%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO924_1.002 : TPTP v9.3.1. Released v9.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:45:43 AM UTC 2026
% Result : Theorem 74.92s 44.66s
% Output : Refutation 76.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 132
% Syntax : Number of formulae : 207 ( 140 unt; 0 typ; 130 def)
% Number of atoms : 4868 ( 146 equ; 0 cnn)
% Maximal formula atoms : 1964 ( 23 avg)
% Number of connectives : 15001 (2118 ~;2278 |;1601 &;8384 @)
% ( 0 <=>; 620 =>; 0 <=; 0 <~>)
% Maximal formula depth : 378 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 193 ( 190 usr; 20 con; 0-5 aty)
% Number of variables : 2022 ( 318 ^; 812 !; 762 ?;2022 :)
% ( 0 !>; 0 ?*; 0 @-; 130 @+)
% Comments :
%------------------------------------------------------------------------------
thf('$world_type',type,
'$world': $tType ).
thf('$local_world_decl',type,
'$local_world': '$world' ).
thf('$accessible_world_decl',type,
'$accessible_world': '$world' > '$world' > $o ).
thf(p0_decl,type,
p0: '$world' > $o ).
thf(p1_decl,type,
p1: '$world' > $o ).
thf(p3_decl,type,
p3: '$world' > $o ).
thf(p4_decl,type,
p4: '$world' > $o ).
thf(x0_decl,type,
x0: '$world' > $o ).
thf(y0_decl,type,
y0: '$world' > $o ).
thf(y1_decl,type,
y1: '$world' > $o ).
thf(y3_decl,type,
y3: '$world' > $o ).
thf(y4_decl,type,
y4: '$world' > $o ).
thf(z0_decl,type,
z0: '$world' > $o ).
thf(z1_decl,type,
z1: '$world' > $o ).
thf(z3_decl,type,
z3: '$world' > $o ).
thf(z4_decl,type,
z4: '$world' > $o ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: '$world' > $o ).
thf(sk3_decl,type,
sk3: '$world' > '$world' ).
thf(sk4_decl,type,
sk4: '$world' > $o ).
thf(sk5_decl,type,
sk5: '$world' > '$world' ).
thf(sk6_decl,type,
sk6: '$world' > '$world' ).
thf(sk7_decl,type,
sk7: '$world' > '$world' ).
thf(sk8_decl,type,
sk8: '$world' > $o ).
thf(sk9_decl,type,
sk9: '$world' > '$world' > '$world' > '$world' ).
thf(sk10_decl,type,
sk10: '$world' > '$world' > '$world' > '$world' ).
thf(sk11_decl,type,
sk11: '$world' > '$world' > '$world' > '$world' ).
thf(sk12_decl,type,
sk12: '$world' ).
thf(sk13_decl,type,
sk13: '$world' > $o ).
thf(sk14_decl,type,
sk14: '$world' > '$world' ).
thf(sk15_decl,type,
sk15: '$world' > $o ).
thf(sk16_decl,type,
sk16: '$world' > '$world' ).
thf(sk17_decl,type,
sk17: '$world' > '$world' ).
thf(sk18_decl,type,
sk18: '$world' > '$world' ).
thf(sk19_decl,type,
sk19: '$world' > $o ).
thf(sk20_decl,type,
sk20: '$world' > '$world' > '$world' > '$world' ).
thf(sk21_decl,type,
sk21: '$world' > '$world' > '$world' > '$world' ).
thf(sk22_decl,type,
sk22: '$world' > '$world' > '$world' > '$world' ).
thf(sk23_decl,type,
sk23: '$world' ).
thf(sk24_decl,type,
sk24: '$world' > '$world' ).
thf(sk25_decl,type,
sk25: '$world' > $o ).
thf(sk26_decl,type,
sk26: '$world' > '$world' ).
thf(sk27_decl,type,
sk27: '$world' > '$world' ).
thf(sk28_decl,type,
sk28: '$world' > '$world' ).
thf(sk29_decl,type,
sk29: '$world' ).
thf(sk30_decl,type,
sk30: '$world' ).
thf(sk31_decl,type,
sk31: $o ).
thf(sk32_decl,type,
sk32: '$world' ).
thf(sk33_decl,type,
sk33: '$world' ).
thf(sk34_decl,type,
sk34: '$world' ).
thf(sk35_decl,type,
sk35: '$world' ).
thf(sk36_decl,type,
sk36: '$world' > $o ).
thf(sk37_decl,type,
sk37: '$world' > '$world' ).
thf(sk38_decl,type,
sk38: '$world' > '$world' ).
thf(sk39_decl,type,
sk39: '$world' > '$world' ).
thf(sk40_decl,type,
sk40: '$world' ).
thf(sk41_decl,type,
sk41: '$world' ).
thf(sk42_decl,type,
sk42: $o ).
thf(sk43_decl,type,
sk43: '$world' ).
thf(sk44_decl,type,
sk44: '$world' ).
thf(sk45_decl,type,
sk45: '$world' ).
thf(sk46_decl,type,
sk46: '$world' ).
thf(sk47_decl,type,
sk47: '$world' > $o ).
thf(sk48_decl,type,
sk48: '$world' > '$world' ).
thf(sk49_decl,type,
sk49: '$world' > '$world' ).
thf(sk50_decl,type,
sk50: '$world' > '$world' ).
thf(sk51_decl,type,
sk51: '$world' > $o ).
thf(sk52_decl,type,
sk52: '$world' > '$world' ).
thf(sk53_decl,type,
sk53: '$world' > $o ).
thf(sk54_decl,type,
sk54: '$world' > '$world' ).
thf(sk55_decl,type,
sk55: '$world' > '$world' ).
thf(sk56_decl,type,
sk56: '$world' > '$world' ).
thf(sk57_decl,type,
sk57: '$world' > $o ).
thf(sk58_decl,type,
sk58: '$world' > '$world' > '$world' > '$world' ).
thf(sk59_decl,type,
sk59: '$world' > '$world' > '$world' > '$world' ).
thf(sk60_decl,type,
sk60: '$world' > '$world' > '$world' > '$world' ).
thf(sk61_decl,type,
sk61: '$world' > $o ).
thf(sk62_decl,type,
sk62: '$world' > '$world' > '$world' ).
thf(sk63_decl,type,
sk63: '$world' > '$world' > $o ).
thf(sk64_decl,type,
sk64: '$world' > '$world' > '$world' ).
thf(sk65_decl,type,
sk65: '$world' > '$world' > '$world' ).
thf(sk66_decl,type,
sk66: '$world' > '$world' > '$world' ).
thf(sk67_decl,type,
sk67: '$world' > $o ).
thf(sk68_decl,type,
sk68: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk69_decl,type,
sk69: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk70_decl,type,
sk70: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk71_decl,type,
sk71: '$world' > $o ).
thf(sk72_decl,type,
sk72: '$world' > '$world' > '$world' ).
thf(sk73_decl,type,
sk73: '$world' > $o ).
thf(sk74_decl,type,
sk74: '$world' > '$world' > '$world' > '$world' ).
thf(sk75_decl,type,
sk75: '$world' > '$world' > '$world' > '$world' ).
thf(sk76_decl,type,
sk76: '$world' > '$world' > '$world' > '$world' ).
thf(sk77_decl,type,
sk77: '$world' > '$world' > '$world' ).
thf(sk78_decl,type,
sk78: '$world' > '$world' > $o ).
thf(sk79_decl,type,
sk79: '$world' > '$world' > '$world' ).
thf(sk80_decl,type,
sk80: '$world' > '$world' > '$world' ).
