 89.60/14.05 inference(avatar_component_clause,[status(thm)],[f3303])).
% 89.60/14.05 thf(f800,plain,(
% 89.60/14.05 ( ! [X9 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v6 @ Y13))))))))))))) | (~ (v10 @ Y9))))))))))))))) | (v14 @ Y5)))))))))))))))))))) | (~ (v20 @ X9))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f799])).
% 89.60/14.05 thf(f799,plain,(
% 89.60/14.05 ( ! [X9 : mworld] : ((($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))))))))))))) | (~ (v10 @ Y9))))))))))))))) | (v14 @ Y5)))))))))))))))))))) | (~ (v20 @ X9)))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f798,f358])).
% 89.60/14.05 thf(f798,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y9))))))))))))))) | (v14 @ Y5)))))))))))))))))))) | (~ (v20 @ X9)))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f797])).
% 89.60/14.05 thf(f797,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X9 : mworld] : (($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))))))))))))) | (~ (v10 @ Y10))))))))))))))) | (v14 @ Y6)))))))))))))))))))) | (~ (v20 @ Y0))))) @ X9))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f796])).
% 89.60/14.05 thf(f796,plain,(
% 89.60/14.05 ( ! [X8 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v6 @ Y14))))))))))))) | (~ (v10 @ Y10))))))))))))))) | (v14 @ Y6)))))))))))))))))))) | (~ (v20 @ Y0)))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f795])).
% 89.60/14.05 thf(f795,plain,(
% 89.60/14.05 ( ! [X8 : mworld] : (($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) => (v6 @ Y14))))))))))))) | (~ (v10 @ Y10))))))))))))))) | (v14 @ Y6)))))))))))))))))))) | (~ (v20 @ Y0))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f794,f358])).
% 89.60/14.05 thf(f794,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y14))))))))))))) | (~ (v10 @ Y10))))))))))))))) | (v14 @ Y6)))))))))))))))))))) | (~ (v20 @ Y0))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f793])).
% 89.60/14.05 thf(f793,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X7 : mworld] : (($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) => (v6 @ Y15))))))))))))) | (~ (v10 @ Y11))))))))))))))) | (v14 @ Y7)))))))))))))))))))) | (~ (v20 @ Y1)))))))) @ X8))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f792])).
% 89.60/14.05 thf(f792,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y11))))))))))))))) | (v14 @ Y7)))))))))))))))))))) | (~ (v20 @ Y1))))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f791])).
% 89.60/14.05 thf(f791,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v6 @ Y15))))))))))))) | (~ (v10 @ Y11))))))))))))))) | (v14 @ Y7)))))))))))))))))))) | (~ (v20 @ Y1)))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f790,f358])).
% 89.60/14.05 thf(f790,plain,(
% 89.60/14.05 ( ! [X6 : mworld,X7 : mworld] : (($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) => (v6 @ Y15))))))))))))) | (~ (v10 @ Y11))))))))))))))) | (v14 @ Y7)))))))))))))))))))) | (~ (v20 @ Y1)))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f789])).
% 89.60/14.05 thf(f789,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y12))))))))))))))) | (v14 @ Y8)))))))))))))))))))) | (~ (v20 @ Y2))))))))))) @ X7) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f788])).
% 89.60/14.05 thf(f788,plain,(
% 89.60/14.05 ( ! [X6 : mworld] : (($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))))))))))))) | (~ (v10 @ Y12))))))))))))))) | (v14 @ Y8)))))))))))))))))))) | (~ (v20 @ Y2)))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f787])).
% 89.60/14.05 thf(f787,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y16))))))))))))) | (~ (v10 @ Y12))))))))))))))) | (v14 @ Y8)))))))))))))))))))) | (~ (v20 @ Y2))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f786,f358])).
% 89.60/14.05 thf(f786,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v6 @ Y16))))))))))))) | (~ (v10 @ Y12))))))))))))))) | (v14 @ Y8)))))))))))))))))))) | (~ (v20 @ Y2))))))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f785])).
% 89.60/14.05 thf(f785,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y17))))))))))))) | (~ (v10 @ Y13))))))))))))))) | (v14 @ Y9)))))))))))))))))))) | (~ (v20 @ Y3)))))))))))))) @ X6) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f784])).
% 89.60/14.05 thf(f784,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($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))))))))))))) | (~ (v10 @ Y13))))))))))))))) | (v14 @ Y9)))))))))))))))))))) | (~ (v20 @ Y3))))))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f783])).
% 89.60/14.05 thf(f783,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v6 @ Y17))))))))))))) | (~ (v10 @ Y13))))))))))))))) | (v14 @ Y9)))))))))))))))))))) | (~ (v20 @ Y3)))))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f782,f358])).
% 89.60/14.05 thf(f782,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y17))))))))))))) | (~ (v10 @ Y13))))))))))))))) | (v14 @ Y9)))))))))))))))))))) | (~ (v20 @ Y3)))))))))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f781])).
% 89.60/14.05 thf(f781,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y14))))))))))))))) | (v14 @ Y10)))))))))))))))))))) | (~ (v20 @ Y4))))))))))))))))) @ X5) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f780])).
% 89.60/14.05 thf(f780,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($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))))))))))))) | (~ (v10 @ Y14))))))))))))))) | (v14 @ Y10)))))))))))))))))))) | (~ (v20 @ Y4)))))))))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f779])).
% 89.60/14.05 thf(f779,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y14))))))))))))))) | (v14 @ Y10)))))))))))))))))))) | (~ (v20 @ Y4))))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f778,f358])).
% 89.60/14.05 thf(f778,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y14))))))))))))))) | (v14 @ Y10)))))))))))))))))))) | (~ (v20 @ Y4))))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f777])).
% 89.60/14.05 thf(f777,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y15))))))))))))))) | (v14 @ Y11)))))))))))))))))))) | (~ (v20 @ Y5)))))))))))))))))))) @ X4) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f776])).
% 89.60/14.05 thf(f776,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($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))))))))))))) | (~ (v10 @ Y15))))))))))))))) | (v14 @ Y11)))))))))))))))))))) | (~ (v20 @ Y5))))))))))))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f775])).
% 89.60/14.05 thf(f775,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y15))))))))))))))) | (v14 @ Y11)))))))))))))))))))) | (~ (v20 @ Y5)))))))))))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f774,f358])).
% 89.60/14.05 thf(f774,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y15))))))))))))))) | (v14 @ Y11)))))))))))))))))))) | (~ (v20 @ Y5)))))))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f773])).
% 89.60/14.05 thf(f773,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y16))))))))))))))) | (v14 @ Y12)))))))))))))))))))) | (~ (v20 @ Y6))))))))))))))))))))))) @ X3) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f772])).
% 89.60/14.05 thf(f772,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($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) => (v6 @ Y20))))))))))))) | (~ (v10 @ Y16))))))))))))))) | (v14 @ Y12)))))))))))))))))))) | (~ (v20 @ Y6)))))))))))))))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f771])).
% 89.60/14.05 thf(f771,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y16))))))))))))))) | (v14 @ Y12)))))))))))))))))))) | (~ (v20 @ Y6))))))))))))))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f770,f358])).
% 89.60/14.05 thf(f770,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (v6 @ Y20))))))))))))) | (~ (v10 @ Y16))))))))))))))) | (v14 @ Y12)))))))))))))))))))) | (~ (v20 @ Y6))))))))))))))))))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f769])).
% 89.60/14.05 thf(f769,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($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) => (v6 @ Y21))))))))))))) | (~ (v10 @ Y17))))))))))))))) | (v14 @ Y13)))))))))))))))))))) | (~ (v20 @ Y7)))))))))))))))))))))))))) @ X2))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f768])).
% 89.60/14.05 thf(f768,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v6 @ Y21))))))))))))) | (~ (v10 @ Y17))))))))))))))) | (v14 @ Y13)))))))))))))))))))) | (~ (v20 @ Y7))))))))))))))))))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f767])).
% 89.60/14.05 thf(f767,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($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) => (v6 @ Y21))))))))))))) | (~ (v10 @ Y17))))))))))))))) | (v14 @ Y13)))))))))))))))))))) | (~ (v20 @ Y7)))))))))))))))))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f766,f358])).
% 89.60/14.05 thf(f766,plain,(
% 89.60/14.05 ( ! [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))))))))))))) | (~ (v10 @ Y17))))))))))))))) | (v14 @ Y13)))))))))))))))))))) | (~ (v20 @ Y7)))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f765])).
% 89.60/14.05 thf(f765,plain,(
% 89.60/14.05 ( ! [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) => (v6 @ Y22))))))))))))) | (~ (v10 @ Y18))))))))))))))) | (v14 @ Y14)))))))))))))))))))) | (~ (v20 @ Y8))))))))))))))))))))))))))))) @ X1) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f341])).
% 89.60/14.05 thf(f341,plain,(
% 89.60/14.05 ((!! @ 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))))))))))))) | (~ (v10 @ Y18))))))))))))))) | (v14 @ Y14)))))))))))))))))))) | (~ (v20 @ Y8)))))))))))))))))))))))))))))) = $true)),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f286])).
% 89.60/14.05 thf(f286,plain,(
% 89.60/14.05 (((^[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 > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v20) @ ((^[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))))))) @ 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 > $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]: (!! @ 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))))))) @ v6))))))))))))))))))))))))))) = $true)),
% 89.60/14.05 inference(definition_unfolding,[status(thm)],[f233,f226,f239,f239,f239,f239,f239,f239,f239,f239,f239,f201,f213,f239,f239,f239,f239,f239,f239,f201,f239,f239,f239,f239,f201,f213,f239,f239,f239,f239])).
% 89.60/14.05 thf(f233,plain,(
% 89.60/14.05 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v20) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v14 @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v10) @ (mbox @ (mbox @ (mbox @ (mbox @ v6))))))))))))))))))))))))))) = $true)),
% 89.60/14.05 inference(cnf_transformation,[status(thm)],[f123])).
% 89.60/14.05 thf(f123,plain,(
% 89.60/14.05 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v20) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v14 @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v10) @ (mbox @ (mbox @ (mbox @ (mbox @ v6))))))))))))))))))))))))))) = $true)),
% 89.60/14.05 inference(fool_elimination,[status(thm)],[f122])).
% 89.60/14.05 thf(f122,plain,(
% 89.60/14.05 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v20) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v14 @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v10) @ (mbox @ (mbox @ (mbox @ (mbox @ v6)))))))))))))))))))))))))))),
% 89.60/14.05 inference(rectify,[status(thm)],[f49])).
% 89.60/14.05 thf(f49,axiom,(
% 89.60/14.05 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v20) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v14 @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v10) @ (mbox @ (mbox @ (mbox @ (mbox @ v6)))))))))))))))))))))))))))),
% 89.60/14.05 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod40)).
% 89.60/14.05 thf(f3476,plain,(
% 89.60/14.05 ~spl0_13 | ~spl0_23),
% 89.60/14.05 inference(avatar_contradiction_clause,[status(thm)],[f3475])).
% 89.60/14.05 thf(f3475,plain,(
% 89.60/14.05 $false | (~spl0_13 | ~spl0_23)),
% 89.60/14.05 inference(trivial_inequality_removal,[status(thm)],[f3474])).
% 89.60/14.05 thf(f3474,plain,(
% 89.60/14.05 ($false = $true) | (~spl0_13 | ~spl0_23)),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3473,f2424])).
% 89.60/14.05 thf(f2424,plain,(
% 89.60/14.05 ( ! [X20 : mworld] : (((v9 @ X20) = $false)) ) | ~spl0_13),
% 89.60/14.05 inference(not_proxy_clausification,[status(thm)],[f2423])).
% 89.60/14.05 thf(f2423,plain,(
% 89.60/14.05 ( ! [X20 : mworld] : (($true = (~ (v9 @ X20)))) ) | ~spl0_13),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2422])).
% 89.60/14.05 thf(f2422,plain,(
% 89.60/14.05 ( ! [X20 : mworld] : ((($true => (~ (v9 @ X20))) = $true)) ) | ~spl0_13),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2421,f358])).
% 89.60/14.05 thf(f2421,plain,(
% 89.60/14.05 ( ! [X19 : mworld,X20 : mworld] : (($true = ((mrel @ X19 @ X20) => (~ (v9 @ X20))))) ) | ~spl0_13),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2420])).
% 89.60/14.05 thf(f2420,plain,(
% 89.60/14.05 ( ! [X19 : mworld,X20 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (~ (v9 @ Y0)))) @ X20))) ) | ~spl0_13),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2419])).
% 89.60/14.05 thf(f2419,plain,(
% 89.60/14.05 ( ! [X19 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (~ (v9 @ Y0))))) = $true)) ) | ~spl0_13),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2418])).
% 89.60/14.05 thf(f2418,plain,(
% 89.60/14.05 ( ! [X19 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (~ (v9 @ Y0)))))) = $true)) ) | ~spl0_13),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2417,f358])).
% 89.60/14.05 thf(f2417,plain,(
% 89.60/14.05 ( ! [X18 : mworld,X19 : mworld] : ((((mrel @ X18 @ X19) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (~ (v9 @ Y0)))))) = $true)) ) | ~spl0_13),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2416])).
% 89.60/14.05 thf(f2416,plain,(
% 89.60/14.05 ( ! [X18 : mworld,X19 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X18 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v9 @ Y1))))))) @ X19))) ) | ~spl0_13),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2414])).
% 89.60/14.05 thf(f2414,plain,(
% 89.60/14.05 ( ! [X18 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v9 @ Y1)))))))) = $true)) ) | ~spl0_13),
% 89.60/14.05 inference(avatar_component_clause,[status(thm)],[f2413])).
% 89.60/14.05 thf(f2413,definition,(
% 89.60/14.05 spl0_13 <=> ! [X18 : mworld] : ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v9 @ Y1)))))))) = $true)),
% 89.60/14.05 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 89.60/14.05 thf(f3473,plain,(
% 89.60/14.05 ( ! [X12 : mworld] : (($true = (v9 @ X12))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3472])).
% 89.60/14.05 thf(f3472,plain,(
% 89.60/14.05 ( ! [X12 : mworld] : ((($true => (v9 @ X12)) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3471,f358])).
% 89.60/14.05 thf(f3471,plain,(
% 89.60/14.05 ( ! [X11 : mworld,X12 : mworld] : (($true = ((mrel @ X11 @ X12) => (v9 @ X12)))) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3470])).
% 89.60/14.05 thf(f3470,plain,(
% 89.60/14.05 ( ! [X11 : mworld,X12 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (v9 @ Y0))) @ X12))) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3465])).
% 89.60/14.05 thf(f3465,plain,(
% 89.60/14.05 ( ! [X11 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (v9 @ Y0)))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3464])).
% 89.60/14.05 thf(f3464,plain,(
% 89.60/14.05 ( ! [X11 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (v9 @ Y0))))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3463,f358])).
% 89.60/14.05 thf(f3463,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X11 : mworld] : (($true = ((mrel @ X10 @ X11) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (v9 @ Y0))))))) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3462])).
% 89.60/14.05 thf(f3462,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X11 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v9 @ Y1)))))) @ X11) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3457])).
% 89.60/14.05 thf(f3457,plain,(
% 89.60/14.05 ( ! [X10 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v9 @ Y1))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3456])).
% 89.60/14.05 thf(f3456,plain,(
% 89.60/14.05 ( ! [X10 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v9 @ Y1)))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3455,f358])).
% 89.60/14.05 thf(f3455,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X9 : mworld] : ((((mrel @ X9 @ X10) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v9 @ Y1)))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3454])).
% 89.60/14.05 thf(f3454,plain,(
% 89.60/14.05 ( ! [X10 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v9 @ Y2))))))))) @ X10))) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3449])).
% 89.60/14.05 thf(f3449,plain,(
% 89.60/14.05 ( ! [X9 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v9 @ Y2)))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3448])).
% 89.60/14.05 thf(f3448,plain,(
% 89.60/14.05 ( ! [X9 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v9 @ Y2))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3447,f358])).
% 89.60/14.05 thf(f3447,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y2))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3446])).
% 89.60/14.05 thf(f3446,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v9 @ Y3)))))))))))) @ X9))) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3441])).
% 89.60/14.05 thf(f3441,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y3))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3440])).
% 89.60/14.05 thf(f3440,plain,(
% 89.60/14.05 ( ! [X8 : mworld] : (($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) => (v9 @ Y3)))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3439,f358])).