thf(sk81_decl,type,
sk81: '$world' > '$world' > '$world' ).
thf(sk82_decl,type,
sk82: '$world' > '$world' > '$world' ).
thf(sk83_decl,type,
sk83: '$world' > '$world' > $o ).
thf(sk84_decl,type,
sk84: '$world' > '$world' > '$world' ).
thf(sk85_decl,type,
sk85: '$world' > '$world' > '$world' ).
thf(sk86_decl,type,
sk86: '$world' > '$world' > '$world' ).
thf(sk87_decl,type,
sk87: '$world' > $o ).
thf(sk88_decl,type,
sk88: '$world' > '$world' > '$world' > '$world' ).
thf(sk89_decl,type,
sk89: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk90_decl,type,
sk90: '$world' > '$world' > '$world' > '$world' > $o ).
thf(sk91_decl,type,
sk91: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk92_decl,type,
sk92: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk93_decl,type,
sk93: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk94_decl,type,
sk94: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk95_decl,type,
sk95: '$world' > '$world' > '$world' > '$world' > $o ).
thf(sk96_decl,type,
sk96: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk97_decl,type,
sk97: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk98_decl,type,
sk98: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk99_decl,type,
sk99: '$world' > '$world' > '$world' > '$world' ).
thf(sk100_decl,type,
sk100: '$world' > $o ).
thf(sk101_decl,type,
sk101: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk102_decl,type,
sk102: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk103_decl,type,
sk103: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk104_decl,type,
sk104: '$world' > $o ).
thf(sk105_decl,type,
sk105: '$world' > '$world' > '$world' ).
thf(sk106_decl,type,
sk106: '$world' > $o ).
thf(sk107_decl,type,
sk107: '$world' > '$world' > '$world' > '$world' ).
thf(sk108_decl,type,
sk108: '$world' > '$world' > '$world' > '$world' ).
thf(sk109_decl,type,
sk109: '$world' > '$world' > '$world' > '$world' ).
thf(sk110_decl,type,
sk110: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk111_decl,type,
sk111: '$world' > '$world' > '$world' > '$world' > $o ).
thf(sk112_decl,type,
sk112: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk113_decl,type,
sk113: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk114_decl,type,
sk114: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk115_decl,type,
sk115: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk116_decl,type,
sk116: '$world' > '$world' > '$world' > '$world' > $o ).
thf(sk117_decl,type,
sk117: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk118_decl,type,
sk118: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk119_decl,type,
sk119: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk120_decl,type,
sk120: '$world' > $o ).
thf(sk121_decl,type,
sk121: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk122_decl,type,
sk122: '$world' > $o ).
thf(sk123_decl,type,
sk123: '$world' > '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk124_decl,type,
sk124: '$world' > '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk125_decl,type,
sk125: '$world' > '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk126_decl,type,
sk126: '$world' > $o ).
thf(sk127_decl,type,
sk127: '$world' > $o ).
thf(sk128_decl,type,
sk128: '$world' > '$world' > '$world' > '$world' ).
thf(sk129_decl,type,
sk129: '$world' > '$world' > '$world' > '$world' ).
thf(sk130_decl,type,
sk130: '$world' > '$world' > '$world' > '$world' ).
thf(sk131_decl,type,
sk131: '$world' > $o ).
thf(sk132_decl,type,
sk132: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk133_decl,type,
sk133: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk134_decl,type,
sk134: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk135_decl,type,
sk135: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk136_decl,type,
sk136: '$world' > '$world' > '$world' > '$world' > $o ).
thf(sk137_decl,type,
sk137: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk138_decl,type,
sk138: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk139_decl,type,
sk139: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk140_decl,type,
sk140: '$world' > '$world' > '$world' > '$world' ).
thf(sk141_decl,type,
sk141: '$world' > '$world' > '$world' > $o ).
thf(sk142_decl,type,
sk142: '$world' > '$world' > '$world' > '$world' ).
thf(sk143_decl,type,
sk143: '$world' > '$world' > '$world' > '$world' ).
thf(sk144_decl,type,
sk144: '$world' > '$world' > '$world' > '$world' ).
thf(sk145_decl,type,
sk145: '$world' > '$world' > '$world' > '$world' ).
thf(sk146_decl,type,
sk146: '$world' > '$world' > '$world' > $o ).
thf(sk147_decl,type,
sk147: '$world' > '$world' > '$world' > '$world' ).
thf(sk148_decl,type,
sk148: '$world' > '$world' > '$world' > '$world' ).
thf(sk149_decl,type,
sk149: '$world' > '$world' > '$world' > '$world' ).
thf(sk150_decl,type,
sk150: '$world' > $o ).
thf(sk151_decl,type,
sk151: '$world' > '$world' > '$world' ).
thf(sk152_decl,type,
sk152: '$world' > $o ).
thf(sk153_decl,type,
sk153: '$world' > '$world' > '$world' > '$world' ).
thf(sk154_decl,type,
sk154: '$world' > '$world' > '$world' > '$world' ).
thf(sk155_decl,type,
sk155: '$world' > '$world' > '$world' > '$world' ).
thf(sk156_decl,type,
sk156: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk157_decl,type,
sk157: '$world' > '$world' > '$world' > '$world' > $o ).
thf(sk158_decl,type,
sk158: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk159_decl,type,
sk159: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk160_decl,type,
sk160: '$world' > '$world' > '$world' > '$world' > '$world' ).
thf(sk161_decl,type,
sk161: '$world' > $o ).
thf(sk162_decl,type,
sk162: '$world' > '$world' ).
thf(sk163_decl,type,
sk163: '$world' > $o ).
thf(sk164_decl,type,
sk164: '$world' > '$world' > '$world' ).
thf(sk165_decl,type,
sk165: '$world' > '$world' > '$world' ).
thf(sk166_decl,type,
sk166: '$world' > '$world' > '$world' ).
thf(sk167_decl,type,
sk167: '$world' > '$world' > '$world' > '$world' ).
thf(sk168_decl,type,
sk168: '$world' > '$world' > '$world' > $o ).
thf(sk169_decl,type,
sk169: '$world' > '$world' > '$world' > '$world' ).
thf(sk170_decl,type,
sk170: '$world' > '$world' > '$world' > '$world' ).
thf(sk171_decl,type,
sk171: '$world' > '$world' > '$world' > '$world' ).
thf(sk172_decl,type,
sk172: '$world' > $o ).
thf(sk173_decl,type,
sk173: '$world' > '$world' ).
thf(sk174_decl,type,
sk174: '$world' > '$world' ).
thf(sk175_decl,type,
sk175: '$world' > '$world' ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ sk3 @ '$accessible_world' ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ sk5 @ '$accessible_world' ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ z1 ) )
& ( B @ ( A @ sk6 @ '$accessible_world' ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk9 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ ( B @ ( A @ sk10 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ~ ( D @ p1 ) ) ) )
| ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ sk14 @ '$accessible_world' ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ sk16 @ '$accessible_world' ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ z1 ) )
& ( B @ ( A @ sk17 @ '$accessible_world' ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk20 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ ( B @ ( A @ sk21 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( @+[A: '$world'] :
( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z0 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y0 ) )
& ~ ( C @ y0 ) )
| ~ ( C @ p0 ) )
& ( C @ ( B @ '$accessible_world' ) ) ) )
& ( A @ ( sk12 @ '$accessible_world' ) ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z0 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z0 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y0 ) )
& ~ ( B @ y0 ) )
| ~ ( B @ p0 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z0 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ sk24 @ '$accessible_world' ) ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z0 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ sk26 @ '$accessible_world' ) ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ z0 ) )
& ( B @ ( A @ sk27 @ '$accessible_world' ) ) ) ) ) ).
thf(sk29_def,definition,
( sk29
= ( @+[A: '$world'] :
( ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ~ ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( sk12 @ '$accessible_world' ) ) ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( @+[A: '$world'] :
( ( ( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ~ ( A @ z1 ) )
| ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ y1 ) )
& ~ ( A @ y1 ) )
| ~ ( A @ p1 ) )
& ( A @ ( sk29 @ '$accessible_world' ) ) ) ) ) ).
thf(sk32_def,definition,
( sk32
= ( @+[A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( sk30 @ '$accessible_world' ) ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( @+[A: '$world'] :
( ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ z1 ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( sk32 @ '$accessible_world' ) ) ) ) ) ).
thf(sk34_def,definition,
( sk34
= ( @+[A: '$world'] :
( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ z1 ) )
& ( A @ ( sk33 @ '$accessible_world' ) ) ) ) ) ).
thf(sk35_def,definition,
( sk35
= ( @+[A: '$world'] :
( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ( B @ p1 ) ) )
& ( A @ ( sk29 @ '$accessible_world' ) ) ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk38_def,definition,
( sk38
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ sk37 @ '$accessible_world' ) ) ) ) ) ).
thf(sk39_def,definition,
( sk39
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ z1 ) )
& ( B @ ( A @ sk38 @ '$accessible_world' ) ) ) ) ) ).
thf(sk40_def,definition,
( sk40
= ( @+[A: '$world'] :
( ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ~ ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ) ).
thf(sk41_def,definition,
( sk41
= ( @+[A: '$world'] :
( ( ( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ~ ( A @ z1 ) )
| ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ y1 ) )
& ~ ( A @ y1 ) )
| ~ ( A @ p1 ) )
& ( A @ ( sk40 @ '$accessible_world' ) ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( @+[A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( sk41 @ '$accessible_world' ) ) ) ) ) ).
thf(sk44_def,definition,
( sk44
= ( @+[A: '$world'] :
( ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ z1 ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( sk43 @ '$accessible_world' ) ) ) ) ) ).
thf(sk45_def,definition,
( sk45
= ( @+[A: '$world'] :
( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ z1 ) )
& ( A @ ( sk44 @ '$accessible_world' ) ) ) ) ) ).
thf(sk46_def,definition,
( sk46
= ( @+[A: '$world'] :
( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ( B @ p1 ) ) )
& ( A @ ( sk40 @ '$accessible_world' ) ) ) ) ) ).
thf(sk48_def,definition,
( sk48
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk49_def,definition,
( sk49
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ sk48 @ '$accessible_world' ) ) ) ) ) ).
thf(sk50_def,definition,
( sk50
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ z1 ) )
& ( B @ ( A @ sk49 @ '$accessible_world' ) ) ) ) ) ).
thf(sk52_def,definition,
( sk52
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ~ ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk54_def,definition,
( sk54
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ sk52 @ '$accessible_world' ) ) ) ) ) ).
thf(sk55_def,definition,
( sk55
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ sk54 @ '$accessible_world' ) ) ) ) ) ).
thf(sk56_def,definition,
( sk56
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ z1 ) )
& ( B @ ( A @ sk55 @ '$accessible_world' ) ) ) ) ) ).
thf(sk58_def,definition,
( sk58
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk59_def,definition,
( sk59
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk58 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk60_def,definition,
( sk60
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ ( B @ ( A @ sk59 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk62_def,definition,
( sk62
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) )
& ( C @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk64_def,definition,
( sk64
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ ( A @ sk62 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk65_def,definition,
( sk65
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ ( A @ sk64 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk66_def,definition,
( sk66
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z1 ) )
& ( C @ ( B @ ( A @ sk65 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk68_def,definition,
( sk68
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk69_def,definition,
( sk69
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk68 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk70_def,definition,
( sk70
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk69 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk72_def,definition,
( sk72
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) ) )
& ( C @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk74_def,definition,
( sk74
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk75_def,definition,
( sk75
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z0 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk74 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk76_def,definition,
( sk76
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z0 ) )
& ( D @ ( C @ ( B @ ( A @ sk75 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk77_def,definition,
( sk77
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z3 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y3 ) )
& ~ ( D @ y3 ) )
| ~ ( D @ p3 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z0 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y0 ) )
& ~ ( C @ y0 ) )
| ( C @ p0 ) )
& ( C @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk79_def,definition,
( sk79
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z0 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ ( A @ sk77 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk80_def,definition,
( sk80
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z0 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ ( A @ sk79 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk81_def,definition,
( sk81
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z0 ) )
& ( C @ ( B @ ( A @ sk80 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk82_def,definition,
( sk82
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z3 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z3 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y3 ) )
& ~ ( C @ y3 ) )
| ~ ( C @ p3 ) )
& ( C @ ( B @ ( A @ sk77 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk84_def,definition,
( sk84
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z3 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ ( A @ sk82 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk85_def,definition,
( sk85
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z3 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ ( A @ sk84 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk86_def,definition,
( sk86
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z3 ) )
& ( C @ ( B @ ( A @ sk85 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk88_def,definition,
( sk88
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ? [F: '$world'] :
( ? [G: '$world'] :
( ( ( ? [H: '$world'] :
( ? [I: '$world'] :
( ? [J: '$world'] :
( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ z3 ) )
& ( J @ ( I @ '$accessible_world' ) ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ~ ( G @ z3 ) )
| ( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ y3 ) )
& ~ ( G @ y3 ) )
| ~ ( G @ p3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z0 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y0 ) )
& ~ ( F @ y0 ) )
| ( F @ p0 ) )
& ( F @ ( E @ '$accessible_world' ) ) ) )
& ( D @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk89_def,definition,
( sk89
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z3 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z3 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y3 ) )
& ~ ( F @ y3 ) )
| ~ ( F @ p3 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z0 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y0 ) )
& ~ ( E @ y0 ) )
| ( E @ p0 ) )
& ( E @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk91_def,definition,
( sk91
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk89 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk92_def,definition,
( sk92
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk91 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk93_def,definition,
( sk93
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z0 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk92 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk94_def,definition,
( sk94
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk89 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk96_def,definition,
( sk96
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk94 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk97_def,definition,
( sk97
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z3 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk96 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk98_def,definition,
( sk98
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z3 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk97 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk99_def,definition,
( sk99
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z0 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y0 ) )
& ~ ( E @ y0 ) )
| ~ ( E @ p0 ) ) )
& ( D @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk101_def,definition,
( sk101
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk102_def,definition,
( sk102