% 89.60/14.05 thf(f3439,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y3)))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3438])).
% 89.60/14.05 thf(f3438,plain,(
% 89.60/14.05 ( ! [X8 : mworld,X7 : mworld] : (($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) => (v9 @ Y4))))))))))))))) @ X8))) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3432])).
% 89.60/14.05 thf(f3432,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v9 @ Y4)))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3431])).
% 89.60/14.05 thf(f3431,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($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) => (v9 @ Y4))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3430,f358])).
% 89.60/14.05 thf(f3430,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y4))))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3429])).
% 89.60/14.05 thf(f3429,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y5)))))))))))))))))) @ X7) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3424])).
% 89.60/14.05 thf(f3424,plain,(
% 89.60/14.05 ( ! [X6 : mworld] : (($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) => (v9 @ Y5))))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3423])).
% 89.60/14.05 thf(f3423,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y5)))))))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3422,f358])).
% 89.60/14.05 thf(f3422,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y5)))))))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3421])).
% 89.60/14.05 thf(f3421,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y6))))))))))))))))))))) @ X6) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3416])).
% 89.60/14.05 thf(f3416,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($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) => (v9 @ Y6)))))))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3415])).
% 89.60/14.05 thf(f3415,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y6))))))))))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3414,f358])).
% 89.60/14.05 thf(f3414,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y6))))))))))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3413])).
% 89.60/14.05 thf(f3413,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($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) => (v9 @ Y7)))))))))))))))))))))))) @ X5))) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3408])).
% 89.60/14.05 thf(f3408,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v9 @ Y7))))))))))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3407])).
% 89.60/14.05 thf(f3407,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($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) => (v9 @ Y7)))))))))))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3406,f358])).
% 89.60/14.05 thf(f3406,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y7)))))))))))))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3405])).
% 89.60/14.05 thf(f3405,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($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) => (v9 @ Y8))))))))))))))))))))))))))) @ X4))) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3400])).
% 89.60/14.05 thf(f3400,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v9 @ Y8)))))))))))))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3399])).
% 89.60/14.05 thf(f3399,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : ((($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) => (v9 @ Y8))))))))))))))))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3398,f358])).
% 89.60/14.05 thf(f3398,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X3 : mworld] : (($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) => (v9 @ Y8))))))))))))))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3397])).
% 89.60/14.05 thf(f3397,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y9)))))))))))))))))))))))))))))) @ X3) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3392])).
% 89.60/14.05 thf(f3392,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($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) => (v9 @ Y9))))))))))))))))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3391])).
% 89.60/14.05 thf(f3391,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y9)))))))))))))))))))))))))))))))))) ) | ~spl0_23),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3390,f358])).
% 89.60/14.05 thf(f3390,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y9)))))))))))))))))))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3389])).
% 89.60/14.05 thf(f3389,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($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) => (v9 @ Y10))))))))))))))))))))))))))))))))) @ X2))) ) | ~spl0_23),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3378])).
% 89.60/14.05 thf(f3378,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y10)))))))))))))))))))))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(trivial_inequality_removal,[status(thm)],[f3377])).
% 89.60/14.05 thf(f3377,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y10)))))))))))))))))))))))))))))))))) = $true) | ($false = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3361])).
% 89.60/14.05 thf(f3361,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($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) => (v9 @ Y10)))))))))))))))))))))))))))))))))) = $true)) ) | ~spl0_23),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f2448,f3304])).
% 89.60/14.05 thf(f2448,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y10)))))))))))))))))))))))))))))))))) = $true) | ((~ (v20 @ X1)) = $true)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f2443])).
% 89.60/14.05 thf(f2443,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y10)))))))))))))))))))))))))))))))))) | (~ (v20 @ X1))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2442])).
% 89.60/14.05 thf(f2442,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($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) => (v9 @ Y10)))))))))))))))))))))))))))))))))) | (~ (v20 @ X1)))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2441,f358])).
% 89.60/14.05 thf(f2441,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ (sK7 @ 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) => (v9 @ Y10)))))))))))))))))))))))))))))))))) | (~ (v20 @ X1)))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2438])).
% 89.60/14.05 thf(f2438,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ (sK7 @ 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) => (v9 @ Y11)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y0))))) @ X1) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2431])).
% 89.60/14.05 thf(f2431,plain,(
% 89.60/14.05 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK7 @ 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) => (v9 @ Y11)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y0)))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2429])).
% 89.60/14.05 thf(f2429,plain,(
% 89.60/14.05 ( ! [X0 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK7 @ 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) => (v9 @ Y11)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y0)))))) | $false))) )),
% 89.60/14.05 inference(superposition,[status(thm)],[f2405,f1918])).
% 89.60/14.05 thf(f1918,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($false = (v21 @ (sK7 @ X7)))) )),
% 89.60/14.05 inference(not_proxy_clausification,[status(thm)],[f1911])).
% 89.60/14.05 thf(f1911,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($true = (~ (v21 @ (sK7 @ X7))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1910])).
% 89.60/14.05 thf(f1910,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($true = ((~ (v21 @ (sK7 @ X7))) & $true))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1904,f358])).
% 89.60/14.05 thf(f1904,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($true = ((~ (v21 @ (sK7 @ X7))) & (mrel @ X7 @ (sK7 @ X7))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f1903])).
% 89.60/14.05 thf(f1903,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($true = ((^[Y0 : mworld]: ((~ (v21 @ Y0)) & (mrel @ X7 @ Y0))) @ (sK7 @ X7)))) )),
% 89.60/14.05 inference(sigma_clausification,[status(thm)],[f1895])).
% 89.60/14.05 thf(f1895,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((~ (v21 @ Y0)) & (mrel @ X7 @ Y0)))) = $true)) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f1894])).
% 89.60/14.05 thf(f1894,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v21 @ Y0)) & (mrel @ X7 @ Y0))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1893])).
% 89.60/14.05 thf(f1893,plain,(
% 89.60/14.05 ( ! [X7 : mworld] : (($true = ($true & ((?? @ mworld @ (^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v21 @ Y0)) & (mrel @ X7 @ Y0)))))))) )),
% 89.60/14.05 inference(backward_demodulation,[status(thm)],[f1878,f1892])).
% 89.60/14.05 thf(f2405,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y11)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y0)))))) | (v21 @ X3)) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2404])).
% 89.60/14.05 thf(f2404,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($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) => (v9 @ Y11)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y0)))))) | (v21 @ X3))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2403,f358])).
% 89.60/14.05 thf(f2403,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y11)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y0)))))) | (v21 @ X3))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2402])).
% 89.60/14.05 thf(f2402,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y12)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y1)))))) | (v21 @ Y0)))) @ X3) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2310])).
% 89.60/14.05 thf(f2310,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($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) => (v9 @ Y12)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y1)))))) | (v21 @ Y0))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2309])).
% 89.60/14.05 thf(f2309,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y12)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y1)))))) | (v21 @ Y0)))))) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2308,f358])).
% 89.60/14.05 thf(f2308,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($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) => (v9 @ Y12)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y1)))))) | (v21 @ Y0)))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2307])).
% 89.60/14.05 thf(f2307,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y13)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y2)))))) | (v21 @ Y1))))))) @ X2))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f2302])).
% 89.60/14.05 thf(f2302,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y13)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y2)))))) | (v21 @ Y1)))))))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f2301])).
% 89.60/14.05 thf(f2301,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($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) => (v9 @ Y13)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y2)))))) | (v21 @ Y1))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f2300,f358])).
% 89.60/14.05 thf(f2300,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : ((((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) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ 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)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y2)))))) | (v21 @ Y1))))))))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f2297])).
% 89.60/14.05 thf(f2297,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : (($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) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ 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)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y3)))))) | (v21 @ Y2)))))))))) @ X1))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f1847])).
% 89.60/14.05 thf(f1847,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ 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)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y3)))))) | (v21 @ Y2))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1846])).
% 89.60/14.05 thf(f1846,plain,(
% 89.60/14.05 ( ! [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) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ 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)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y3)))))) | (v21 @ Y2))))))))))) | $false) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1842])).
% 89.60/14.05 thf(f1842,plain,(
% 89.60/14.05 ( ! [X0 : mworld] : (($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) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ 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)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y3)))))) | (v21 @ Y2))))))))))) | (~ $true)))) )),
% 89.60/14.05 inference(superposition,[status(thm)],[f575,f1822])).
% 89.60/14.05 thf(f1822,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($true = (v24 @ (sK4 @ X4)))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f1821])).
% 89.60/14.05 thf(f1821,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : ((((v24 @ (sK4 @ X4)) & $true) = $true)) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f1820,f358])).
% 89.60/14.05 thf(f1820,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($true = ((v24 @ (sK4 @ X4)) & (mrel @ X4 @ (sK4 @ X4))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f1819])).
% 89.60/14.05 thf(f1819,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : ((((^[Y0 : mworld]: ((v24 @ Y0) & (mrel @ X4 @ Y0))) @ (sK4 @ X4)) = $true)) )),
% 89.60/14.05 inference(sigma_clausification,[status(thm)],[f1812])).
% 89.60/14.05 thf(f1812,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((v24 @ Y0) & (mrel @ X4 @ Y0)))))) )),
% 89.60/14.05 inference(binary_proxy_clausification,[status(thm)],[f1803])).
% 89.60/14.05 thf(f575,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y14)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y3)))))) | (v21 @ Y2))))))))))) | (~ (v24 @ X5))) = $true)) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f574])).
% 89.60/14.05 thf(f574,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($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)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y3)))))) | (v21 @ Y2))))))))))) | (~ (v24 @ X5)))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f573,f358])).
% 89.60/14.05 thf(f573,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y14)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y3)))))) | (v21 @ Y2))))))))))) | (~ (v24 @ X5)))) = $true)) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f572])).
% 89.60/14.05 thf(f572,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($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) => (v9 @ Y15)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y4)))))) | (v21 @ Y3))))))))))) | (~ (v24 @ Y0))))) @ X5))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f571])).
% 89.60/14.05 thf(f571,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v9 @ Y15)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y4)))))) | (v21 @ Y3))))))))))) | (~ (v24 @ Y0)))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f570])).
% 89.60/14.05 thf(f570,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v9 @ Y15)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y4)))))) | (v21 @ Y3))))))))))) | (~ (v24 @ Y0))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f569,f358])).
% 89.60/14.05 thf(f569,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($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)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y4)))))) | (v21 @ Y3))))))))))) | (~ (v24 @ Y0))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f568])).
% 89.60/14.05 thf(f568,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v9 @ Y16)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y5)))))) | (v21 @ Y4))))))))))) | (~ (v24 @ Y1)))))))) @ X4))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f567])).
% 89.60/14.05 thf(f567,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (($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)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y5)))))) | (v21 @ Y4))))))))))) | (~ (v24 @ Y1))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f566])).
% 89.60/14.05 thf(f566,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y16)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y5)))))) | (v21 @ Y4))))))))))) | (~ (v24 @ Y1)))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f565,f358])).
% 89.60/14.05 thf(f565,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y16)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y5)))))) | (v21 @ Y4))))))))))) | (~ (v24 @ Y1)))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f564])).
% 89.60/14.05 thf(f564,plain,(
% 89.60/14.05 ( ! [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)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y6)))))) | (v21 @ Y5))))))))))) | (~ (v24 @ Y2))))))))))) @ X3) = $true)) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f563])).
% 89.60/14.05 thf(f563,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($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)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y6)))))) | (v21 @ Y5))))))))))) | (~ (v24 @ Y2)))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f562])).
% 89.60/14.05 thf(f562,plain,(
% 89.60/14.05 ( ! [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) => (v9 @ Y17)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y6)))))) | (v21 @ Y5))))))))))) | (~ (v24 @ Y2))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f561,f358])).
% 89.60/14.05 thf(f561,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v9 @ Y17)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y6)))))) | (v21 @ Y5))))))))))) | (~ (v24 @ Y2))))))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f560])).
% 89.60/14.05 thf(f560,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($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) => (v9 @ Y18)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y7)))))) | (v21 @ Y6))))))))))) | (~ (v24 @ Y3)))))))))))))) @ X2))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f559])).
% 89.60/14.05 thf(f559,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v9 @ Y18)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y7)))))) | (v21 @ Y6))))))))))) | (~ (v24 @ Y3))))))))))))))))) )),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f558])).
% 89.60/14.05 thf(f558,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v9 @ Y18)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y7)))))) | (v21 @ Y6))))))))))) | (~ (v24 @ Y3)))))))))))))))))) )),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f557,f358])).
% 89.60/14.05 thf(f557,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($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) => (v9 @ Y18)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y7)))))) | (v21 @ Y6))))))))))) | (~ (v24 @ Y3)))))))))))))))))) )),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f556])).
% 89.60/14.05 thf(f556,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v9 @ Y19)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y8)))))) | (v21 @ Y7))))))))))) | (~ (v24 @ Y4))))))))))))))))) @ X1))) )),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f328])).
% 89.60/14.05 thf(f328,plain,(
% 89.60/14.05 ($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)))))))))))))))))))))))))))))))))) | (~ (v20 @ Y8)))))) | (v21 @ Y7))))))))))) | (~ (v24 @ Y4)))))))))))))))))))),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f250])).
% 89.60/14.05 thf(f250,plain,(
% 89.60/14.05 ($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))))))) @ ((^[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]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v21 @ ((^[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))))) @ v20) @ ((^[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))))))) @ v9)))))))))))))))))))))))))),
% 89.60/14.05 inference(definition_unfolding,[status(thm)],[f190,f226,f239,f239,f239,f239,f239,f201,f213,f239,f239,f239,f201,f239,f201,f213,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239])).
% 89.60/14.05 thf(f190,plain,(
% 89.60/14.05 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v24) @ (mbox @ (mbox @ (mbox @ (mor @ v21 @ (mbox @ (mor @ (mnot @ v20) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v9)))))))))))))))))))))))) = $true)),
% 89.60/14.05 inference(cnf_transformation,[status(thm)],[f99])).
% 89.60/14.05 thf(f99,plain,(
% 89.60/14.05 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v24) @ (mbox @ (mbox @ (mbox @ (mor @ v21 @ (mbox @ (mor @ (mnot @ v20) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v9)))))))))))))))))))))))) = $true)),
% 89.60/14.05 inference(fool_elimination,[status(thm)],[f98])).
% 89.60/14.05 thf(f98,plain,(
% 89.60/14.05 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v24) @ (mbox @ (mbox @ (mbox @ (mor @ v21 @ (mbox @ (mor @ (mnot @ v20) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v9))))))))))))))))))))))))),
% 89.60/14.05 inference(rectify,[status(thm)],[f38])).
% 89.60/14.05 thf(f38,axiom,(
% 89.60/14.05 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v24) @ (mbox @ (mbox @ (mbox @ (mor @ v21 @ (mbox @ (mor @ (mnot @ v20) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v9))))))))))))))))))))))))),
% 89.60/14.05 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod29)).
% 89.60/14.05 thf(f3354,plain,(
% 89.60/14.05 ~spl0_15 | ~spl0_22),
% 89.60/14.05 inference(avatar_contradiction_clause,[status(thm)],[f3353])).
% 89.60/14.05 thf(f3353,plain,(
% 89.60/14.05 $false | (~spl0_15 | ~spl0_22)),
% 89.60/14.05 inference(trivial_inequality_removal,[status(thm)],[f3352])).
% 89.60/14.05 thf(f3352,plain,(
% 89.60/14.05 ($false = $true) | (~spl0_15 | ~spl0_22)),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3351])).
% 89.60/14.05 thf(f3351,plain,(
% 89.60/14.05 ($true = (~ $true)) | (~spl0_15 | ~spl0_22)),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3350,f2986])).
% 89.60/14.05 thf(f3350,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (((~ (v10 @ X5)) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3349])).
% 89.60/14.05 thf(f3349,plain,(
% 89.60/14.05 ( ! [X5 : mworld] : (($true = ($true => (~ (v10 @ X5))))) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3348,f358])).
% 89.60/14.05 thf(f3348,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : ((((mrel @ X4 @ X5) => (~ (v10 @ X5))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3347])).
% 89.60/14.05 thf(f3347,plain,(
% 89.60/14.05 ( ! [X4 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (~ (v10 @ Y0)))) @ X5))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3346])).
% 89.60/14.05 thf(f3346,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (~ (v10 @ Y0))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3345])).
% 89.60/14.05 thf(f3345,plain,(
% 89.60/14.05 ( ! [X4 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (~ (v10 @ Y0)))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3344,f358])).
% 89.60/14.05 thf(f3344,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($true = ((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (~ (v10 @ Y0)))))))) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3343])).
% 89.60/14.05 thf(f3343,plain,(
% 89.60/14.05 ( ! [X3 : mworld,X4 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v10 @ Y1))))))) @ X4))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3342])).
% 89.60/14.05 thf(f3342,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v10 @ Y1)))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3341])).
% 89.60/14.05 thf(f3341,plain,(
% 89.60/14.05 ( ! [X3 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v10 @ Y1))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3340,f358])).
% 89.60/14.05 thf(f3340,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X3 : mworld] : (($true = ((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v10 @ Y1))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3339])).
% 89.60/14.05 thf(f3339,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X3 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v10 @ Y2)))))))))) @ X3) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3338])).
% 89.60/14.05 thf(f3338,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v10 @ Y2))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3337])).
% 89.60/14.05 thf(f3337,plain,(
% 89.60/14.05 ( ! [X2 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v10 @ Y2)))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3336,f358])).
% 89.60/14.05 thf(f3336,plain,(
% 89.60/14.05 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v10 @ Y2)))))))))))))) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3335])).
% 89.60/14.05 thf(f3335,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y3))))))))))))) @ X2))) ) | ~spl0_22),
% 89.60/14.05 inference(pi_clausification,[status(thm)],[f3334])).
% 89.60/14.05 thf(f3334,plain,(
% 89.60/14.05 ( ! [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) => (~ (v10 @ Y3)))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(boolean_simplification,[status(thm)],[f3333])).
% 89.60/14.05 thf(f3333,plain,(
% 89.60/14.05 ( ! [X1 : mworld] : ((($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) => (~ (v10 @ Y3))))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(forward_demodulation,[status(thm)],[f3332,f358])).
% 89.60/14.05 thf(f3332,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ (sK15 @ 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) => (~ (v10 @ Y3))))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.05 inference(beta_eta_normalization,[status(thm)],[f3329])).
% 89.60/14.05 thf(f3329,plain,(
% 89.60/14.05 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK15 @ 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) => (~ (v10 @ Y4)))))))))))))))) @ X1))) ) | ~spl0_22),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f3326])).
% 89.60/14.06 thf(f3326,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK15 @ 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) => (~ (v10 @ Y4))))))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f3325])).
% 89.60/14.06 thf(f3325,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK15 @ 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) => (~ (v10 @ Y4))))))))))))))))) | $false) = $true)) ) | ~spl0_22),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f3324])).
% 89.60/14.06 thf(f3324,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK15 @ 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) => (~ (v10 @ Y4))))))))))))))))) | (~ $true)) = $true)) ) | ~spl0_22),
% 89.60/14.06 inference(superposition,[status(thm)],[f3321,f2336])).
% 89.60/14.06 thf(f3321,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (($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) => (~ (v10 @ Y4))))))))))))))))) | (~ (v15 @ X6))))) ) | ~spl0_22),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f3320])).
% 89.60/14.06 thf(f3320,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y4))))))))))))))))) | (~ (v15 @ X6)))) = $true)) ) | ~spl0_22),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f3319,f358])).
% 89.60/14.06 thf(f3319,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y4))))))))))))))))) | (~ (v15 @ X6)))) = $true)) ) | ~spl0_22),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f3318])).
% 89.60/14.06 thf(f3318,plain,(
% 89.60/14.06 ( ! [X6 : mworld,X5 : mworld] : (($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) => (~ (v10 @ Y5))))))))))))))))) | (~ (v15 @ Y0))))) @ X6))) ) | ~spl0_22),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f3317])).
% 89.60/14.06 thf(f3317,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v10 @ Y5))))))))))))))))) | (~ (v15 @ Y0)))))))) ) | ~spl0_22),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f3316])).
% 89.60/14.06 thf(f3316,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : (($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) => (~ (v10 @ Y5))))))))))))))))) | (~ (v15 @ Y0))))))))) ) | ~spl0_22),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f3315,f358])).
% 89.60/14.06 thf(f3315,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y5))))))))))))))))) | (~ (v15 @ Y0))))))) = $true)) ) | ~spl0_22),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f3314])).
% 89.60/14.06 thf(f3314,plain,(
% 89.60/14.06 ( ! [X4 : mworld,X5 : mworld] : (($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) => (~ (v10 @ Y6))))))))))))))))) | (~ (v15 @ Y1)))))))) @ X5))) ) | ~spl0_22),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f3313])).
% 89.60/14.06 thf(f3313,plain,(
% 89.60/14.06 ( ! [X4 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v10 @ Y6))))))))))))))))) | (~ (v15 @ Y1))))))))))) ) | ~spl0_22),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f3312])).
% 89.60/14.06 thf(f3312,plain,(
% 89.60/14.06 ( ! [X4 : mworld] : ((($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) => (~ (v10 @ Y6))))))))))))))))) | (~ (v15 @ Y1)))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f3311,f358])).
% 89.60/14.06 thf(f3311,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y6))))))))))))))))) | (~ (v15 @ Y1)))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f3310])).
% 89.60/14.06 thf(f3310,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y7))))))))))))))))) | (~ (v15 @ Y2))))))))))) @ X4) = $true)) ) | ~spl0_22),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f3309])).
% 89.60/14.06 thf(f3309,plain,(
% 89.60/14.06 ( ! [X3 : mworld] : (($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) => (~ (v10 @ Y7))))))))))))))))) | (~ (v15 @ Y2)))))))))))))) ) | ~spl0_22),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f3308])).
% 89.60/14.06 thf(f3308,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y7))))))))))))))))) | (~ (v15 @ Y2))))))))))))))) ) | ~spl0_22),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f3307,f358])).
% 89.60/14.06 thf(f3307,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y7))))))))))))))))) | (~ (v15 @ Y2))))))))))))) = $true)) ) | ~spl0_22),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f3306])).
% 89.60/14.06 thf(f3306,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X3 : mworld] : (($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) => (~ (v10 @ Y8))))))))))))))))) | (~ (v15 @ Y3)))))))))))))) @ X3))) ) | ~spl0_22),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f3301])).
% 89.60/14.06 thf(f3305,plain,(
% 89.60/14.06 spl0_22 | spl0_23),
% 89.60/14.06 inference(avatar_split_clause,[status(thm)],[f3298,f3303,f3300])).
% 89.60/14.06 thf(f3298,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X1 : mworld] : (($true = (v20 @ X1)) | ($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) => (~ (v10 @ Y8))))))))))))))))) | (~ (v15 @ Y3))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f3297])).
% 89.60/14.06 thf(f3297,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X1 : mworld] : (($true = (v20 @ X1)) | ($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v10 @ Y8))))))))))))))))) | (~ (v15 @ Y3)))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f3295,f358])).
% 89.60/14.06 thf(f3295,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X1 : mworld] : (($true = (v20 @ X1)) | ($true = ((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v10 @ Y8))))))))))))))))) | (~ (v15 @ Y3)))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f3293])).
% 89.60/14.06 thf(f3293,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X1 : mworld] : (($true = (v20 @ X1)) | ($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) => (~ (v10 @ Y9))))))))))))))))) | (~ (v15 @ Y4))))))))))))))))) @ X2))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2042])).
% 89.60/14.06 thf(f2042,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y9))))))))))))))))) | (~ (v15 @ Y4)))))))))))))))))) = $true) | ($true = (v20 @ X1))) )),
% 89.60/14.06 inference(binary_proxy_clausification,[status(thm)],[f2037])).
% 89.60/14.06 thf(f2037,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v10 @ Y9))))))))))))))))) | (~ (v15 @ Y4)))))))))))))))))) | (v20 @ X1)))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2036])).
% 89.60/14.06 thf(f2036,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : ((($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) => (~ (v10 @ Y9))))))))))))))))) | (~ (v15 @ Y4)))))))))))))))))) | (v20 @ X1))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2035,f358])).
% 89.60/14.06 thf(f2035,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : (($true = ((mrel @ (sK7 @ 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) => (~ (v10 @ Y9))))))))))))))))) | (~ (v15 @ Y4)))))))))))))))))) | (v20 @ X1))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2032])).
% 89.60/14.06 thf(f2032,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK7 @ 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) => (~ (v10 @ Y10))))))))))))))))) | (~ (v15 @ Y5)))))))))))))))))) | (v20 @ Y0)))) @ X1))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1927])).
% 89.60/14.06 thf(f1927,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK7 @ 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) => (~ (v10 @ Y10))))))))))))))))) | (~ (v15 @ Y5)))))))))))))))))) | (v20 @ Y0))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1924])).
% 89.60/14.06 thf(f1924,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK7 @ 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) => (~ (v10 @ Y10))))))))))))))))) | (~ (v15 @ Y5)))))))))))))))))) | (v20 @ Y0))))) | $false) = $true)) )),
% 89.60/14.06 inference(superposition,[status(thm)],[f500,f1918])).
% 89.60/14.06 thf(f500,plain,(
% 89.60/14.06 ( ! [X8 : mworld] : (($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) => (~ (v10 @ Y10))))))))))))))))) | (~ (v15 @ Y5)))))))))))))))))) | (v20 @ Y0))))) | (v21 @ X8)))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f499])).
% 89.60/14.06 thf(f499,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y10))))))))))))))))) | (~ (v15 @ Y5)))))))))))))))))) | (v20 @ Y0))))) | (v21 @ X8))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f498,f358])).
% 89.60/14.06 thf(f498,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y10))))))))))))))))) | (~ (v15 @ Y5)))))))))))))))))) | (v20 @ Y0))))) | (v21 @ X8))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f497])).
% 89.60/14.06 thf(f497,plain,(
% 89.60/14.06 ( ! [X8 : mworld,X7 : mworld] : (($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) => (~ (v10 @ Y11))))))))))))))))) | (~ (v15 @ Y6)))))))))))))))))) | (v20 @ Y1))))) | (v21 @ Y0)))) @ X8))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f496])).
% 89.60/14.06 thf(f496,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v10 @ Y11))))))))))))))))) | (~ (v15 @ Y6)))))))))))))))))) | (v20 @ Y1))))) | (v21 @ Y0))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f495])).
% 89.60/14.06 thf(f495,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : (($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) => (~ (v10 @ Y11))))))))))))))))) | (~ (v15 @ Y6)))))))))))))))))) | (v20 @ Y1))))) | (v21 @ Y0)))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f494,f358])).
% 89.60/14.06 thf(f494,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y11))))))))))))))))) | (~ (v15 @ Y6)))))))))))))))))) | (v20 @ Y1))))) | (v21 @ Y0)))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f493])).
% 89.60/14.06 thf(f493,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y12))))))))))))))))) | (~ (v15 @ Y7)))))))))))))))))) | (v20 @ Y2))))) | (v21 @ Y1))))))) @ X7) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f492])).
% 89.60/14.06 thf(f492,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y12))))))))))))))))) | (~ (v15 @ Y7)))))))))))))))))) | (v20 @ Y2))))) | (v21 @ Y1)))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f491])).
% 89.60/14.06 thf(f491,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : ((($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) => (~ (v10 @ Y12))))))))))))))))) | (~ (v15 @ Y7)))))))))))))))))) | (v20 @ Y2))))) | (v21 @ Y1))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f490,f358])).
% 89.60/14.06 thf(f490,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y12))))))))))))))))) | (~ (v15 @ Y7)))))))))))))))))) | (v20 @ Y2))))) | (v21 @ Y1))))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f489])).
% 89.60/14.06 thf(f489,plain,(
% 89.60/14.06 ( ! [X6 : mworld,X5 : mworld] : (($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) => (~ (v10 @ Y13))))))))))))))))) | (~ (v15 @ Y8)))))))))))))))))) | (v20 @ Y3))))) | (v21 @ Y2)))))))))) @ X6))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f488])).
% 89.60/14.06 thf(f488,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v10 @ Y13))))))))))))))))) | (~ (v15 @ Y8)))))))))))))))))) | (v20 @ Y3))))) | (v21 @ Y2))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f487])).
% 89.60/14.06 thf(f487,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v10 @ Y13))))))))))))))))) | (~ (v15 @ Y8)))))))))))))))))) | (v20 @ Y3))))) | (v21 @ Y2)))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f486,f358])).
% 89.60/14.06 thf(f486,plain,(
% 89.60/14.06 ( ! [X4 : mworld,X5 : mworld] : (($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) => (~ (v10 @ Y13))))))))))))))))) | (~ (v15 @ Y8)))))))))))))))))) | (v20 @ Y3))))) | (v21 @ Y2)))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f485])).
% 89.60/14.06 thf(f485,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y14))))))))))))))))) | (~ (v15 @ Y9)))))))))))))))))) | (v20 @ Y4))))) | (v21 @ Y3))))))))))))) @ X5) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f484])).
% 89.60/14.06 thf(f484,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y14))))))))))))))))) | (~ (v15 @ Y9)))))))))))))))))) | (v20 @ Y4))))) | (v21 @ Y3)))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f483])).
% 89.60/14.06 thf(f483,plain,(
% 89.60/14.06 ( ! [X4 : mworld] : (($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) => (~ (v10 @ Y14))))))))))))))))) | (~ (v15 @ Y9)))))))))))))))))) | (v20 @ Y4))))) | (v21 @ Y3))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f482,f358])).
% 89.60/14.06 thf(f482,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y14))))))))))))))))) | (~ (v15 @ Y9)))))))))))))))))) | (v20 @ Y4))))) | (v21 @ Y3))))))))))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f481])).
% 89.60/14.06 thf(f481,plain,(
% 89.60/14.06 ( ! [X3 : mworld,X4 : mworld] : (($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) => (~ (v10 @ Y15))))))))))))))))) | (~ (v15 @ Y10)))))))))))))))))) | (v20 @ Y5))))) | (v21 @ Y4)))))))))))))))) @ X4))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f480])).
% 89.60/14.06 thf(f480,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y15))))))))))))))))) | (~ (v15 @ Y10)))))))))))))))))) | (v20 @ Y5))))) | (v21 @ Y4))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f479])).
% 89.60/14.06 thf(f479,plain,(
% 89.60/14.06 ( ! [X3 : mworld] : (($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) => (~ (v10 @ Y15))))))))))))))))) | (~ (v15 @ Y10)))))))))))))))))) | (v20 @ Y5))))) | (v21 @ Y4)))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f478,f358])).
% 89.60/14.06 thf(f478,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y15))))))))))))))))) | (~ (v15 @ Y10)))))))))))))))))) | (v20 @ Y5))))) | (v21 @ Y4)))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f477])).
% 89.60/14.06 thf(f477,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y16))))))))))))))))) | (~ (v15 @ Y11)))))))))))))))))) | (v20 @ Y6))))) | (v21 @ Y5))))))))))))))))))) @ X3) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f476])).
% 89.60/14.06 thf(f476,plain,(
% 89.60/14.06 ( ! [X2 : mworld] : (($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) => (~ (v10 @ Y16))))))))))))))))) | (~ (v15 @ Y11)))))))))))))))))) | (v20 @ Y6))))) | (v21 @ Y5)))))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f475])).
% 89.60/14.06 thf(f475,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y16))))))))))))))))) | (~ (v15 @ Y11)))))))))))))))))) | (v20 @ Y6))))) | (v21 @ Y5))))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f474,f358])).
% 89.60/14.06 thf(f474,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y16))))))))))))))))) | (~ (v15 @ Y11)))))))))))))))))) | (v20 @ Y6))))) | (v21 @ Y5))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f473])).
% 89.60/14.06 thf(f473,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y17))))))))))))))))) | (~ (v15 @ Y12)))))))))))))))))) | (v20 @ Y7))))) | (v21 @ Y6)))))))))))))))))))))) @ X2) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f472])).
% 89.60/14.06 thf(f472,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($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) => (~ (v10 @ Y17))))))))))))))))) | (~ (v15 @ Y12)))))))))))))))))) | (v20 @ Y7))))) | (v21 @ Y6))))))))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f471])).
% 89.60/14.06 thf(f471,plain,(
% 89.60/14.06 ( ! [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) => (~ (v10 @ Y17))))))))))))))))) | (~ (v15 @ Y12)))))))))))))))))) | (v20 @ Y7))))) | (v21 @ Y6)))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f470,f358])).