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk101 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk103_def,definition,
( sk103
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z0 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk102 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk105_def,definition,
( sk105
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) ) )
& ( C @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk107_def,definition,
( sk107
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk108_def,definition,
( sk108
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z0 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk107 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk109_def,definition,
( sk109
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z0 ) )
& ( D @ ( C @ ( B @ ( A @ sk108 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk110_def,definition,
( sk110
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z3 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z3 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y3 ) )
& ~ ( F @ y3 ) )
| ~ ( F @ p3 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z0 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y0 ) )
& ~ ( E @ y0 ) )
| ( E @ p0 ) )
& ( E @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk112_def,definition,
( sk112
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk110 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk113_def,definition,
( sk113
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk112 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk114_def,definition,
( sk114
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z0 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk113 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk115_def,definition,
( sk115
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk110 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk117_def,definition,
( sk117
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk115 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk118_def,definition,
( sk118
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z3 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk117 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk119_def,definition,
( sk119
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z3 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk118 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk121_def,definition,
( sk121
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z0 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y0 ) )
& ~ ( F @ y0 ) )
| ~ ( F @ p0 ) ) )
& ( E @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk123_def,definition,
( sk123
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world',E: '$world'] :
@+[F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk124_def,definition,
( sk124
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world',E: '$world'] :
@+[F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ sk123 ) ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk125_def,definition,
( sk125
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world',E: '$world'] :
@+[F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ sk124 ) ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk128_def,definition,
( sk128
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk129_def,definition,
( sk129
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z0 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk128 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk130_def,definition,
( sk130
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z0 ) )
& ( D @ ( C @ ( B @ ( A @ sk129 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk132_def,definition,
( sk132
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk133_def,definition,
( sk133
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk132 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk134_def,definition,
( sk134
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z0 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk133 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk135_def,definition,
( sk135
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk137_def,definition,
( sk137
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk135 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk138_def,definition,
( sk138
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z3 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk137 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk139_def,definition,
( sk139
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z3 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk138 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk140_def,definition,
( sk140
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ( D @ p0 ) )
& ( D @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk142_def,definition,
( sk142
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk140 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk143_def,definition,
( sk143
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z0 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk142 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk144_def,definition,
( sk144
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z0 ) )
& ( D @ ( C @ ( B @ ( A @ sk143 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk145_def,definition,
( sk145
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z3 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y3 ) )
& ~ ( D @ y3 ) )
| ~ ( D @ p3 ) )
& ( D @ ( C @ ( B @ ( A @ sk140 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk147_def,definition,
( sk147
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z3 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk145 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk148_def,definition,
( sk148
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z3 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk147 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk149_def,definition,
( sk149
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z3 ) )
& ( D @ ( C @ ( B @ ( A @ sk148 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk151_def,definition,
( sk151
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ~ ( D @ p1 ) ) )
& ( C @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk153_def,definition,
( sk153
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk154_def,definition,
( sk154
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk153 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk155_def,definition,
( sk155
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ ( B @ ( A @ sk154 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk156_def,definition,
( sk156
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z1 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z1 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y1 ) )
& ~ ( E @ y1 ) )
| ( E @ p1 ) )
& ( E @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk158_def,definition,
( sk158
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk156 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk159_def,definition,
( sk159
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk158 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk160_def,definition,
( sk160
= ( ^ [A: '$world',B: '$world',C: '$world',D: '$world'] :
@+[E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ sk159 ) ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk162_def,definition,
( sk162
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk164_def,definition,
( sk164
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk165_def,definition,
( sk165
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ ( A @ sk164 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk166_def,definition,
( sk166
= ( ^ [A: '$world',B: '$world'] :
@+[C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z1 ) )
& ( C @ ( B @ ( A @ sk165 ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk167_def,definition,
( sk167
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) )
& ( D @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk169_def,definition,
( sk169
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk167 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk170_def,definition,
( sk170
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ ( B @ ( A @ sk169 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk171_def,definition,
( sk171
= ( ^ [A: '$world',B: '$world',C: '$world'] :
@+[D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z1 ) )
& ( D @ ( C @ ( B @ ( A @ sk170 ) ) @ '$accessible_world' ) ) ) ) ) ).
thf(sk173_def,definition,
( sk173
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z4 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) ).
thf(sk174_def,definition,
( sk174
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ z4 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ sk173 @ '$accessible_world' ) ) ) ) ) ).
thf(sk175_def,definition,
( sk175
= ( ^ [A: '$world'] :
@+[B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ z4 ) )
& ( B @ ( A @ sk174 @ '$accessible_world' ) ) ) ) ) ).
thf(1,conjecture,
~ ( ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z4 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ~ ( A @ z4 ) )
| ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ y4 ) )
& ~ ( A @ y4 ) )
| ~ ( A @ p4 ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) ) )
| ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z1 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z1 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y1 ) )
& ~ ( E @ y1 ) )
| ( E @ p1 ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ~ ( D @ p1 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ( D @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) )
& ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ( D @ p0 ) ) ) )
| ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z0 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y0 ) )
& ~ ( C @ y0 ) )
| ~ ( C @ p0 )
| ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z0 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y0 ) )
& ~ ( F @ y0 ) )
| ~ ( F @ p0 ) ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) ) )
& ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ? [F: '$world'] :
( ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z3 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z3 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y3 ) )
& ~ ( F @ y3 ) )
| ~ ( F @ p3 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z0 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y0 ) )
& ~ ( E @ y0 ) )
| ( E @ p0 ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) )
& ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z0 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y0 ) )
& ~ ( E @ y0 ) )
| ~ ( E @ p0 ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
| ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ? [F: '$world'] :
( ? [G: '$world'] :
( ( ( ? [H: '$world'] :
( ? [I: '$world'] :
( ? [J: '$world'] :
( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ z3 ) )
& ( J @ ( I @ '$accessible_world' ) ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ~ ( G @ z3 ) )
| ( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ y3 ) )
& ~ ( G @ y3 ) )
| ~ ( G @ p3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z0 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y0 ) )
& ~ ( F @ y0 ) )
| ( F @ p0 ) )
& ( F @ ( E @ '$accessible_world' ) ) ) )
& ( D @ ( C @ '$accessible_world' ) ) ) ) )
& ( ? [C: '$world'] :
( ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z3 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y3 ) )
& ~ ( D @ y3 ) )
| ~ ( D @ p3 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z0 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y0 ) )
& ~ ( C @ y0 ) )
| ( C @ p0 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) ) ) )
| ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) ) ) )
| ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ~ ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) )
& ? [A: '$world'] :
( ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ~ ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
& ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ~ ( D @ p1 ) ) ) )
| ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) ) ) )
| ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) )
| ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ~ ( A @ x0 ) )
& ( '$local_world' @ x0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ~ ( ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z4 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ~ ( A @ z4 ) )
| ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ y4 ) )
& ~ ( A @ y4 ) )
| ~ ( A @ p4 ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) ) )
| ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z1 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z1 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y1 ) )
& ~ ( E @ y1 ) )
| ( E @ p1 ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ~ ( D @ p1 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ( D @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) )
& ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ( D @ p0 ) ) ) )
| ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z0 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y0 ) )
& ~ ( C @ y0 ) )
| ~ ( C @ p0 )
| ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z0 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y0 ) )
& ~ ( F @ y0 ) )
| ~ ( F @ p0 ) ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) ) )
& ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ? [F: '$world'] :
( ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z3 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z3 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y3 ) )
& ~ ( F @ y3 ) )
| ~ ( F @ p3 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z0 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y0 ) )
& ~ ( E @ y0 ) )
| ( E @ p0 ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) )
& ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z0 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y0 ) )
& ~ ( E @ y0 ) )
| ~ ( E @ p0 ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
| ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ? [F: '$world'] :
( ? [G: '$world'] :
( ( ( ? [H: '$world'] :
( ? [I: '$world'] :
( ? [J: '$world'] :
( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ z3 ) )
& ( J @ ( I @ '$accessible_world' ) ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ~ ( G @ z3 ) )
| ( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ y3 ) )
& ~ ( G @ y3 ) )
| ~ ( G @ p3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z0 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y0 ) )
& ~ ( F @ y0 ) )
| ( F @ p0 ) )
& ( F @ ( E @ '$accessible_world' ) ) ) )
& ( D @ ( C @ '$accessible_world' ) ) ) ) )
& ( ? [C: '$world'] :
( ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z3 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y3 ) )
& ~ ( D @ y3 ) )
| ~ ( D @ p3 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z0 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y0 ) )
& ~ ( C @ y0 ) )
| ( C @ p0 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) ) ) )
| ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) ) ) )
| ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ~ ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) )
& ? [A: '$world'] :
( ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ~ ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
& ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ~ ( D @ p1 ) ) ) )
| ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) ) ) )
| ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) )
| ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ~ ( A @ x0 ) )
& ( '$local_world' @ x0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ~ ( ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z4 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ~ ( A @ z4 ) )
| ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ y4 ) )
& ~ ( A @ y4 ) )
| ~ ( A @ p4 ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) ) )
| ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z1 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z1 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y1 ) )
& ~ ( E @ y1 ) )
| ( E @ p1 ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ~ ( D @ p1 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ( D @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) )
& ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ( D @ p0 ) ) ) )
| ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z0 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y0 ) )
& ~ ( C @ y0 ) )
| ~ ( C @ p0 )
| ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z0 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y0 ) )
& ~ ( F @ y0 ) )
| ~ ( F @ p0 ) ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) ) )
& ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ? [F: '$world'] :
( ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z3 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z3 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y3 ) )
& ~ ( F @ y3 ) )
| ~ ( F @ p3 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z0 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y0 ) )
& ~ ( E @ y0 ) )
| ( E @ p0 ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) )
& ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z0 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y0 ) )
& ~ ( E @ y0 ) )
| ~ ( E @ p0 ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
| ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ? [F: '$world'] :
( ? [G: '$world'] :
( ( ( ? [H: '$world'] :
( ? [I: '$world'] :
( ? [J: '$world'] :
( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ z3 ) )
& ( J @ ( I @ '$accessible_world' ) ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ~ ( G @ z3 ) )
| ( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ y3 ) )
& ~ ( G @ y3 ) )
| ~ ( G @ p3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z0 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y0 ) )
& ~ ( F @ y0 ) )
| ( F @ p0 ) )
& ( F @ ( E @ '$accessible_world' ) ) ) )
& ( D @ ( C @ '$accessible_world' ) ) ) ) )
& ( ? [C: '$world'] :
( ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z3 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y3 ) )
& ~ ( D @ y3 ) )
| ~ ( D @ p3 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z0 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y0 ) )
& ~ ( C @ y0 ) )
| ( C @ p0 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) ) ) )
| ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) ) ) )
| ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ~ ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) )
& ? [A: '$world'] :
( ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ~ ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
& ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ~ ( D @ p1 ) ) ) )
| ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) ) ) )
| ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) )
| ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ~ ( A @ x0 ) )
& ( '$local_world' @ x0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ( ? [B: '$world'] :
( ? [C: '$world'] :
( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ z4 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ~ ( A @ z4 ) )
| ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ y4 ) )