% 89.60/14.06 thf(f470,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($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) => (~ (v10 @ Y17))))))))))))))))) | (~ (v15 @ Y12)))))))))))))))))) | (v20 @ Y7))))) | (v21 @ Y6)))))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f469])).
% 89.60/14.06 thf(f469,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (~ (v10 @ Y18))))))))))))))))) | (~ (v15 @ Y13)))))))))))))))))) | (v20 @ Y8))))) | (v21 @ Y7))))))))))))))))))))))))) @ X1))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f348])).
% 89.60/14.06 thf(f348,plain,(
% 89.60/14.06 ($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) => (~ (v10 @ Y18))))))))))))))))) | (~ (v15 @ Y13)))))))))))))))))) | (v20 @ Y8))))) | (v21 @ Y7)))))))))))))))))))))))))))),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f284])).
% 89.60/14.06 thf(f284,plain,(
% 89.60/14.06 ($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]: (!! @ 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))))))) @ v21 @ ((^[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))))))) @ v20 @ ((^[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]: (!! @ 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]: (~ (Y0 @ Y1))))) @ v10)))))))))))))))))))))))))),
% 89.60/14.06 inference(definition_unfolding,[status(thm)],[f231,f226,f239,f239,f239,f239,f239,f239,f239,f239,f201,f239,f201,f239,f239,f239,f239,f239,f201,f213,f239,f239,f239,f239,f239,f213])).
% 89.60/14.06 thf(f231,plain,(
% 89.60/14.06 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v21 @ (mbox @ (mor @ v20 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v15) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mnot @ v10)))))))))))))))))))))))) = $true)),
% 89.60/14.06 inference(cnf_transformation,[status(thm)],[f147])).
% 89.60/14.06 thf(f147,plain,(
% 89.60/14.06 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v21 @ (mbox @ (mor @ v20 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v15) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mnot @ v10)))))))))))))))))))))))) = $true)),
% 89.60/14.06 inference(fool_elimination,[status(thm)],[f146])).
% 89.60/14.06 thf(f146,plain,(
% 89.60/14.06 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v21 @ (mbox @ (mor @ v20 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v15) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mnot @ v10))))))))))))))))))))))))),
% 89.60/14.06 inference(rectify,[status(thm)],[f45])).
% 89.60/14.06 thf(f45,axiom,(
% 89.60/14.06 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v21 @ (mbox @ (mor @ v20 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v15) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mnot @ v10))))))))))))))))))))))))),
% 89.60/14.06 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod36)).
% 89.60/14.06 thf(f2969,plain,(
% 89.60/14.06 spl0_5),
% 89.60/14.06 inference(avatar_split_clause,[status(thm)],[f2760,f1067])).
% 89.60/14.06 thf(f1067,definition,(
% 89.60/14.06 spl0_5 <=> ! [X17 : mworld] : ($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) => (~ (v3 @ Y8))))))))))) | (v6 @ Y5)))))))))))))))))))) | (v12 @ X17)))),
% 89.60/14.06 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 89.60/14.06 thf(f2760,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v3 @ Y8))))))))))) | (v6 @ Y5)))))))))))))))))))) | (v12 @ X1)))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2759])).
% 89.60/14.06 thf(f2759,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : ((($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) => (~ (v3 @ Y8))))))))))) | (v6 @ Y5)))))))))))))))))))) | (v12 @ X1))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2757,f358])).
% 89.60/14.06 thf(f2757,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : (($true = ((mrel @ (sK19 @ 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) => (~ (v3 @ Y8))))))))))) | (v6 @ Y5)))))))))))))))))))) | (v12 @ X1))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2755])).
% 89.60/14.06 thf(f2755,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ (sK19 @ 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) => (~ (v3 @ Y9))))))))))) | (v6 @ Y6)))))))))))))))))))) | (v12 @ Y0)))) @ X1) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2726])).
% 89.60/14.06 thf(f2726,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK19 @ 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) => (~ (v3 @ Y9))))))))))) | (v6 @ Y6)))))))))))))))))))) | (v12 @ Y0))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2725])).
% 89.60/14.06 thf(f2725,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK19 @ 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) => (~ (v3 @ Y9))))))))))) | (v6 @ Y6)))))))))))))))))))) | (v12 @ Y0))))) | $false))) )),
% 89.60/14.06 inference(superposition,[status(thm)],[f1054,f2700])).
% 89.60/14.06 thf(f2700,plain,(
% 89.60/14.06 ( ! [X15 : mworld] : (((v13 @ (sK19 @ X15)) = $false)) )),
% 89.60/14.06 inference(not_proxy_clausification,[status(thm)],[f2659])).
% 89.60/14.06 thf(f2659,plain,(
% 89.60/14.06 ( ! [X15 : mworld] : (((~ (v13 @ (sK19 @ X15))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2658])).
% 89.60/14.06 thf(f2658,plain,(
% 89.60/14.06 ( ! [X15 : mworld] : (($true = ((~ (v13 @ (sK19 @ X15))) & $true))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2650,f358])).
% 89.60/14.06 thf(f2650,plain,(
% 89.60/14.06 ( ! [X15 : mworld] : ((((~ (v13 @ (sK19 @ X15))) & (mrel @ X15 @ (sK19 @ X15))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2649])).
% 89.60/14.06 thf(f2649,plain,(
% 89.60/14.06 ( ! [X15 : mworld] : (($true = ((^[Y0 : mworld]: ((~ (v13 @ Y0)) & (mrel @ X15 @ Y0))) @ (sK19 @ X15)))) )),
% 89.60/14.06 inference(sigma_clausification,[status(thm)],[f2641])).
% 89.60/14.06 thf(f1054,plain,(
% 89.60/14.06 ( ! [X16 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v3 @ Y9))))))))))) | (v6 @ Y6)))))))))))))))))))) | (v12 @ Y0))))) | (v13 @ X16)))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1053])).
% 89.60/14.06 thf(f1053,plain,(
% 89.60/14.06 ( ! [X16 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v3 @ Y9))))))))))) | (v6 @ Y6)))))))))))))))))))) | (v12 @ Y0))))) | (v13 @ X16))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1052,f358])).
% 89.60/14.06 thf(f1052,plain,(
% 89.60/14.06 ( ! [X16 : mworld,X15 : mworld] : (($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) => (~ (v3 @ Y9))))))))))) | (v6 @ Y6)))))))))))))))))))) | (v12 @ Y0))))) | (v13 @ X16))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1051])).
% 89.60/14.06 thf(f1051,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y10))))))))))) | (v6 @ Y7)))))))))))))))))))) | (v12 @ Y1))))) | (v13 @ Y0)))) @ X16) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1050])).
% 89.60/14.06 thf(f1050,plain,(
% 89.60/14.06 ( ! [X15 : mworld] : (($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) => (~ (v3 @ Y10))))))))))) | (v6 @ Y7)))))))))))))))))))) | (v12 @ Y1))))) | (v13 @ Y0))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1049])).
% 89.60/14.06 thf(f1049,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y10))))))))))) | (v6 @ Y7)))))))))))))))))))) | (v12 @ Y1))))) | (v13 @ Y0)))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1048,f358])).
% 89.60/14.06 thf(f1048,plain,(
% 89.60/14.06 ( ! [X14 : mworld,X15 : mworld] : (($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) => (~ (v3 @ Y10))))))))))) | (v6 @ Y7)))))))))))))))))))) | (v12 @ Y1))))) | (v13 @ Y0)))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1047])).
% 89.60/14.06 thf(f1047,plain,(
% 89.60/14.06 ( ! [X14 : mworld,X15 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v3 @ Y11))))))))))) | (v6 @ Y8)))))))))))))))))))) | (v12 @ Y2))))) | (v13 @ Y1))))))) @ X15))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1046])).
% 89.60/14.06 thf(f1046,plain,(
% 89.60/14.06 ( ! [X14 : mworld] : (($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) => (~ (v3 @ Y11))))))))))) | (v6 @ Y8)))))))))))))))))))) | (v12 @ Y2))))) | (v13 @ Y1)))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1045])).
% 89.60/14.06 thf(f1045,plain,(
% 89.60/14.06 ( ! [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) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v3 @ Y11))))))))))) | (v6 @ Y8)))))))))))))))))))) | (v12 @ Y2))))) | (v13 @ Y1))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1044,f358])).
% 89.60/14.06 thf(f1044,plain,(
% 89.60/14.06 ( ! [X14 : mworld,X13 : mworld] : (($true = ((mrel @ X13 @ X14) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v3 @ Y11))))))))))) | (v6 @ Y8)))))))))))))))))))) | (v12 @ Y2))))) | (v13 @ Y1))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1043])).
% 89.60/14.06 thf(f1043,plain,(
% 89.60/14.06 ( ! [X14 : mworld,X13 : mworld] : (($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) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v3 @ Y12))))))))))) | (v6 @ Y9)))))))))))))))))))) | (v12 @ Y3))))) | (v13 @ Y2)))))))))) @ X14))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1042])).
% 89.60/14.06 thf(f1042,plain,(
% 89.60/14.06 ( ! [X13 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v3 @ Y12))))))))))) | (v6 @ Y9)))))))))))))))))))) | (v12 @ Y3))))) | (v13 @ Y2))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1041])).
% 89.60/14.06 thf(f1041,plain,(
% 89.60/14.06 ( ! [X13 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v3 @ Y12))))))))))) | (v6 @ Y9)))))))))))))))))))) | (v12 @ Y3))))) | (v13 @ Y2)))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1040,f358])).
% 89.60/14.06 thf(f1040,plain,(
% 89.60/14.06 ( ! [X12 : mworld,X13 : mworld] : (($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) => (~ (v3 @ Y12))))))))))) | (v6 @ Y9)))))))))))))))))))) | (v12 @ Y3))))) | (v13 @ Y2)))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1039])).
% 89.60/14.06 thf(f1039,plain,(
% 89.60/14.06 ( ! [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) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v3 @ Y13))))))))))) | (v6 @ Y10)))))))))))))))))))) | (v12 @ Y4))))) | (v13 @ Y3))))))))))))) @ X13) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1038])).
% 89.60/14.06 thf(f1038,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y13))))))))))) | (v6 @ Y10)))))))))))))))))))) | (v12 @ Y4))))) | (v13 @ Y3)))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1037])).
% 89.60/14.06 thf(f1037,plain,(
% 89.60/14.06 ( ! [X12 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v3 @ Y13))))))))))) | (v6 @ Y10)))))))))))))))))))) | (v12 @ Y4))))) | (v13 @ Y3))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1036,f358])).
% 89.60/14.06 thf(f1036,plain,(
% 89.60/14.06 ( ! [X11 : mworld,X12 : mworld] : (($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) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v3 @ Y13))))))))))) | (v6 @ Y10)))))))))))))))))))) | (v12 @ Y4))))) | (v13 @ Y3))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1035])).
% 89.60/14.06 thf(f1035,plain,(
% 89.60/14.06 ( ! [X11 : mworld,X12 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v3 @ Y14))))))))))) | (v6 @ Y11)))))))))))))))))))) | (v12 @ Y5))))) | (v13 @ Y4)))))))))))))))) @ X12))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1034])).
% 89.60/14.06 thf(f1034,plain,(
% 89.60/14.06 ( ! [X11 : mworld] : (($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) => (~ (v3 @ Y14))))))))))) | (v6 @ Y11)))))))))))))))))))) | (v12 @ Y5))))) | (v13 @ Y4))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1033])).
% 89.60/14.06 thf(f1033,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y14))))))))))) | (v6 @ Y11)))))))))))))))))))) | (v12 @ Y5))))) | (v13 @ Y4)))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1032,f358])).
% 89.60/14.06 thf(f1032,plain,(
% 89.60/14.06 ( ! [X10 : mworld,X11 : mworld] : (($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) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v3 @ Y14))))))))))) | (v6 @ Y11)))))))))))))))))))) | (v12 @ Y5))))) | (v13 @ Y4)))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1031])).
% 89.60/14.06 thf(f1031,plain,(
% 89.60/14.06 ( ! [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) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v3 @ Y15))))))))))) | (v6 @ Y12)))))))))))))))))))) | (v12 @ Y6))))) | (v13 @ Y5))))))))))))))))))) @ X11))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1030])).
% 89.60/14.06 thf(f1030,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y15))))))))))) | (v6 @ Y12)))))))))))))))))))) | (v12 @ Y6))))) | (v13 @ Y5)))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1029])).
% 89.60/14.06 thf(f1029,plain,(
% 89.60/14.06 ( ! [X10 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v3 @ Y15))))))))))) | (v6 @ Y12)))))))))))))))))))) | (v12 @ Y6))))) | (v13 @ Y5))))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1028,f358])).
% 89.60/14.06 thf(f1028,plain,(
% 89.60/14.06 ( ! [X10 : mworld,X9 : mworld] : (($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) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v3 @ Y15))))))))))) | (v6 @ Y12)))))))))))))))))))) | (v12 @ Y6))))) | (v13 @ Y5))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1027])).
% 89.60/14.06 thf(f1027,plain,(
% 89.60/14.06 ( ! [X10 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (~ (v3 @ Y16))))))))))) | (v6 @ Y13)))))))))))))))))))) | (v12 @ Y7))))) | (v13 @ Y6)))))))))))))))))))))) @ X10))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1026])).
% 89.60/14.06 thf(f1026,plain,(
% 89.60/14.06 ( ! [X9 : mworld] : (($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) => (~ (v3 @ Y16))))))))))) | (v6 @ Y13)))))))))))))))))))) | (v12 @ Y7))))) | (v13 @ Y6))))))))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1025])).
% 89.60/14.06 thf(f1025,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y16))))))))))) | (v6 @ Y13)))))))))))))))))))) | (v12 @ Y7))))) | (v13 @ Y6)))))))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1024,f358])).
% 89.60/14.06 thf(f1024,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y16))))))))))) | (v6 @ Y13)))))))))))))))))))) | (v12 @ Y7))))) | (v13 @ Y6)))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1023])).
% 89.60/14.06 thf(f1023,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y17))))))))))) | (v6 @ Y14)))))))))))))))))))) | (v12 @ Y8))))) | (v13 @ Y7))))))))))))))))))))))))) @ X9) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1022])).
% 89.60/14.06 thf(f1022,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y17))))))))))) | (v6 @ Y14)))))))))))))))))))) | (v12 @ Y8))))) | (v13 @ Y7)))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1021])).
% 89.60/14.06 thf(f1021,plain,(
% 89.60/14.06 ( ! [X8 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (~ (v3 @ Y17))))))))))) | (v6 @ Y14)))))))))))))))))))) | (v12 @ Y8))))) | (v13 @ Y7))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1020,f358])).
% 89.60/14.06 thf(f1020,plain,(
% 89.60/14.06 ( ! [X8 : mworld,X7 : mworld] : (($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) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (~ (v3 @ Y17))))))))))) | (v6 @ Y14)))))))))))))))))))) | (v12 @ Y8))))) | (v13 @ Y7))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1019])).
% 89.60/14.06 thf(f1019,plain,(
% 89.60/14.06 ( ! [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) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (~ (v3 @ Y18))))))))))) | (v6 @ Y15)))))))))))))))))))) | (v12 @ Y9))))) | (v13 @ Y8)))))))))))))))))))))))))))) @ X8))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1018])).
% 89.60/14.06 thf(f1018,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y18))))))))))) | (v6 @ Y15)))))))))))))))))))) | (v12 @ Y9))))) | (v13 @ Y8))))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1017])).
% 89.60/14.06 thf(f1017,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (~ (v3 @ Y18))))))))))) | (v6 @ Y15)))))))))))))))))))) | (v12 @ Y9))))) | (v13 @ Y8)))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1016,f358])).
% 89.60/14.06 thf(f1016,plain,(
% 89.60/14.06 ( ! [X6 : mworld,X7 : mworld] : (($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) => (~ (v3 @ Y18))))))))))) | (v6 @ Y15)))))))))))))))))))) | (v12 @ Y9))))) | (v13 @ Y8)))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1015])).
% 89.60/14.06 thf(f1015,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y19))))))))))) | (v6 @ Y16)))))))))))))))))))) | (v12 @ Y10))))) | (v13 @ Y9))))))))))))))))))))))))))))))) @ X7) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1014])).
% 89.60/14.06 thf(f1014,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (($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) => (~ (v3 @ Y19))))))))))) | (v6 @ Y16)))))))))))))))))))) | (v12 @ Y10))))) | (v13 @ Y9)))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1013])).
% 89.60/14.06 thf(f1013,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y19))))))))))) | (v6 @ Y16)))))))))))))))))))) | (v12 @ Y10))))) | (v13 @ Y9))))))))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1012,f358])).
% 89.60/14.06 thf(f1012,plain,(
% 89.60/14.06 ( ! [X6 : mworld,X5 : mworld] : (($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) => (~ (v3 @ Y19))))))))))) | (v6 @ Y16)))))))))))))))))))) | (v12 @ Y10))))) | (v13 @ Y9))))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1011])).
% 89.60/14.06 thf(f1011,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y20))))))))))) | (v6 @ Y17)))))))))))))))))))) | (v12 @ Y11))))) | (v13 @ Y10)))))))))))))))))))))))))))))))))) @ X6) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1010])).
% 89.60/14.06 thf(f1010,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : (($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) => (~ (v3 @ Y20))))))))))) | (v6 @ Y17)))))))))))))))))))) | (v12 @ Y11))))) | (v13 @ Y10))))))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1009])).
% 89.60/14.06 thf(f1009,plain,(
% 89.60/14.06 ( ! [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) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ 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) => (~ (v3 @ Y20))))))))))) | (v6 @ Y17)))))))))))))))))))) | (v12 @ Y11))))) | (v13 @ Y10)))))))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1008,f358])).
% 89.60/14.06 thf(f1008,plain,(
% 89.60/14.06 ( ! [X4 : mworld,X5 : mworld] : (($true = ((mrel @ X4 @ X5) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (~ (v3 @ Y20))))))))))) | (v6 @ Y17)))))))))))))))))))) | (v12 @ Y11))))) | (v13 @ Y10)))))))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1007])).
% 89.60/14.06 thf(f1007,plain,(
% 89.60/14.06 ( ! [X4 : mworld,X5 : mworld] : (($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) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (~ (v3 @ Y21))))))))))) | (v6 @ Y18)))))))))))))))))))) | (v12 @ Y12))))) | (v13 @ Y11))))))))))))))))))))))))))))))))))))) @ X5))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1006])).
% 89.60/14.06 thf(f1006,plain,(
% 89.60/14.06 ( ! [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) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (~ (v3 @ Y21))))))))))) | (v6 @ Y18)))))))))))))))))))) | (v12 @ Y12))))) | (v13 @ Y11)))))))))))))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1005])).
% 89.60/14.06 thf(f1005,plain,(
% 89.60/14.06 ( ! [X4 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (~ (v3 @ Y21))))))))))) | (v6 @ Y18)))))))))))))))))))) | (v12 @ Y12))))) | (v13 @ Y11))))))))))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1004,f358])).
% 89.60/14.06 thf(f1004,plain,(
% 89.60/14.06 ( ! [X3 : mworld,X4 : mworld] : (($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) => (!! @ 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) => (~ (v3 @ Y21))))))))))) | (v6 @ Y18)))))))))))))))))))) | (v12 @ Y12))))) | (v13 @ Y11))))))))))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1003])).
% 89.60/14.06 thf(f1003,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y22))))))))))) | (v6 @ Y19)))))))))))))))))))) | (v12 @ Y13))))) | (v13 @ Y12)))))))))))))))))))))))))))))))))))))))) @ X4) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1002])).
% 89.60/14.06 thf(f1002,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y22))))))))))) | (v6 @ Y19)))))))))))))))))))) | (v12 @ Y13))))) | (v13 @ Y12))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1001])).
% 89.60/14.06 thf(f1001,plain,(
% 89.60/14.06 ( ! [X3 : mworld] : (($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) => (~ (v3 @ Y22))))))))))) | (v6 @ Y19)))))))))))))))))))) | (v12 @ Y13))))) | (v13 @ Y12)))))))))))))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1000,f358])).
% 89.60/14.06 thf(f1000,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y22))))))))))) | (v6 @ Y19)))))))))))))))))))) | (v12 @ Y13))))) | (v13 @ Y12)))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f999])).
% 89.60/14.06 thf(f999,plain,(
% 89.60/14.06 ( ! [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) => (!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (~ (v3 @ Y23))))))))))) | (v6 @ Y20)))))))))))))))))))) | (v12 @ Y14))))) | (v13 @ Y13))))))))))))))))))))))))))))))))))))))))))) @ X3) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f998])).
% 89.60/14.06 thf(f998,plain,(
% 89.60/14.06 ( ! [X2 : mworld] : (($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) => (~ (v3 @ Y23))))))))))) | (v6 @ Y20)))))))))))))))))))) | (v12 @ Y14))))) | (v13 @ Y13)))))))))))))))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f997])).
% 89.60/14.06 thf(f997,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y23))))))))))) | (v6 @ Y20)))))))))))))))))))) | (v12 @ Y14))))) | (v13 @ Y13))))))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f996,f358])).
% 89.60/14.06 thf(f996,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X1 : mworld] : (($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) => (~ (v3 @ Y23))))))))))) | (v6 @ Y20)))))))))))))))))))) | (v12 @ Y14))))) | (v13 @ Y13))))))))))))))))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f995])).
% 89.60/14.06 thf(f995,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y24))))))))))) | (v6 @ Y21)))))))))))))))))))) | (v12 @ Y15))))) | (v13 @ Y14)))))))))))))))))))))))))))))))))))))))))))))) @ X2))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f994])).
% 89.60/14.06 thf(f994,plain,(
% 89.60/14.06 ( ! [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) => (!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (~ (v3 @ Y24))))))))))) | (v6 @ Y21)))))))))))))))))))) | (v12 @ Y15))))) | (v13 @ Y14))))))))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f993])).
% 89.60/14.06 thf(f993,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($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) => (!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (~ (v3 @ Y24))))))))))) | (v6 @ Y21)))))))))))))))))))) | (v12 @ Y15))))) | (v13 @ Y14)))))))))))))))))))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f992,f358])).
% 89.60/14.06 thf(f992,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y24))))))))))) | (v6 @ Y21)))))))))))))))))))) | (v12 @ Y15))))) | (v13 @ Y14)))))))))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f991])).
% 89.60/14.06 thf(f991,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y25))))))))))) | (v6 @ Y22)))))))))))))))))))) | (v12 @ Y16))))) | (v13 @ Y15))))))))))))))))))))))))))))))))))))))))))))))))) @ X1) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f355])).
% 89.60/14.06 thf(f355,plain,(
% 89.60/14.06 ((!! @ 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) => (~ (v3 @ Y25))))))))))) | (v6 @ Y22)))))))))))))))))))) | (v12 @ Y16))))) | (v13 @ Y15)))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f246])).
% 89.60/14.06 thf(f246,plain,(
% 89.60/14.06 ($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]: (!! @ 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))))))) @ v13 @ ((^[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))))))) @ v12 @ ((^[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))))))) @ 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))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3))))))))))))))))))))))))))))))))),
% 89.60/14.06 inference(definition_unfolding,[status(thm)],[f185,f226,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f201,f239,f201,f239,f239,f239,f239,f239,f239,f201,f239,f239,f239,f213])).
% 89.60/14.06 thf(f185,plain,(
% 89.60/14.06 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v13 @ (mbox @ (mor @ v12 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v6 @ (mbox @ (mbox @ (mbox @ (mnot @ v3))))))))))))))))))))))))))))))) = $true)),
% 89.60/14.06 inference(cnf_transformation,[status(thm)],[f174])).
% 89.60/14.06 thf(f174,plain,(
% 89.60/14.06 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v13 @ (mbox @ (mor @ v12 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v6 @ (mbox @ (mbox @ (mbox @ (mnot @ v3))))))))))))))))))))))))))))))) = $true)),
% 89.60/14.06 inference(fool_elimination,[status(thm)],[f173])).
% 89.60/14.06 thf(f173,plain,(
% 89.60/14.06 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v13 @ (mbox @ (mor @ v12 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v6 @ (mbox @ (mbox @ (mbox @ (mnot @ v3)))))))))))))))))))))))))))))))),
% 89.60/14.06 inference(rectify,[status(thm)],[f55])).
% 89.60/14.06 thf(f55,axiom,(
% 89.60/14.06 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v13 @ (mbox @ (mor @ v12 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v6 @ (mbox @ (mbox @ (mbox @ (mnot @ v3)))))))))))))))))))))))))))))))),
% 89.60/14.06 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod46)).
% 89.60/14.06 thf(f2968,plain,(
% 89.60/14.06 spl0_8 | ~spl0_5 | ~spl0_14),
% 89.60/14.06 inference(avatar_split_clause,[status(thm)],[f2715,f2675,f1067,f1324])).
% 89.60/14.06 thf(f1324,definition,(
% 89.60/14.06 spl0_8 <=> ! [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) => (~ (v3 @ Y7))))))))))) | (v6 @ Y4))))))))))))))))) = $true)),
% 89.60/14.06 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 89.60/14.06 thf(f2675,definition,(
% 89.60/14.06 spl0_14 <=> ! [X10 : mworld] : ($true = (~ (v12 @ X10)))),
% 89.60/14.06 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 89.60/14.06 thf(f2715,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y7))))))))))) | (v6 @ Y4))))))))))))))))) = $true)) ) | (~spl0_5 | ~spl0_14)),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2714])).
% 89.60/14.06 thf(f2714,plain,(
% 89.60/14.06 ( ! [X18 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v3 @ Y7))))))))))) | (v6 @ Y4)))))))))))))))))))) ) | (~spl0_5 | ~spl0_14)),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2713,f358])).
% 89.60/14.06 thf(f2713,plain,(
% 89.60/14.06 ( ! [X18 : mworld,X17 : mworld] : (($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) => (~ (v3 @ Y7))))))))))) | (v6 @ Y4)))))))))))))))))))) ) | (~spl0_5 | ~spl0_14)),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2712])).
% 89.60/14.06 thf(f2712,plain,(
% 89.60/14.06 ( ! [X18 : mworld,X17 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v3 @ Y8))))))))))) | (v6 @ Y5))))))))))))))))))) @ X18))) ) | (~spl0_5 | ~spl0_14)),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2688])).
% 89.60/14.06 thf(f2688,plain,(
% 89.60/14.06 ( ! [X17 : mworld] : (($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) => (~ (v3 @ Y8))))))))))) | (v6 @ Y5)))))))))))))))))))))) ) | (~spl0_5 | ~spl0_14)),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2685])).
% 89.60/14.06 thf(f2685,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y8))))))))))) | (v6 @ Y5)))))))))))))))))))) | $false) = $true)) ) | (~spl0_5 | ~spl0_14)),
% 89.60/14.06 inference(backward_demodulation,[status(thm)],[f1068,f2683])).
% 89.60/14.06 thf(f2683,plain,(
% 89.60/14.06 ( ! [X10 : mworld] : (($false = (v12 @ X10))) ) | ~spl0_14),
% 89.60/14.06 inference(not_proxy_clausification,[status(thm)],[f2676])).
% 89.60/14.06 thf(f2676,plain,(
% 89.60/14.06 ( ! [X10 : mworld] : (($true = (~ (v12 @ X10)))) ) | ~spl0_14),
% 89.60/14.06 inference(avatar_component_clause,[status(thm)],[f2675])).
% 89.60/14.06 thf(f1068,plain,(
% 89.60/14.06 ( ! [X17 : mworld] : (($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) => (~ (v3 @ Y8))))))))))) | (v6 @ Y5)))))))))))))))))))) | (v12 @ X17)))) ) | ~spl0_5),
% 89.60/14.06 inference(avatar_component_clause,[status(thm)],[f1067])).
% 89.60/14.06 thf(f2967,plain,(
% 89.60/14.06 ~spl0_7 | ~spl0_14),
% 89.60/14.06 inference(avatar_contradiction_clause,[status(thm)],[f2966])).
% 89.60/14.06 thf(f2966,plain,(
% 89.60/14.06 $false | (~spl0_7 | ~spl0_14)),
% 89.60/14.06 inference(trivial_inequality_removal,[status(thm)],[f2965])).
% 89.60/14.06 thf(f2965,plain,(
% 89.60/14.06 ($false = $true) | (~spl0_7 | ~spl0_14)),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1322,f2683])).
% 89.60/14.06 thf(f1322,plain,(
% 89.60/14.06 ( ! [X17 : mworld] : (($true = (v12 @ X17))) ) | ~spl0_7),
% 89.60/14.06 inference(avatar_component_clause,[status(thm)],[f1321])).
% 89.60/14.06 thf(f1321,definition,(
% 89.60/14.06 spl0_7 <=> ! [X17 : mworld] : ($true = (v12 @ X17))),
% 89.60/14.06 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 89.60/14.06 thf(f2964,plain,(
% 89.60/14.06 spl0_16 | spl0_17 | ~spl0_8),
% 89.60/14.06 inference(avatar_split_clause,[status(thm)],[f2957,f1324,f2962,f2959])).
% 89.60/14.06 thf(f2957,plain,(
% 89.60/14.06 ( ! [X24 : mworld,X23 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))))) | ((v6 @ X23) = $true)) ) | ~spl0_8),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2956])).
% 89.60/14.06 thf(f2956,plain,(
% 89.60/14.06 ( ! [X24 : mworld,X23 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))))) | ((v6 @ X23) = $true)) ) | ~spl0_8),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2954,f358])).
% 89.60/14.06 thf(f2954,plain,(
% 89.60/14.06 ( ! [X24 : mworld,X23 : mworld] : (($true = ((mrel @ X23 @ X24) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))))) | ((v6 @ X23) = $true)) ) | ~spl0_8),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2952])).
% 89.60/14.06 thf(f2952,plain,(
% 89.60/14.06 ( ! [X24 : mworld,X23 : mworld] : (((v6 @ X23) = $true) | ($true = ((^[Y0 : mworld]: ((mrel @ X23 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v3 @ Y2)))))))))) @ X24))) ) | ~spl0_8),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2711])).
% 89.60/14.06 thf(f2711,plain,(
% 89.60/14.06 ( ! [X23 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X23 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v3 @ Y2)))))))))))) | ((v6 @ X23) = $true)) ) | ~spl0_8),
% 89.60/14.06 inference(binary_proxy_clausification,[status(thm)],[f2710])).
% 89.60/14.06 thf(f2710,plain,(
% 89.60/14.06 ( ! [X23 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X23 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v3 @ Y2))))))))))) | (v6 @ X23)) = $true)) ) | ~spl0_8),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2709])).
% 89.60/14.06 thf(f2709,plain,(
% 89.60/14.06 ( ! [X23 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X23 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v3 @ Y2))))))))))) | (v6 @ X23))))) ) | ~spl0_8),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2708,f358])).
% 89.60/14.06 thf(f2708,plain,(
% 89.60/14.06 ( ! [X22 : mworld,X23 : mworld] : (($true = ((mrel @ X22 @ X23) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X23 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v3 @ Y2))))))))))) | (v6 @ X23))))) ) | ~spl0_8),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2707])).
% 89.60/14.06 thf(f2707,plain,(
% 89.60/14.06 ( ! [X22 : mworld,X23 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X22 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v3 @ Y3))))))))))) | (v6 @ Y0)))) @ X23))) ) | ~spl0_8),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2706])).
% 89.60/14.06 thf(f2706,plain,(
% 89.60/14.06 ( ! [X22 : mworld] : (($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) => (~ (v3 @ Y3))))))))))) | (v6 @ Y0))))))) ) | ~spl0_8),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2705])).
% 89.60/14.06 thf(f2705,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y3))))))))))) | (v6 @ Y0)))))) = $true)) ) | ~spl0_8),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2704,f358])).
% 89.60/14.06 thf(f2704,plain,(
% 89.60/14.06 ( ! [X21 : mworld,X22 : mworld] : ((((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) => (~ (v3 @ Y3))))))))))) | (v6 @ Y0)))))) = $true)) ) | ~spl0_8),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2703])).
% 89.60/14.06 thf(f2703,plain,(
% 89.60/14.06 ( ! [X21 : mworld,X22 : mworld] : (($true = ((^[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) => (~ (v3 @ Y4))))))))))) | (v6 @ Y1))))))) @ X22))) ) | ~spl0_8),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2699])).
% 89.60/14.06 thf(f2699,plain,(
% 89.60/14.06 ( ! [X21 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v3 @ Y4))))))))))) | (v6 @ Y1)))))))))) ) | ~spl0_8),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2698])).