& ~ ( A @ y4 ) )
| ~ ( A @ p4 ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) ) )
| ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z1 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z1 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y1 ) )
& ~ ( E @ y1 ) )
| ( E @ p1 ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ~ ( D @ p1 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ( D @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) )
& ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ? [E: '$world'] :
( ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z3 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z3 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y3 ) )
& ~ ( E @ y3 ) )
| ~ ( E @ p3 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ( D @ p0 ) ) ) )
| ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z0 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y0 ) )
& ~ ( C @ y0 ) )
| ~ ( C @ p0 )
| ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z0 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y0 ) )
& ~ ( F @ y0 ) )
| ~ ( F @ p0 ) ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) ) )
& ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ? [E: '$world'] :
( ? [F: '$world'] :
( ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z3 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z3 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y3 ) )
& ~ ( F @ y3 ) )
| ~ ( F @ p3 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z0 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y0 ) )
& ~ ( E @ y0 ) )
| ( E @ p0 ) )
& ( E @ ( D @ '$accessible_world' ) ) ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) )
& ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( ( ? [F: '$world'] :
( ? [G: '$world'] :
( ? [H: '$world'] :
( ! [I: '$world'] :
( ( I @ ( H @ '$accessible_world' ) )
=> ( I @ z0 ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ~ ( E @ z0 ) )
| ( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ y0 ) )
& ~ ( E @ y0 ) )
| ~ ( E @ p0 ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
| ? [D: '$world'] :
( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ? [F: '$world'] :
( ? [G: '$world'] :
( ( ( ? [H: '$world'] :
( ? [I: '$world'] :
( ? [J: '$world'] :
( ! [K: '$world'] :
( ( K @ ( J @ '$accessible_world' ) )
=> ( K @ z3 ) )
& ( J @ ( I @ '$accessible_world' ) ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ~ ( G @ z3 ) )
| ( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ y3 ) )
& ~ ( G @ y3 ) )
| ~ ( G @ p3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( ( ? [G: '$world'] :
( ? [H: '$world'] :
( ? [I: '$world'] :
( ! [J: '$world'] :
( ( J @ ( I @ '$accessible_world' ) )
=> ( J @ z0 ) )
& ( I @ ( H @ '$accessible_world' ) ) )
& ( H @ ( G @ '$accessible_world' ) ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ~ ( F @ z0 ) )
| ( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ y0 ) )
& ~ ( F @ y0 ) )
| ( F @ p0 ) )
& ( F @ ( E @ '$accessible_world' ) ) ) )
& ( D @ ( C @ '$accessible_world' ) ) ) ) )
& ( ? [C: '$world'] :
( ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z3 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z3 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y3 ) )
& ~ ( D @ y3 ) )
| ~ ( D @ p3 ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z0 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z0 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y0 ) )
& ~ ( C @ y0 ) )
| ( C @ p0 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
| ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) ) ) )
| ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) ) ) )
| ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ~ ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) )
& ? [A: '$world'] :
( ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ~ ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
& ? [A: '$world'] :
( ? [B: '$world'] :
( ? [C: '$world'] :
( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ( D @ p1 ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ? [B: '$world'] :
( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ? [D: '$world'] :
( ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z0 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z0 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y0 ) )
& ~ ( D @ y0 ) )
| ~ ( D @ p0 ) )
& ( D @ ( C @ '$accessible_world' ) ) ) )
& ( B @ ( A @ '$accessible_world' ) ) )
& ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( ( ? [E: '$world'] :
( ? [F: '$world'] :
( ? [G: '$world'] :
( ! [H: '$world'] :
( ( H @ ( G @ '$accessible_world' ) )
=> ( H @ z1 ) )
& ( G @ ( F @ '$accessible_world' ) ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ~ ( D @ z1 ) )
| ( ! [E: '$world'] :
( ( E @ ( D @ '$accessible_world' ) )
=> ( E @ y1 ) )
& ~ ( D @ y1 ) )
| ~ ( D @ p1 ) ) ) )
| ? [C: '$world'] :
( ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ( C @ p1 ) )
& ( C @ ( B @ '$accessible_world' ) ) ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
& ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( ( ? [D: '$world'] :
( ? [E: '$world'] :
( ? [F: '$world'] :
( ! [G: '$world'] :
( ( G @ ( F @ '$accessible_world' ) )
=> ( G @ z1 ) )
& ( F @ ( E @ '$accessible_world' ) ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ~ ( C @ z1 ) )
| ( ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( D @ y1 ) )
& ~ ( C @ y1 ) )
| ~ ( C @ p1 ) ) ) )
| ? [B: '$world'] :
( ( ( ? [C: '$world'] :
( ? [D: '$world'] :
( ? [E: '$world'] :
( ! [F: '$world'] :
( ( F @ ( E @ '$accessible_world' ) )
=> ( F @ z1 ) )
& ( E @ ( D @ '$accessible_world' ) ) )
& ( D @ ( C @ '$accessible_world' ) ) )
& ( C @ ( B @ '$accessible_world' ) ) )
& ~ ( B @ z1 ) )
| ( ! [C: '$world'] :
( ( C @ ( B @ '$accessible_world' ) )
=> ( C @ y1 ) )
& ~ ( B @ y1 ) )
| ( B @ p1 ) )
& ( B @ ( A @ '$accessible_world' ) ) ) ) ) )
| ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ~ ( A @ x0 ) )
& ( '$local_world' @ x0 ) ) ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
! [ZZZZA: '$world',ZZZZ: '$world',ZZZY: '$world',ZZZX: '$world',ZZZW: '$world',ZZZV: '$world',ZZZU: '$world',ZZZT: '$world',ZZZS: '$world',ZZZR: '$world',ZZZQ: '$world',ZZZP: '$world',ZZZO: '$world',ZZZN: '$world',ZZZM: '$world',ZZZL: '$world',ZZZK: '$world',ZZZJ: '$world',ZZZI: '$world',ZZZH: '$world',ZZZG: '$world',ZZZF: '$world',ZZZE: '$world',ZZZD: '$world',ZZZC: '$world',ZZZB: '$world',ZZZA: '$world',ZZZ: '$world',ZZY: '$world',ZZX: '$world',ZZW: '$world',ZZV: '$world',ZZU: '$world',ZZT: '$world',ZZS: '$world',ZZR: '$world',ZZQ: '$world',ZZP: '$world',ZZO: '$world',ZZN: '$world',ZZM: '$world',ZZL: '$world',ZZK: '$world',ZZJ: '$world',ZZI: '$world',ZZH: '$world',ZZG: '$world',ZZF: '$world',ZZE: '$world',ZZD: '$world',ZZC: '$world',ZZB: '$world',ZZA: '$world',ZZ: '$world',ZY: '$world',ZX: '$world',ZW: '$world',ZV: '$world',ZU: '$world',ZT: '$world',ZS: '$world',ZR: '$world',ZQ: '$world',ZP: '$world',ZO: '$world',ZN: '$world',ZM: '$world',ZL: '$world',ZK: '$world',ZJ: '$world',ZI: '$world',ZH: '$world',ZG: '$world',ZF: '$world',ZE: '$world',ZD: '$world',ZC: '$world',ZB: '$world',ZA: '$world',Z: '$world',Y: '$world',X: '$world',W: '$world',V: '$world',U: '$world',T: '$world',S: '$world',R: '$world',Q: '$world',P: '$world',O: '$world',N: '$world',M: '$world',L: '$world',K: '$world',J: '$world',I: '$world',H: '$world',G: '$world',F: '$world',E: '$world',D: '$world',C: '$world',B: '$world',A: '$world'] :
( ( ( ZZZZA @ z4 )
| ~ ( ZZZZA @ ( ZZZY @ sk175 @ '$accessible_world' ) )
| ~ ( ZZZY @ sk172 )
| ~ ( ZZZY @ p4 )
| ~ ( ZZZY @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZY @ sk175 @ ( ZZZY @ sk174 @ '$accessible_world' ) )
| ~ ( ZZZY @ sk172 )
| ~ ( ZZZY @ p4 )
| ~ ( ZZZY @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZY @ sk174 @ ( ZZZY @ sk173 @ '$accessible_world' ) )
| ~ ( ZZZY @ sk172 )
| ~ ( ZZZY @ p4 )
| ~ ( ZZZY @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZY @ sk173 @ ( ZZZY @ '$accessible_world' ) )
| ~ ( ZZZY @ sk172 )
| ~ ( ZZZY @ p4 )
| ~ ( ZZZY @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( ZZZY @ z4 )
| ~ ( ZZZY @ sk172 )
| ~ ( ZZZY @ p4 )
| ~ ( ZZZY @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZY @ sk172 )
| ( ZZZZ @ y4 )
| ~ ( ZZZZ @ ( ZZZY @ '$accessible_world' ) )
| ~ ( ZZZY @ p4 )
| ~ ( ZZZY @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZY @ sk172 )
| ~ ( ZZZY @ y4 )
| ~ ( ZZZY @ p4 )
| ~ ( ZZZY @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZX @ z1 )
| ~ ( ZZZX @ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk171 ) ) @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk168 ) ) )
| ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ p1 )
| ~ ( ZZZV @ ( ZZZU @ '$accessible_world' ) )
| ~ ( ZZZU @ ( ZZZQ @ '$accessible_world' ) )
| ~ ( ZZZQ @ sk161 )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk171 ) ) @ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk170 ) ) @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk168 ) ) )
| ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ p1 )
| ~ ( ZZZV @ ( ZZZU @ '$accessible_world' ) )
| ~ ( ZZZU @ ( ZZZQ @ '$accessible_world' ) )
| ~ ( ZZZQ @ sk161 )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk170 ) ) @ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk169 ) ) @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk168 ) ) )
| ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ p1 )
| ~ ( ZZZV @ ( ZZZU @ '$accessible_world' ) )
| ~ ( ZZZU @ ( ZZZQ @ '$accessible_world' ) )
| ~ ( ZZZQ @ sk161 )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk169 ) ) @ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk168 ) ) )
| ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ p1 )
| ~ ( ZZZV @ ( ZZZU @ '$accessible_world' ) )
| ~ ( ZZZU @ ( ZZZQ @ '$accessible_world' ) )