% 89.60/14.06 thf(f2698,plain,(
% 89.60/14.06 ( ! [X21 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v3 @ Y4))))))))))) | (v6 @ Y1))))))))))) ) | ~spl0_8),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2697,f358])).
% 89.60/14.06 thf(f2697,plain,(
% 89.60/14.06 ( ! [X21 : mworld,X20 : mworld] : (($true = ((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) => (~ (v3 @ Y4))))))))))) | (v6 @ Y1))))))))))) ) | ~spl0_8),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2696])).
% 89.60/14.06 thf(f2696,plain,(
% 89.60/14.06 ( ! [X21 : mworld,X20 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X20 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v3 @ Y5))))))))))) | (v6 @ Y2)))))))))) @ X21))) ) | ~spl0_8),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2667])).
% 89.60/14.06 thf(f2667,plain,(
% 89.60/14.06 ( ! [X20 : mworld] : (($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) => (~ (v3 @ Y5))))))))))) | (v6 @ Y2))))))))))))) ) | ~spl0_8),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2666])).
% 89.60/14.06 thf(f2666,plain,(
% 89.60/14.06 ( ! [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) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v3 @ Y5))))))))))) | (v6 @ Y2)))))))))))))) ) | ~spl0_8),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2665,f358])).
% 89.60/14.06 thf(f2665,plain,(
% 89.60/14.06 ( ! [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) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v3 @ Y5))))))))))) | (v6 @ Y2)))))))))))) = $true)) ) | ~spl0_8),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2664])).
% 89.60/14.06 thf(f2664,plain,(
% 89.60/14.06 ( ! [X19 : mworld,X20 : mworld] : (($true = ((^[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) => (~ (v3 @ Y6))))))))))) | (v6 @ Y3))))))))))))) @ X20))) ) | ~spl0_8),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2663])).
% 89.60/14.06 thf(f2663,plain,(
% 89.60/14.06 ( ! [X19 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v3 @ Y6))))))))))) | (v6 @ Y3)))))))))))))))) ) | ~spl0_8),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2662])).
% 89.60/14.06 thf(f2662,plain,(
% 89.60/14.06 ( ! [X19 : mworld] : ((($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) => (~ (v3 @ Y6))))))))))) | (v6 @ Y3))))))))))))))) = $true)) ) | ~spl0_8),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2661,f358])).
% 89.60/14.06 thf(f2661,plain,(
% 89.60/14.06 ( ! [X18 : mworld,X19 : mworld] : (($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) => (~ (v3 @ Y6))))))))))) | (v6 @ Y3))))))))))))))))) ) | ~spl0_8),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2660])).
% 89.60/14.06 thf(f2660,plain,(
% 89.60/14.06 ( ! [X18 : mworld,X19 : mworld] : (($true = ((^[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) => (~ (v3 @ Y7))))))))))) | (v6 @ Y4)))))))))))))))) @ X19))) ) | ~spl0_8),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1325])).
% 89.60/14.06 thf(f1325,plain,(
% 89.60/14.06 ( ! [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) => (~ (v3 @ Y7))))))))))) | (v6 @ Y4))))))))))))))))) = $true)) ) | ~spl0_8),
% 89.60/14.06 inference(avatar_component_clause,[status(thm)],[f1324])).
% 89.60/14.06 thf(f2680,plain,(
% 89.60/14.06 spl0_14 | spl0_15),
% 89.60/14.06 inference(avatar_split_clause,[status(thm)],[f2673,f2678,f2675])).
% 89.60/14.06 thf(f2673,plain,(
% 89.60/14.06 ( ! [X10 : mworld,X11 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (v10 @ Y0)))) = $true) | ($true = (~ (v12 @ X10)))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2672])).
% 89.60/14.06 thf(f2672,plain,(
% 89.60/14.06 ( ! [X10 : mworld,X11 : mworld] : (($true = (~ (v12 @ X10))) | ($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (v10 @ Y0))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2671,f358])).
% 89.60/14.06 thf(f2671,plain,(
% 89.60/14.06 ( ! [X10 : mworld,X11 : mworld] : (($true = (~ (v12 @ X10))) | (((mrel @ X10 @ X11) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (v10 @ Y0))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2668])).
% 89.60/14.06 thf(f2668,plain,(
% 89.60/14.06 ( ! [X10 : mworld,X11 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v10 @ Y1)))))) @ X11)) | ($true = (~ (v12 @ X10)))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2214])).
% 89.60/14.06 thf(f2214,plain,(
% 89.60/14.06 ( ! [X10 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v10 @ Y1)))))))) | ($true = (~ (v12 @ X10)))) )),
% 89.60/14.06 inference(binary_proxy_clausification,[status(thm)],[f2209])).
% 89.60/14.06 thf(f2209,plain,(
% 89.60/14.06 ( ! [X10 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v10 @ Y1))))))) | (~ (v12 @ X10))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2208])).
% 89.60/14.06 thf(f2208,plain,(
% 89.60/14.06 ( ! [X10 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v10 @ Y1))))))) | (~ (v12 @ X10)))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2207,f358])).
% 89.60/14.06 thf(f2207,plain,(
% 89.60/14.06 ( ! [X10 : mworld,X9 : mworld] : (($true = ((mrel @ X9 @ X10) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v10 @ Y1))))))) | (~ (v12 @ X10)))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2206])).
% 89.60/14.06 thf(f2206,plain,(
% 89.60/14.06 ( ! [X10 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v10 @ Y2))))))) | (~ (v12 @ Y0))))) @ X10))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2201])).
% 89.60/14.06 thf(f2201,plain,(
% 89.60/14.06 ( ! [X9 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v10 @ Y2))))))) | (~ (v12 @ Y0)))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2200])).
% 89.60/14.06 thf(f2200,plain,(
% 89.60/14.06 ( ! [X9 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v10 @ Y2))))))) | (~ (v12 @ Y0))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2199,f358])).
% 89.60/14.06 thf(f2199,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y2))))))) | (~ (v12 @ Y0))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2198])).
% 89.60/14.06 thf(f2198,plain,(
% 89.60/14.06 ( ! [X8 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v10 @ Y3))))))) | (~ (v12 @ Y1)))))))) @ X9))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2193])).
% 89.60/14.06 thf(f2193,plain,(
% 89.60/14.06 ( ! [X8 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v10 @ Y3))))))) | (~ (v12 @ Y1))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2192])).
% 89.60/14.06 thf(f2192,plain,(
% 89.60/14.06 ( ! [X8 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v10 @ Y3))))))) | (~ (v12 @ Y1)))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2191,f358])).
% 89.60/14.06 thf(f2191,plain,(
% 89.60/14.06 ( ! [X8 : mworld,X7 : mworld] : (($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) => (v10 @ Y3))))))) | (~ (v12 @ Y1)))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2190])).
% 89.60/14.06 thf(f2190,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y4))))))) | (~ (v12 @ Y2))))))))))) @ X8))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2185])).
% 89.60/14.06 thf(f2185,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y4))))))) | (~ (v12 @ Y2)))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2184])).
% 89.60/14.06 thf(f2184,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v10 @ Y4))))))) | (~ (v12 @ Y2))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2183,f358])).
% 89.60/14.06 thf(f2183,plain,(
% 89.60/14.06 ( ! [X6 : mworld,X7 : mworld] : (($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) => (v10 @ Y4))))))) | (~ (v12 @ Y2))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2182])).
% 89.60/14.06 thf(f2182,plain,(
% 89.60/14.06 ( ! [X6 : mworld,X7 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v10 @ Y5))))))) | (~ (v12 @ Y3)))))))))))))) @ X7))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2175])).
% 89.60/14.06 thf(f2175,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (($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) => (v10 @ Y5))))))) | (~ (v12 @ Y3))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2174])).
% 89.60/14.06 thf(f2174,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y5))))))) | (~ (v12 @ Y3)))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2173,f358])).
% 89.60/14.06 thf(f2173,plain,(
% 89.60/14.06 ( ! [X6 : mworld,X5 : mworld] : (($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) => (v10 @ Y5))))))) | (~ (v12 @ Y3)))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2172])).
% 89.60/14.06 thf(f2172,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y6))))))) | (~ (v12 @ Y4))))))))))))))))) @ X6) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2170])).
% 89.60/14.06 thf(f2170,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : (($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) => (v10 @ Y6))))))) | (~ (v12 @ Y4)))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2169])).
% 89.60/14.06 thf(f2169,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y6))))))) | (~ (v12 @ Y4))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2168,f358])).
% 89.60/14.06 thf(f2168,plain,(
% 89.60/14.06 ( ! [X4 : mworld,X5 : mworld] : (($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) => (v10 @ Y6))))))) | (~ (v12 @ Y4))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2167])).
% 89.60/14.06 thf(f2167,plain,(
% 89.60/14.06 ( ! [X4 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v10 @ Y7))))))) | (~ (v12 @ Y5)))))))))))))))))))) @ X5))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2100])).
% 89.60/14.06 thf(f2100,plain,(
% 89.60/14.06 ( ! [X4 : mworld] : (($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) => (v10 @ Y7))))))) | (~ (v12 @ Y5))))))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2099])).
% 89.60/14.06 thf(f2099,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y7))))))) | (~ (v12 @ Y5)))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2098,f358])).
% 89.60/14.06 thf(f2098,plain,(
% 89.60/14.06 ( ! [X3 : mworld,X4 : mworld] : (($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) => (v10 @ Y7))))))) | (~ (v12 @ Y5)))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2097])).
% 89.60/14.06 thf(f2097,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y8))))))) | (~ (v12 @ Y6))))))))))))))))))))))) @ X4) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2092])).
% 89.60/14.06 thf(f2092,plain,(
% 89.60/14.06 ( ! [X3 : mworld] : (($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) => (v10 @ Y8))))))) | (~ (v12 @ Y6)))))))))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2091])).
% 89.60/14.06 thf(f2091,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y8))))))) | (~ (v12 @ Y6))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2090,f358])).
% 89.60/14.06 thf(f2090,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X3 : mworld] : (($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) => (v10 @ Y8))))))) | (~ (v12 @ Y6))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2089])).
% 89.60/14.06 thf(f2089,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X3 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v10 @ Y9))))))) | (~ (v12 @ Y7)))))))))))))))))))))))))) @ X3))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2082])).
% 89.60/14.06 thf(f2082,plain,(
% 89.60/14.06 ( ! [X2 : mworld] : (($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) => (v10 @ Y9))))))) | (~ (v12 @ Y7))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2081])).
% 89.60/14.06 thf(f2081,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y9))))))) | (~ (v12 @ Y7)))))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2080,f358])).
% 89.60/14.06 thf(f2080,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X1 : mworld] : (($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) => (v10 @ Y9))))))) | (~ (v12 @ Y7)))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2079])).
% 89.60/14.06 thf(f2079,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v10 @ Y10))))))) | (~ (v12 @ Y8))))))))))))))))))))))))))))) @ X2))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2072])).
% 89.60/14.06 thf(f2072,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($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) => (v10 @ Y10))))))) | (~ (v12 @ Y8)))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2071])).
% 89.60/14.06 thf(f2071,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y10))))))) | (~ (v12 @ Y8))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2070,f358])).
% 89.60/14.06 thf(f2070,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : (($true = ((mrel @ (sK11 @ X0) @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v10 @ Y10))))))) | (~ (v12 @ Y8))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2067])).
% 89.60/14.06 thf(f2067,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : (($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) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v10 @ Y11))))))) | (~ (v12 @ Y9)))))))))))))))))))))))))))))))) @ X1))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2059])).
% 89.60/14.06 thf(f2059,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK11 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v10 @ Y11))))))) | (~ (v12 @ Y9))))))))))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2058])).
% 89.60/14.06 thf(f2058,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (($true = ((!! @ 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) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v10 @ Y11))))))) | (~ (v12 @ Y9))))))))))))))))))))))))))))))))) | $false))) )),
% 89.60/14.06 inference(superposition,[status(thm)],[f2049,f1993])).
% 89.60/14.06 thf(f1993,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (($false = (v22 @ (sK11 @ X6)))) )),
% 89.60/14.06 inference(not_proxy_clausification,[status(thm)],[f1992])).
% 89.60/14.06 thf(f1992,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (((~ (v22 @ (sK11 @ X6))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1991])).
% 89.60/14.06 thf(f1991,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : ((((~ (v22 @ (sK11 @ X6))) & $true) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1990,f358])).
% 89.60/14.06 thf(f1990,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (($true = ((~ (v22 @ (sK11 @ X6))) & (mrel @ X6 @ (sK11 @ X6))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1989])).
% 89.60/14.06 thf(f1989,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (($true = ((^[Y0 : mworld]: ((~ (v22 @ Y0)) & (mrel @ X6 @ Y0))) @ (sK11 @ X6)))) )),
% 89.60/14.06 inference(sigma_clausification,[status(thm)],[f1984])).
% 89.60/14.06 thf(f1984,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((~ (v22 @ Y0)) & (mrel @ X6 @ Y0)))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1983])).
% 89.60/14.06 thf(f1983,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (($true = ($true & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v22 @ Y0)) & (mrel @ X6 @ Y0))))))) )),
% 89.60/14.06 inference(backward_demodulation,[status(thm)],[f1860,f1982])).
% 89.60/14.06 thf(f1982,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((v22 @ Y0) & (mrel @ X6 @ Y0)))) = $true)) )),
% 89.60/14.06 inference(binary_proxy_clausification,[status(thm)],[f1860])).
% 89.60/14.06 thf(f2049,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($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) => (v10 @ Y11))))))) | (~ (v12 @ Y9))))))))))))))))))))))))))))))))) | (v22 @ X1)))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2048])).
% 89.60/14.06 thf(f2048,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y11))))))) | (~ (v12 @ Y9))))))))))))))))))))))))))))))))) | (v22 @ X1))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2047,f358])).
% 89.60/14.06 thf(f2047,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : (($true = ((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) => (v10 @ Y11))))))) | (~ (v12 @ Y9))))))))))))))))))))))))))))))))) | (v22 @ X1))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2044])).
% 89.60/14.06 thf(f2044,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK8 @ X0) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v10 @ Y12))))))) | (~ (v12 @ Y10))))))))))))))))))))))))))))))))) | (v22 @ Y0)))) @ X1))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1963])).
% 89.60/14.06 thf(f1963,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (($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) => (v10 @ Y12))))))) | (~ (v12 @ Y10))))))))))))))))))))))))))))))))) | (v22 @ Y0))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1962])).
% 89.60/14.06 thf(f1962,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y12))))))) | (~ (v12 @ Y10))))))))))))))))))))))))))))))))) | (v22 @ Y0))))) | $false) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1957])).
% 89.60/14.06 thf(f1957,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (($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) => (v10 @ Y12))))))) | (~ (v12 @ Y10))))))))))))))))))))))))))))))))) | (v22 @ Y0))))) | (~ $true)))) )),
% 89.60/14.06 inference(superposition,[status(thm)],[f467,f1949])).
% 89.60/14.06 thf(f1949,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : (($true = (v23 @ (sK8 @ X5)))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1948])).
% 89.60/14.06 thf(f1948,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : (($true = ((v23 @ (sK8 @ X5)) & $true))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1947,f358])).
% 89.60/14.06 thf(f1947,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : (($true = ((v23 @ (sK8 @ X5)) & (mrel @ X5 @ (sK8 @ X5))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1946])).
% 89.60/14.06 thf(f1946,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : ((((^[Y0 : mworld]: ((v23 @ Y0) & (mrel @ X5 @ Y0))) @ (sK8 @ X5)) = $true)) )),
% 89.60/14.06 inference(sigma_clausification,[status(thm)],[f1936])).
% 89.60/14.06 thf(f467,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (($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) => (v10 @ Y12))))))) | (~ (v12 @ Y10))))))))))))))))))))))))))))))))) | (v22 @ Y0))))) | (~ (v23 @ X6))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f466])).
% 89.60/14.06 thf(f466,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y12))))))) | (~ (v12 @ Y10))))))))))))))))))))))))))))))))) | (v22 @ Y0))))) | (~ (v23 @ X6)))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f465,f358])).
% 89.60/14.06 thf(f465,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y12))))))) | (~ (v12 @ Y10))))))))))))))))))))))))))))))))) | (v22 @ Y0))))) | (~ (v23 @ X6)))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f464])).
% 89.60/14.06 thf(f464,plain,(
% 89.60/14.06 ( ! [X6 : mworld,X5 : mworld] : (($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) => (v10 @ Y13))))))) | (~ (v12 @ Y11))))))))))))))))))))))))))))))))) | (v22 @ Y1))))) | (~ (v23 @ Y0))))) @ X6))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f463])).
% 89.60/14.06 thf(f463,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v10 @ Y13))))))) | (~ (v12 @ Y11))))))))))))))))))))))))))))))))) | (v22 @ Y1))))) | (~ (v23 @ Y0)))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f462])).
% 89.60/14.06 thf(f462,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : ((($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) => (v10 @ Y13))))))) | (~ (v12 @ Y11))))))))))))))))))))))))))))))))) | (v22 @ Y1))))) | (~ (v23 @ Y0))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f461,f358])).
% 89.60/14.06 thf(f461,plain,(
% 89.60/14.06 ( ! [X4 : mworld,X5 : mworld] : (($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) => (v10 @ Y13))))))) | (~ (v12 @ Y11))))))))))))))))))))))))))))))))) | (v22 @ Y1))))) | (~ (v23 @ Y0))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f460])).
% 89.60/14.06 thf(f460,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y14))))))) | (~ (v12 @ Y12))))))))))))))))))))))))))))))))) | (v22 @ Y2))))) | (~ (v23 @ Y1)))))))) @ X5) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f459])).
% 89.60/14.06 thf(f459,plain,(
% 89.60/14.06 ( ! [X4 : mworld] : (($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) => (v10 @ Y14))))))) | (~ (v12 @ Y12))))))))))))))))))))))))))))))))) | (v22 @ Y2))))) | (~ (v23 @ Y1))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f458])).
% 89.60/14.06 thf(f458,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y14))))))) | (~ (v12 @ Y12))))))))))))))))))))))))))))))))) | (v22 @ Y2))))) | (~ (v23 @ Y1)))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f457,f358])).
% 89.60/14.06 thf(f457,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y14))))))) | (~ (v12 @ Y12))))))))))))))))))))))))))))))))) | (v22 @ Y2))))) | (~ (v23 @ Y1)))))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f456])).
% 89.60/14.06 thf(f456,plain,(
% 89.60/14.06 ( ! [X3 : mworld,X4 : mworld] : (($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) => (v10 @ Y15))))))) | (~ (v12 @ Y13))))))))))))))))))))))))))))))))) | (v22 @ Y3))))) | (~ (v23 @ Y2))))))))))) @ X4))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f455])).
% 89.60/14.06 thf(f455,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y15))))))) | (~ (v12 @ Y13))))))))))))))))))))))))))))))))) | (v22 @ Y3))))) | (~ (v23 @ Y2)))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f454])).
% 89.60/14.06 thf(f454,plain,(
% 89.60/14.06 ( ! [X3 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v10 @ Y15))))))) | (~ (v12 @ Y13))))))))))))))))))))))))))))))))) | (v22 @ Y3))))) | (~ (v23 @ Y2))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f453,f358])).
% 89.60/14.06 thf(f453,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X3 : mworld] : (($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) => (v10 @ Y15))))))) | (~ (v12 @ Y13))))))))))))))))))))))))))))))))) | (v22 @ Y3))))) | (~ (v23 @ Y2))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f452])).
% 89.60/14.06 thf(f452,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y16))))))) | (~ (v12 @ Y14))))))))))))))))))))))))))))))))) | (v22 @ Y4))))) | (~ (v23 @ Y3)))))))))))))) @ X3) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f451])).
% 89.60/14.06 thf(f451,plain,(
% 89.60/14.06 ( ! [X2 : mworld] : (($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) => (v10 @ Y16))))))) | (~ (v12 @ Y14))))))))))))))))))))))))))))))))) | (v22 @ Y4))))) | (~ (v23 @ Y3))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f450])).
% 89.60/14.06 thf(f450,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y16))))))) | (~ (v12 @ Y14))))))))))))))))))))))))))))))))) | (v22 @ Y4))))) | (~ (v23 @ Y3)))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f449,f358])).
% 89.60/14.06 thf(f449,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y16))))))) | (~ (v12 @ Y14))))))))))))))))))))))))))))))))) | (v22 @ Y4))))) | (~ (v23 @ Y3)))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f448])).
% 89.60/14.06 thf(f448,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y17))))))) | (~ (v12 @ Y15))))))))))))))))))))))))))))))))) | (v22 @ Y5))))) | (~ (v23 @ Y4))))))))))))))))) @ X2) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f447])).
% 89.60/14.06 thf(f447,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($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) => (v10 @ Y17))))))) | (~ (v12 @ Y15))))))))))))))))))))))))))))))))) | (v22 @ Y5))))) | (~ (v23 @ Y4)))))))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f446])).
% 89.60/14.06 thf(f446,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y17))))))) | (~ (v12 @ Y15))))))))))))))))))))))))))))))))) | (v22 @ Y5))))) | (~ (v23 @ Y4))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f445,f358])).
% 89.60/14.06 thf(f445,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($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) => (v10 @ Y17))))))) | (~ (v12 @ Y15))))))))))))))))))))))))))))))))) | (v22 @ Y5))))) | (~ (v23 @ Y4))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f444])).
% 89.60/14.06 thf(f444,plain,(
% 89.60/14.06 ( ! [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) => (v10 @ Y18))))))) | (~ (v12 @ Y16))))))))))))))))))))))))))))))))) | (v22 @ Y6))))) | (~ (v23 @ Y5)))))))))))))))))))) @ X1) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f307])).
% 89.60/14.06 thf(f307,plain,(
% 89.60/14.06 ((!! @ 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) => (v10 @ Y18))))))) | (~ (v12 @ Y16))))))))))))))))))))))))))))))))) | (v22 @ Y6))))) | (~ (v23 @ Y5))))))))))))))))))))) = $true)),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f289])).
% 89.60/14.06 thf(f289,plain,(
% 89.60/14.06 ($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]: (!! @ 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))))) @ v23) @ ((^[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))))))) @ ((^[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))))) @ v12) @ ((^[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))))))) @ v10))))))))))))))))))))))))),
% 89.60/14.06 inference(definition_unfolding,[status(thm)],[f236,f226,f239,f239,f239,f239,f239,f239,f201,f213,f239,f201,f239,f239,f239,f239,f239,f239,f239,f239,f239,f239,f201,f213,f239,f239])).
% 89.60/14.06 thf(f236,plain,(
% 89.60/14.06 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v23) @ (mbox @ (mor @ v22 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v12) @ (mbox @ (mbox @ v10))))))))))))))))))))))) = $true)),
% 89.60/14.06 inference(cnf_transformation,[status(thm)],[f139])).
% 89.60/14.06 thf(f139,plain,(
% 89.60/14.06 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v23) @ (mbox @ (mor @ v22 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v12) @ (mbox @ (mbox @ v10))))))))))))))))))))))) = $true)),
% 89.60/14.06 inference(fool_elimination,[status(thm)],[f138])).
% 89.60/14.06 thf(f138,plain,(
% 89.60/14.06 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v23) @ (mbox @ (mor @ v22 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v12) @ (mbox @ (mbox @ v10)))))))))))))))))))))))),
% 89.60/14.06 inference(rectify,[status(thm)],[f43])).
% 89.60/14.06 thf(f43,axiom,(
% 89.60/14.06 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v23) @ (mbox @ (mor @ v22 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v12) @ (mbox @ (mbox @ v10)))))))))))))))))))))))),
% 89.60/14.06 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod34)).
% 89.60/14.06 thf(f2415,plain,(
% 89.60/14.06 spl0_7 | spl0_13 | ~spl0_4),
% 89.60/14.06 inference(avatar_split_clause,[status(thm)],[f2411,f833,f2413,f1321])).
% 89.60/14.06 thf(f833,definition,(
% 89.60/14.06 spl0_4 <=> ! [X14 : mworld] : ($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))))))))))) | (v12 @ Y2))))))))))))),
% 89.60/14.06 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 89.60/14.06 thf(f2411,plain,(
% 89.60/14.06 ( ! [X18 : mworld,X17 : mworld] : (($true = (v12 @ X17)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v9 @ Y1)))))))) = $true)) ) | ~spl0_4),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2410])).
% 89.60/14.06 thf(f2410,plain,(
% 89.60/14.06 ( ! [X18 : mworld,X17 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v9 @ Y1)))))))))) | ($true = (v12 @ X17))) ) | ~spl0_4),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2408,f358])).
% 89.60/14.06 thf(f2408,plain,(
% 89.60/14.06 ( ! [X18 : mworld,X17 : mworld] : (($true = (v12 @ X17)) | ($true = ((mrel @ X17 @ X18) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v9 @ Y1))))))))))) ) | ~spl0_4),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2406])).
% 89.60/14.06 thf(f2406,plain,(
% 89.60/14.06 ( ! [X18 : mworld,X17 : mworld] : (($true = (v12 @ X17)) | (((^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v9 @ Y2)))))))))) @ X18) = $true)) ) | ~spl0_4),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2160])).
% 89.60/14.06 thf(f2160,plain,(
% 89.60/14.06 ( ! [X17 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v9 @ Y2))))))))))) = $true) | ($true = (v12 @ X17))) ) | ~spl0_4),
% 89.60/14.06 inference(binary_proxy_clausification,[status(thm)],[f2159])).
% 89.60/14.06 thf(f2159,plain,(
% 89.60/14.06 ( ! [X17 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v9 @ Y2))))))))))) | (v12 @ X17)) = $true)) ) | ~spl0_4),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2158])).
% 89.60/14.06 thf(f2158,plain,(
% 89.60/14.06 ( ! [X17 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v9 @ Y2))))))))))) | (v12 @ X17))))) ) | ~spl0_4),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2157,f358])).
% 89.60/14.06 thf(f2157,plain,(
% 89.60/14.06 ( ! [X16 : mworld,X17 : mworld] : (($true = ((mrel @ X16 @ X17) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v9 @ Y2))))))))))) | (v12 @ X17))))) ) | ~spl0_4),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2156])).
% 89.60/14.06 thf(f2156,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y3))))))))))) | (v12 @ Y0)))) @ X17) = $true)) ) | ~spl0_4),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2155])).
% 89.60/14.06 thf(f2155,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y3))))))))))) | (v12 @ Y0))))) = $true)) ) | ~spl0_4),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2154])).
% 89.60/14.06 thf(f2154,plain,(
% 89.60/14.06 ( ! [X16 : mworld] : (($true = ($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) => (~ (v9 @ Y3))))))))))) | (v12 @ Y0)))))))) ) | ~spl0_4),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2153,f358])).
% 89.60/14.06 thf(f2153,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y3))))))))))) | (v12 @ Y0)))))) = $true)) ) | ~spl0_4),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2152])).
% 89.60/14.06 thf(f2152,plain,(
% 89.60/14.06 ( ! [X16 : mworld,X15 : mworld] : (($true = ((^[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) => (~ (v9 @ Y4))))))))))) | (v12 @ Y1))))))) @ X16))) ) | ~spl0_4),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2151])).
% 89.60/14.06 thf(f2151,plain,(
% 89.60/14.06 ( ! [X15 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v9 @ Y4))))))))))) | (v12 @ Y1)))))))))) ) | ~spl0_4),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2150])).
% 89.60/14.06 thf(f2150,plain,(
% 89.60/14.06 ( ! [X15 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v9 @ Y4))))))))))) | (v12 @ Y1))))))))))) ) | ~spl0_4),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2149,f358])).
% 89.60/14.06 thf(f2149,plain,(
% 89.60/14.06 ( ! [X14 : mworld,X15 : mworld] : (($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) => (~ (v9 @ Y4))))))))))) | (v12 @ Y1))))))))))) ) | ~spl0_4),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2148])).
% 89.60/14.06 thf(f2148,plain,(
% 89.60/14.06 ( ! [X14 : mworld,X15 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v9 @ Y5))))))))))) | (v12 @ Y2)))))))))) @ X15))) ) | ~spl0_4),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f834])).
% 89.60/14.06 thf(f834,plain,(
% 89.60/14.06 ( ! [X14 : mworld] : (($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))))))))))) | (v12 @ Y2))))))))))))) ) | ~spl0_4),
% 89.60/14.06 inference(avatar_component_clause,[status(thm)],[f833])).
% 89.60/14.06 thf(f2141,plain,(
% 89.60/14.06 spl0_4),
% 89.60/14.06 inference(avatar_split_clause,[status(thm)],[f2140,f833])).
% 89.60/14.06 thf(f2140,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v9 @ Y5))))))))))) | (v12 @ Y2))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2139])).
% 89.60/14.06 thf(f2139,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v9 @ Y5))))))))))) | (v12 @ Y2)))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2138,f358])).
% 89.60/14.06 thf(f2138,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : (($true = ((mrel @ (sK12 @ 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) => (~ (v9 @ Y5))))))))))) | (v12 @ Y2)))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2135])).
% 89.60/14.06 thf(f2135,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK12 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v9 @ Y6))))))))))) | (v12 @ Y3))))))))))))) @ X1))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2126])).
% 89.60/14.06 thf(f2126,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK12 @ 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) => (~ (v9 @ Y6))))))))))) | (v12 @ Y3)))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2125])).
% 89.60/14.06 thf(f2125,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK12 @ 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) => (~ (v9 @ Y6))))))))))) | (v12 @ Y3)))))))))))))) | $false))) )),
% 89.60/14.06 inference(superposition,[status(thm)],[f2023,f2118])).
% 89.60/14.06 thf(f2118,plain,(
% 89.60/14.06 ( ! [X12 : mworld] : (($false = (v16 @ (sK12 @ X12)))) )),
% 89.60/14.06 inference(not_proxy_clausification,[status(thm)],[f2117])).
% 89.60/14.06 thf(f2117,plain,(
% 89.60/14.06 ( ! [X12 : mworld] : (($true = (~ (v16 @ (sK12 @ X12))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2116])).
% 89.60/14.06 thf(f2116,plain,(
% 89.60/14.06 ( ! [X12 : mworld] : (($true = ((~ (v16 @ (sK12 @ X12))) & $true))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2110,f358])).
% 89.60/14.06 thf(f2110,plain,(
% 89.60/14.06 ( ! [X12 : mworld] : (($true = ((~ (v16 @ (sK12 @ X12))) & (mrel @ X12 @ (sK12 @ X12))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2109])).
% 89.60/14.06 thf(f2109,plain,(
% 89.60/14.06 ( ! [X12 : mworld] : ((((^[Y0 : mworld]: ((~ (v16 @ Y0)) & (mrel @ X12 @ Y0))) @ (sK12 @ X12)) = $true)) )),
% 89.60/14.06 inference(sigma_clausification,[status(thm)],[f2108])).
% 89.60/14.06 thf(f2108,plain,(
% 89.60/14.06 ( ! [X12 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((~ (v16 @ Y0)) & (mrel @ X12 @ Y0)))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2107])).
% 89.60/14.06 thf(f2107,plain,(
% 89.60/14.06 ( ! [X12 : mworld] : ((($true & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v16 @ Y0)) & (mrel @ X12 @ Y0))))) = $true)) )),
% 89.60/14.06 inference(backward_demodulation,[status(thm)],[f2104,f2106])).
% 89.60/14.06 thf(f2106,plain,(
% 89.60/14.06 ( ! [X12 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((v16 @ Y0) & (mrel @ X12 @ Y0)))) = $true)) )),
% 89.60/14.06 inference(binary_proxy_clausification,[status(thm)],[f2104])).
% 89.60/14.06 thf(f2104,plain,(
% 89.60/14.06 ( ! [X12 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v16 @ Y0) & (mrel @ X12 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v16 @ Y0)) & (mrel @ X12 @ Y0))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2103])).
% 89.60/14.06 thf(f2103,plain,(
% 89.60/14.06 ( ! [X12 : mworld] : ((($true & ((?? @ mworld @ (^[Y0 : mworld]: ((v16 @ Y0) & (mrel @ X12 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v16 @ Y0)) & (mrel @ X12 @ Y0)))))) = $true)) )),
% 89.60/14.06 inference(backward_demodulation,[status(thm)],[f2096,f2102])).
% 89.60/14.06 thf(f2023,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y6))))))))))) | (v12 @ Y3)))))))))))))) | (v16 @ X5)) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2022])).