| ~ ( ZZZQ @ sk161 )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ z1 )
| ~ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk168 ) ) )
| ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ p1 )
| ~ ( ZZZV @ ( ZZZU @ '$accessible_world' ) )
| ~ ( ZZZU @ ( ZZZQ @ '$accessible_world' ) )
| ~ ( ZZZQ @ sk161 )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk168 ) ) )
| ( ZZZW @ y1 )
| ~ ( ZZZW @ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ '$accessible_world' ) )
| ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ p1 )
| ~ ( ZZZV @ ( ZZZU @ '$accessible_world' ) )
| ~ ( ZZZU @ ( ZZZQ @ '$accessible_world' ) )
| ~ ( ZZZQ @ sk161 )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk168 ) ) )
| ~ ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ y1 )
| ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ p1 )
| ~ ( ZZZV @ ( ZZZU @ '$accessible_world' ) )
| ~ ( ZZZU @ ( ZZZQ @ '$accessible_world' ) )
| ~ ( ZZZQ @ sk161 )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ ( ZZZU @ ( ZZZV @ sk167 ) ) @ ( ZZZV @ '$accessible_world' ) )
| ~ ( ZZZV @ ( ZZZU @ '$accessible_world' ) )
| ~ ( ZZZU @ ( ZZZQ @ '$accessible_world' ) )
| ~ ( ZZZQ @ sk161 )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ sk161 )
| ( ZZZT @ z1 )
| ~ ( ZZZT @ ( ZZZQ @ ( ZZZR @ sk166 ) @ '$accessible_world' ) )
| ~ ( ZZZR @ sk163 )
| ~ ( ZZZR @ p1 )
| ~ ( ZZZR @ ( ZZZQ @ sk162 @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ sk161 )
| ( ZZZQ @ ( ZZZR @ sk166 ) @ ( ZZZQ @ ( ZZZR @ sk165 ) @ '$accessible_world' ) )
| ~ ( ZZZR @ sk163 )
| ~ ( ZZZR @ p1 )
| ~ ( ZZZR @ ( ZZZQ @ sk162 @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ sk161 )
| ( ZZZQ @ ( ZZZR @ sk165 ) @ ( ZZZQ @ ( ZZZR @ sk164 ) @ '$accessible_world' ) )
| ~ ( ZZZR @ sk163 )
| ~ ( ZZZR @ p1 )
| ~ ( ZZZR @ ( ZZZQ @ sk162 @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ sk161 )
| ( ZZZQ @ ( ZZZR @ sk164 ) @ ( ZZZR @ '$accessible_world' ) )
| ~ ( ZZZR @ sk163 )
| ~ ( ZZZR @ p1 )
| ~ ( ZZZR @ ( ZZZQ @ sk162 @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ sk161 )
| ~ ( ZZZR @ z1 )
| ~ ( ZZZR @ sk163 )
| ~ ( ZZZR @ p1 )
| ~ ( ZZZR @ ( ZZZQ @ sk162 @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ sk161 )
| ( ZZZR @ sk163 )
| ( ZZZS @ y1 )
| ~ ( ZZZS @ ( ZZZR @ '$accessible_world' ) )
| ~ ( ZZZR @ p1 )
| ~ ( ZZZR @ ( ZZZQ @ sk162 @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ sk161 )
| ( ZZZR @ sk163 )
| ~ ( ZZZR @ y1 )
| ~ ( ZZZR @ p1 )
| ~ ( ZZZR @ ( ZZZQ @ sk162 @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZQ @ sk161 )
| ( ZZZQ @ sk162 @ ( ZZZQ @ '$accessible_world' ) )
| ~ ( ZZZQ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZP @ z1 )
| ~ ( ZZZP @ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk160 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk157 ) ) ) )
| ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ p1 )
| ~ ( ZZZN @ ( ZZZM @ '$accessible_world' ) )
| ~ ( ZZZM @ ( ZZZI @ '$accessible_world' ) )
| ~ ( ZZZI @ sk150 )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk160 ) ) ) @ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk159 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk157 ) ) ) )
| ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ p1 )
| ~ ( ZZZN @ ( ZZZM @ '$accessible_world' ) )
| ~ ( ZZZM @ ( ZZZI @ '$accessible_world' ) )
| ~ ( ZZZI @ sk150 )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk159 ) ) ) @ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk158 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk157 ) ) ) )
| ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ p1 )
| ~ ( ZZZN @ ( ZZZM @ '$accessible_world' ) )
| ~ ( ZZZM @ ( ZZZI @ '$accessible_world' ) )
| ~ ( ZZZI @ sk150 )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk158 ) ) ) @ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk157 ) ) ) )
| ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ p1 )
| ~ ( ZZZN @ ( ZZZM @ '$accessible_world' ) )
| ~ ( ZZZM @ ( ZZZI @ '$accessible_world' ) )
| ~ ( ZZZI @ sk150 )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ z1 )
| ~ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk157 ) ) ) )
| ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ p1 )
| ~ ( ZZZN @ ( ZZZM @ '$accessible_world' ) )
| ~ ( ZZZM @ ( ZZZI @ '$accessible_world' ) )
| ~ ( ZZZI @ sk150 )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk157 ) ) ) )
| ( ZZZO @ y1 )
| ~ ( ZZZO @ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ '$accessible_world' ) )
| ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ p1 )
| ~ ( ZZZN @ ( ZZZM @ '$accessible_world' ) )
| ~ ( ZZZM @ ( ZZZI @ '$accessible_world' ) )
| ~ ( ZZZI @ sk150 )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk157 ) ) ) )
| ~ ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ y1 )
| ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ p1 )
| ~ ( ZZZN @ ( ZZZM @ '$accessible_world' ) )
| ~ ( ZZZM @ ( ZZZI @ '$accessible_world' ) )
| ~ ( ZZZI @ sk150 )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZZZI @ ( ZZZM @ ( ZZZN @ sk156 ) ) ) @ ( ZZZN @ '$accessible_world' ) )
| ~ ( ZZZN @ ( ZZZM @ '$accessible_world' ) )
| ~ ( ZZZM @ ( ZZZI @ '$accessible_world' ) )
| ~ ( ZZZI @ sk150 )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZI @ sk150 )
| ( ZZZL @ z1 )
| ~ ( ZZZL @ ( ZJ @ ( ZZZI @ ( ZZZJ @ sk155 ) ) @ '$accessible_world' ) )
| ~ ( ZZZJ @ sk152 )
| ~ ( ZZZJ @ p1 )
| ~ ( ZZZJ @ ( ZJ @ ( ZZZI @ sk151 ) @ '$accessible_world' ) )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZI @ sk150 )
| ( ZJ @ ( ZZZI @ ( ZZZJ @ sk155 ) ) @ ( ZJ @ ( ZZZI @ ( ZZZJ @ sk154 ) ) @ '$accessible_world' ) )
| ~ ( ZZZJ @ sk152 )
| ~ ( ZZZJ @ p1 )
| ~ ( ZZZJ @ ( ZJ @ ( ZZZI @ sk151 ) @ '$accessible_world' ) )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZI @ sk150 )
| ( ZJ @ ( ZZZI @ ( ZZZJ @ sk154 ) ) @ ( ZJ @ ( ZZZI @ ( ZZZJ @ sk153 ) ) @ '$accessible_world' ) )
| ~ ( ZZZJ @ sk152 )
| ~ ( ZZZJ @ p1 )
| ~ ( ZZZJ @ ( ZJ @ ( ZZZI @ sk151 ) @ '$accessible_world' ) )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZI @ sk150 )
| ( ZJ @ ( ZZZI @ ( ZZZJ @ sk153 ) ) @ ( ZZZJ @ '$accessible_world' ) )
| ~ ( ZZZJ @ sk152 )
| ~ ( ZZZJ @ p1 )
| ~ ( ZZZJ @ ( ZJ @ ( ZZZI @ sk151 ) @ '$accessible_world' ) )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZI @ sk150 )
| ~ ( ZZZJ @ z1 )
| ~ ( ZZZJ @ sk152 )
| ~ ( ZZZJ @ p1 )
| ~ ( ZZZJ @ ( ZJ @ ( ZZZI @ sk151 ) @ '$accessible_world' ) )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZI @ sk150 )
| ( ZZZJ @ sk152 )
| ( ZZZK @ y1 )
| ~ ( ZZZK @ ( ZZZJ @ '$accessible_world' ) )
| ~ ( ZZZJ @ p1 )
| ~ ( ZZZJ @ ( ZJ @ ( ZZZI @ sk151 ) @ '$accessible_world' ) )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZI @ sk150 )
| ( ZZZJ @ sk152 )
| ~ ( ZZZJ @ y1 )
| ~ ( ZZZJ @ p1 )
| ~ ( ZZZJ @ ( ZJ @ ( ZZZI @ sk151 ) @ '$accessible_world' ) )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZI @ sk150 )
| ( ZJ @ ( ZZZI @ sk151 ) @ ( ZZZI @ '$accessible_world' ) )
| ~ ( ZZZI @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZH @ z3 )
| ~ ( ZZZH @ ( ZJ @ ( ZR @ ( ZZZD @ sk149 ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk146 ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ p3 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk149 ) ) @ ( ZJ @ ( ZR @ ( ZZZD @ sk148 ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk146 ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ p3 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk148 ) ) @ ( ZJ @ ( ZR @ ( ZZZD @ sk147 ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk146 ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ p3 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk147 ) ) @ ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk146 ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ p3 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ z3 )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk146 ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ p3 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk146 ) ) )
| ( ZZZG @ y3 )
| ~ ( ZZZG @ ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ p3 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk146 ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ y3 )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ p3 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk145 ) ) @ ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ '$accessible_world' ) )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZF @ z0 )
| ~ ( ZZZF @ ( ZJ @ ( ZR @ ( ZZZD @ sk144 ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk141 ) ) )
| ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ p0 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk144 ) ) @ ( ZJ @ ( ZR @ ( ZZZD @ sk143 ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk141 ) ) )
| ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ p0 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk143 ) ) @ ( ZJ @ ( ZR @ ( ZZZD @ sk142 ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk141 ) ) )
| ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ p0 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk142 ) ) @ ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk141 ) ) )
| ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ p0 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ z0 )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk141 ) ) )
| ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ p0 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk141 ) ) )
| ( ZZZE @ y0 )
| ~ ( ZZZE @ ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ '$accessible_world' ) )
| ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ p0 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk141 ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ y0 )
| ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ p0 )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZZD @ sk140 ) ) @ ( ZZZD @ '$accessible_world' ) )