% 89.60/14.06 thf(f2022,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : ((($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) => (~ (v9 @ Y6))))))))))) | (v12 @ Y3)))))))))))))) | (v16 @ X5))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2021,f358])).
% 89.60/14.06 thf(f2021,plain,(
% 89.60/14.06 ( ! [X4 : mworld,X5 : mworld] : (($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) => (~ (v9 @ Y6))))))))))) | (v12 @ Y3)))))))))))))) | (v16 @ X5))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2020])).
% 89.60/14.06 thf(f2020,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y7))))))))))) | (v12 @ Y4)))))))))))))) | (v16 @ Y0)))) @ X5))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2019])).
% 89.60/14.06 thf(f2019,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y7))))))))))) | (v12 @ Y4)))))))))))))) | (v16 @ Y0))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2018])).
% 89.60/14.06 thf(f2018,plain,(
% 89.60/14.06 ( ! [X4 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v9 @ Y7))))))))))) | (v12 @ Y4)))))))))))))) | (v16 @ Y0)))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2017,f358])).
% 89.60/14.06 thf(f2017,plain,(
% 89.60/14.06 ( ! [X3 : mworld,X4 : mworld] : (($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) => (~ (v9 @ Y7))))))))))) | (v12 @ Y4)))))))))))))) | (v16 @ Y0)))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2016])).
% 89.60/14.06 thf(f2016,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y8))))))))))) | (v12 @ Y5)))))))))))))) | (v16 @ Y1))))))) @ X4) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2015])).
% 89.60/14.06 thf(f2015,plain,(
% 89.60/14.06 ( ! [X3 : mworld] : (($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) => (~ (v9 @ Y8))))))))))) | (v12 @ Y5)))))))))))))) | (v16 @ Y1)))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2014])).
% 89.60/14.06 thf(f2014,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y8))))))))))) | (v12 @ Y5)))))))))))))) | (v16 @ Y1))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2013,f358])).
% 89.60/14.06 thf(f2013,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X3 : mworld] : (($true = ((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v9 @ Y8))))))))))) | (v12 @ Y5)))))))))))))) | (v16 @ Y1))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2012])).
% 89.60/14.06 thf(f2012,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X3 : mworld] : (($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) => (~ (v9 @ Y9))))))))))) | (v12 @ Y6)))))))))))))) | (v16 @ Y2)))))))))) @ X3))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2011])).
% 89.60/14.06 thf(f2011,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y9))))))))))) | (v12 @ Y6)))))))))))))) | (v16 @ Y2))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2010])).
% 89.60/14.06 thf(f2010,plain,(
% 89.60/14.06 ( ! [X2 : mworld] : ((($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) => (~ (v9 @ Y9))))))))))) | (v12 @ Y6)))))))))))))) | (v16 @ Y2)))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f2009,f358])).
% 89.60/14.06 thf(f2009,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X1 : mworld] : (($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) => (~ (v9 @ Y9))))))))))) | (v12 @ Y6)))))))))))))) | (v16 @ Y2)))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f2008])).
% 89.60/14.06 thf(f2008,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y10))))))))))) | (v12 @ Y7)))))))))))))) | (v16 @ Y3))))))))))))) @ X2) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f2001])).
% 89.60/14.06 thf(f2001,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($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) => (~ (v9 @ Y10))))))))))) | (v12 @ Y7)))))))))))))) | (v16 @ Y3)))))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f2000])).
% 89.60/14.06 thf(f2000,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y10))))))))))) | (v12 @ Y7)))))))))))))) | (v16 @ Y3))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1999,f358])).
% 89.60/14.06 thf(f1999,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : (($true = ((mrel @ (sK6 @ 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) => (~ (v9 @ Y10))))))))))) | (v12 @ Y7)))))))))))))) | (v16 @ Y3))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1996])).
% 89.60/14.06 thf(f1996,plain,(
% 89.60/14.06 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK6 @ 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) => (~ (v9 @ Y11))))))))))) | (v12 @ Y8)))))))))))))) | (v16 @ Y4)))))))))))))))) @ X1))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f1934])).
% 89.60/14.06 thf(f1934,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK6 @ 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) => (~ (v9 @ Y11))))))))))) | (v12 @ Y8)))))))))))))) | (v16 @ Y4))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1933])).
% 89.60/14.06 thf(f1933,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK6 @ 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) => (~ (v9 @ Y11))))))))))) | (v12 @ Y8)))))))))))))) | (v16 @ Y4))))))))))))))))) | $false) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1929])).
% 89.60/14.06 thf(f1929,plain,(
% 89.60/14.06 ( ! [X0 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK6 @ 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) => (~ (v9 @ Y11))))))))))) | (v12 @ Y8)))))))))))))) | (v16 @ Y4))))))))))))))))) | (~ $true)))) )),
% 89.60/14.06 inference(superposition,[status(thm)],[f554,f1913])).
% 89.60/14.06 thf(f1913,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : (($true = (v21 @ (sK6 @ X7)))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1912])).
% 89.60/14.06 thf(f1912,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : (($true = ((v21 @ (sK6 @ X7)) & $true))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f1900,f358])).
% 89.60/14.06 thf(f1900,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : ((((v21 @ (sK6 @ X7)) & (mrel @ X7 @ (sK6 @ X7))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f1899])).
% 89.60/14.06 thf(f1899,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : (($true = ((^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0))) @ (sK6 @ X7)))) )),
% 89.60/14.06 inference(sigma_clausification,[status(thm)],[f1898])).
% 89.60/14.06 thf(f1898,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0)))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f1897])).
% 89.60/14.06 thf(f1897,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : (($true = ((?? @ mworld @ (^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0)))) & $true))) )),
% 89.60/14.06 inference(backward_demodulation,[status(thm)],[f1894,f1895])).
% 89.60/14.06 thf(f554,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y11))))))))))) | (v12 @ Y8)))))))))))))) | (v16 @ Y4))))))))))))))))) | (~ (v21 @ X8))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f553])).
% 89.60/14.06 thf(f553,plain,(
% 89.60/14.06 ( ! [X8 : mworld] : ((($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))))))))))) | (v12 @ Y8)))))))))))))) | (v16 @ Y4))))))))))))))))) | (~ (v21 @ X8)))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f552,f358])).
% 89.60/14.06 thf(f552,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y8)))))))))))))) | (v16 @ Y4))))))))))))))))) | (~ (v21 @ X8)))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f551])).
% 89.60/14.06 thf(f551,plain,(
% 89.60/14.06 ( ! [X8 : mworld,X7 : mworld] : (($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) => (~ (v9 @ Y12))))))))))) | (v12 @ Y9)))))))))))))) | (v16 @ Y5))))))))))))))))) | (~ (v21 @ Y0))))) @ X8))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f550])).
% 89.60/14.06 thf(f550,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v9 @ Y12))))))))))) | (v12 @ Y9)))))))))))))) | (v16 @ Y5))))))))))))))))) | (~ (v21 @ Y0)))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f549])).
% 89.60/14.06 thf(f549,plain,(
% 89.60/14.06 ( ! [X7 : mworld] : ((($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))))))))))) | (v12 @ Y9)))))))))))))) | (v16 @ Y5))))))))))))))))) | (~ (v21 @ Y0))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f548,f358])).
% 89.60/14.06 thf(f548,plain,(
% 89.60/14.06 ( ! [X6 : mworld,X7 : mworld] : (($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) => (~ (v9 @ Y12))))))))))) | (v12 @ Y9)))))))))))))) | (v16 @ Y5))))))))))))))))) | (~ (v21 @ Y0))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f547])).
% 89.60/14.06 thf(f547,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y13))))))))))) | (v12 @ Y10)))))))))))))) | (v16 @ Y6))))))))))))))))) | (~ (v21 @ Y1)))))))) @ X7))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f546])).
% 89.60/14.06 thf(f546,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y10)))))))))))))) | (v16 @ Y6))))))))))))))))) | (~ (v21 @ Y1))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f545])).
% 89.60/14.06 thf(f545,plain,(
% 89.60/14.06 ( ! [X6 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v9 @ Y13))))))))))) | (v12 @ Y10)))))))))))))) | (v16 @ Y6))))))))))))))))) | (~ (v21 @ Y1)))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f544,f358])).
% 89.60/14.06 thf(f544,plain,(
% 89.60/14.06 ( ! [X6 : mworld,X5 : mworld] : (($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))))))))))) | (v12 @ Y10)))))))))))))) | (v16 @ Y6))))))))))))))))) | (~ (v21 @ Y1)))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f543])).
% 89.60/14.06 thf(f543,plain,(
% 89.60/14.06 ( ! [X6 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v9 @ Y14))))))))))) | (v12 @ Y11)))))))))))))) | (v16 @ Y7))))))))))))))))) | (~ (v21 @ Y2))))))))))) @ X6))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f542])).
% 89.60/14.06 thf(f542,plain,(
% 89.60/14.06 ( ! [X5 : mworld] : (($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))))))))))) | (v12 @ Y11)))))))))))))) | (v16 @ Y7))))))))))))))))) | (~ (v21 @ Y2)))))))))))))) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f541])).
% 89.60/14.06 thf(f541,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y11)))))))))))))) | (v16 @ Y7))))))))))))))))) | (~ (v21 @ Y2))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f540,f358])).
% 89.60/14.06 thf(f540,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y11)))))))))))))) | (v16 @ Y7))))))))))))))))) | (~ (v21 @ Y2))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f539])).
% 89.60/14.06 thf(f539,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y12)))))))))))))) | (v16 @ Y8))))))))))))))))) | (~ (v21 @ Y3)))))))))))))) @ X5) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f538])).
% 89.60/14.06 thf(f538,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y12)))))))))))))) | (v16 @ Y8))))))))))))))))) | (~ (v21 @ Y3))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f537])).
% 89.60/14.06 thf(f537,plain,(
% 89.60/14.06 ( ! [X4 : mworld] : (($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) => (~ (v9 @ Y15))))))))))) | (v12 @ Y12)))))))))))))) | (v16 @ Y8))))))))))))))))) | (~ (v21 @ Y3)))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f536,f358])).
% 89.60/14.06 thf(f536,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y15))))))))))) | (v12 @ Y12)))))))))))))) | (v16 @ Y8))))))))))))))))) | (~ (v21 @ Y3)))))))))))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f535])).
% 89.60/14.06 thf(f535,plain,(
% 89.60/14.06 ( ! [X3 : mworld,X4 : mworld] : (($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) => (~ (v9 @ Y16))))))))))) | (v12 @ Y13)))))))))))))) | (v16 @ Y9))))))))))))))))) | (~ (v21 @ Y4))))))))))))))))) @ X4))) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f534])).
% 89.60/14.06 thf(f534,plain,(
% 89.60/14.06 ( ! [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) => (~ (v9 @ Y16))))))))))) | (v12 @ Y13)))))))))))))) | (v16 @ Y9))))))))))))))))) | (~ (v21 @ Y4)))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f533])).
% 89.60/14.06 thf(f533,plain,(
% 89.60/14.06 ( ! [X3 : mworld] : (($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) => (~ (v9 @ Y16))))))))))) | (v12 @ Y13)))))))))))))) | (v16 @ Y9))))))))))))))))) | (~ (v21 @ Y4))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f532,f358])).
% 89.60/14.06 thf(f532,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y13)))))))))))))) | (v16 @ Y9))))))))))))))))) | (~ (v21 @ Y4))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f531])).
% 89.60/14.06 thf(f531,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y14)))))))))))))) | (v16 @ Y10))))))))))))))))) | (~ (v21 @ Y5)))))))))))))))))))) @ X3) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f530])).
% 89.60/14.06 thf(f530,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y14)))))))))))))) | (v16 @ Y10))))))))))))))))) | (~ (v21 @ Y5))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f529])).
% 89.60/14.06 thf(f529,plain,(
% 89.60/14.06 ( ! [X2 : mworld] : ((($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))))))))))) | (v12 @ Y14)))))))))))))) | (v16 @ Y10))))))))))))))))) | (~ (v21 @ Y5)))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f528,f358])).
% 89.60/14.06 thf(f528,plain,(
% 89.60/14.06 ( ! [X2 : mworld,X1 : mworld] : (($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))))))))))) | (v12 @ Y14)))))))))))))) | (v16 @ Y10))))))))))))))))) | (~ (v21 @ Y5)))))))))))))))))))))))) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f527])).
% 89.60/14.06 thf(f527,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y15)))))))))))))) | (v16 @ Y11))))))))))))))))) | (~ (v21 @ Y6))))))))))))))))))))))) @ X2) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f526])).
% 89.60/14.06 thf(f526,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y15)))))))))))))) | (v16 @ Y11))))))))))))))))) | (~ (v21 @ Y6)))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(boolean_simplification,[status(thm)],[f525])).
% 89.60/14.06 thf(f525,plain,(
% 89.60/14.06 ( ! [X1 : mworld] : (($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) => (~ (v9 @ Y18))))))))))) | (v12 @ Y15)))))))))))))) | (v16 @ Y11))))))))))))))))) | (~ (v21 @ Y6))))))))))))))))))))))))))) )),
% 89.60/14.06 inference(forward_demodulation,[status(thm)],[f524,f358])).
% 89.60/14.06 thf(f524,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y15)))))))))))))) | (v16 @ Y11))))))))))))))))) | (~ (v21 @ Y6))))))))))))))))))))))))) = $true)) )),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f523])).
% 89.60/14.06 thf(f523,plain,(
% 89.60/14.06 ( ! [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))))))))))) | (v12 @ Y16)))))))))))))) | (v16 @ Y12))))))))))))))))) | (~ (v21 @ Y7)))))))))))))))))))))))))) @ X1) = $true)) )),
% 89.60/14.06 inference(pi_clausification,[status(thm)],[f327])).
% 89.60/14.06 thf(f327,plain,(
% 89.60/14.06 ($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))))))))))) | (v12 @ Y16)))))))))))))) | (v16 @ Y12))))))))))))))))) | (~ (v21 @ Y7))))))))))))))))))))))))))))),
% 89.60/14.06 inference(beta_eta_normalization,[status(thm)],[f274])).
% 89.60/14.06 thf(f274,plain,(
% 89.60/14.06 ($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]: (!! @ 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 > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ 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]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v12 @ ((^[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))))) @ v9))))))))))))))))))))))))))),
% 89.60/14.06 inference(definition_unfolding,[status(thm)],[f218,f226,f239,f239,f239,f239,f239,f239,f239,f239,f201,f213,f239,f239,f239,f239,f239,f201,f239,f239,f239,f239,f201,f239,f239,f239,f213])).
% 89.60/14.06 thf(f218,plain,(
% 89.60/14.06 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v21) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v16 @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v12 @ (mbox @ (mbox @ (mbox @ (mnot @ v9))))))))))))))))))))))))) = $true)),
% 89.60/14.06 inference(cnf_transformation,[status(thm)],[f145])).
% 89.60/14.06 thf(f145,plain,(
% 89.60/14.06 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v21) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v16 @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v12 @ (mbox @ (mbox @ (mbox @ (mnot @ v9))))))))))))))))))))))))) = $true)),
% 89.60/14.06 inference(fool_elimination,[status(thm)],[f144])).
% 89.60/14.06 thf(f144,plain,(
% 89.60/14.06 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v21) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v16 @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v12 @ (mbox @ (mbox @ (mbox @ (mnot @ v9)))))))))))))))))))))))))),
% 89.60/14.06 inference(rectify,[status(thm)],[f48])).
% 89.60/14.06 thf(f48,axiom,(
% 89.60/14.06 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v21) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v16 @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v12 @ (mbox @ (mbox @ (mbox @ (mnot @ v9)))))))))))))))))))))))))),
% 89.60/14.06 file('/export/starexec/sandbox/tmp/tmp.aSc01fn5sj/DTF2THF_26726.p',mod39)).
% 89.60/14.06 % SZS output end Proof for DTF2THF_26726
% 89.60/14.06 % (27322)------------------------------
% 89.60/14.06 % (27322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.60/14.06 % (27322)Termination reason: Refutation
% 89.60/14.06
% 89.60/14.06 % (27322)Memory used [KB]: 15863
% 89.60/14.06 % (27322)Time elapsed: 2.620 s
% 89.60/14.06 % (27322)Instructions burned: 9841 (million)
% 89.60/14.06 % (27322)------------------------------
% 89.60/14.06 % (27322)------------------------------
% 89.60/14.06 % (26823)Success in time 12.452 s
%------------------------------------------------------------------------------