| ~ ( ZZZD @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZC @ z3 )
| ~ ( ZZZC @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk139 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk136 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ p3 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk139 ) ) ) @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk138 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk136 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ p3 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk138 ) ) ) @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk137 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk136 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ p3 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk137 ) ) ) @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk136 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ p3 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ z3 )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk136 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ p3 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk136 ) ) ) )
| ( ZZZB @ y3 )
| ~ ( ZZZB @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ p3 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk136 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ y3 )
| ~ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ p3 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk135 ) ) ) @ ( ZZY @ '$accessible_world' ) )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZZA @ z0 )
| ~ ( ZZZA @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk134 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZY @ sk131 )
| ( ZZY @ p0 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk134 ) ) ) @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk133 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZY @ sk131 )
| ( ZZY @ p0 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk133 ) ) ) @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk132 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZY @ sk131 )
| ( ZZY @ p0 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZR @ ( ZZY @ sk132 ) ) ) @ ( ZZY @ '$accessible_world' ) )
| ~ ( ZZY @ sk131 )
| ( ZZY @ p0 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( ZZY @ z0 )
| ~ ( ZZY @ sk131 )
| ( ZZY @ p0 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZY @ sk131 )
| ( ZZZ @ y0 )
| ~ ( ZZZ @ ( ZZY @ '$accessible_world' ) )
| ( ZZY @ p0 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZY @ sk131 )
| ~ ( ZZY @ y0 )
| ( ZZY @ p0 )
| ~ ( ZZY @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk127 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk127 )
| ( ZZX @ z0 )
| ~ ( ZZX @ ( ZJ @ ( ZR @ ( ZZR @ sk130 ) ) @ '$accessible_world' ) )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk127 )
| ( ZJ @ ( ZR @ ( ZZR @ sk130 ) ) @ ( ZJ @ ( ZR @ ( ZZR @ sk129 ) ) @ '$accessible_world' ) )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk127 )
| ( ZJ @ ( ZR @ ( ZZR @ sk129 ) ) @ ( ZJ @ ( ZR @ ( ZZR @ sk128 ) ) @ '$accessible_world' ) )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk127 )
| ( ZJ @ ( ZR @ ( ZZR @ sk128 ) ) @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk127 )
| ~ ( ZZR @ z0 )
| ~ ( ZZR @ sk126 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk126 )
| ( ZZW @ y0 )
| ~ ( ZZW @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk126 )
| ~ ( ZZR @ y0 )
| ~ ( ZZR @ p0 )
| ~ ( ZZR @ sk120 )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk120 )
| ( ZZV @ z0 )
| ~ ( ZZV @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ ( ZZT @ sk125 ) ) ) ) @ '$accessible_world' ) )
| ~ ( ZZT @ sk122 )
| ~ ( ZZT @ p0 )
| ~ ( ZZT @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ sk121 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZS @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk120 )
| ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ ( ZZT @ sk125 ) ) ) ) @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ ( ZZT @ sk124 ) ) ) ) @ '$accessible_world' ) )
| ~ ( ZZT @ sk122 )
| ~ ( ZZT @ p0 )
| ~ ( ZZT @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ sk121 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZS @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk120 )
| ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ ( ZZT @ sk124 ) ) ) ) @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ ( ZZT @ sk123 ) ) ) ) @ '$accessible_world' ) )
| ~ ( ZZT @ sk122 )
| ~ ( ZZT @ p0 )
| ~ ( ZZT @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ sk121 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZS @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk120 )
| ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ ( ZZT @ sk123 ) ) ) ) @ ( ZZT @ '$accessible_world' ) )
| ~ ( ZZT @ sk122 )
| ~ ( ZZT @ p0 )
| ~ ( ZZT @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ sk121 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZS @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk120 )
| ~ ( ZZT @ z0 )
| ~ ( ZZT @ sk122 )
| ~ ( ZZT @ p0 )
| ~ ( ZZT @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ sk121 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZS @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk120 )
| ( ZZT @ sk122 )
| ( ZZU @ y0 )
| ~ ( ZZU @ ( ZZT @ '$accessible_world' ) )
| ~ ( ZZT @ p0 )
| ~ ( ZZT @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ sk121 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZS @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk120 )
| ( ZZT @ sk122 )
| ~ ( ZZT @ y0 )
| ~ ( ZZT @ p0 )
| ~ ( ZZT @ ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ sk121 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZS @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZR @ sk120 )
| ( ZJ @ ( ZR @ ( ZZR @ ( ZZS @ sk121 ) ) ) @ ( ZZS @ '$accessible_world' ) )
| ~ ( ZZS @ ( ZZR @ '$accessible_world' ) )
| ~ ( ZZR @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZQ @ z3 )
| ~ ( ZZQ @ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk119 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk116 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ p3 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk119 ) ) ) @ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk118 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk116 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ p3 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk118 ) ) ) @ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk117 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk116 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ p3 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk117 ) ) ) @ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk116 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ p3 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ z3 )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk116 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ p3 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk116 ) ) ) )
| ( ZZP @ y3 )
| ~ ( ZZP @ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ p3 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk116 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ y3 )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ p3 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk115 ) ) ) @ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZO @ z0 )
| ~ ( ZZO @ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk114 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk111 ) ) ) )
| ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ p0 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk114 ) ) ) @ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk113 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk111 ) ) ) )
| ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ p0 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk113 ) ) ) @ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk112 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk111 ) ) ) )
| ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ p0 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk112 ) ) ) @ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk111 ) ) ) )
| ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ p0 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ z0 )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk111 ) ) ) )
| ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ p0 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk111 ) ) ) )
| ( ZZN @ y0 )
| ~ ( ZZN @ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ '$accessible_world' ) )
| ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ p0 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk111 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ y0 )
| ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ p0 )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZL @ ( ZZM @ sk110 ) ) ) @ ( ZZM @ '$accessible_world' ) )
| ~ ( ZZM @ ( ZZL @ '$accessible_world' ) )
| ~ ( ZZL @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ sk104 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZR @ sk104 )
| ( ZZK @ z0 )
| ~ ( ZZK @ ( ZJ @ ( ZR @ ( ZZI @ sk109 ) ) @ '$accessible_world' ) )
| ~ ( ZZI @ sk106 )
| ~ ( ZZI @ p0 )
| ~ ( ZZI @ ( ZJ @ ( ZR @ sk105 ) @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZR @ sk104 )
| ( ZJ @ ( ZR @ ( ZZI @ sk109 ) ) @ ( ZJ @ ( ZR @ ( ZZI @ sk108 ) ) @ '$accessible_world' ) )
| ~ ( ZZI @ sk106 )
| ~ ( ZZI @ p0 )
| ~ ( ZZI @ ( ZJ @ ( ZR @ sk105 ) @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZR @ sk104 )
| ( ZJ @ ( ZR @ ( ZZI @ sk108 ) ) @ ( ZJ @ ( ZR @ ( ZZI @ sk107 ) ) @ '$accessible_world' ) )
| ~ ( ZZI @ sk106 )
| ~ ( ZZI @ p0 )
| ~ ( ZZI @ ( ZJ @ ( ZR @ sk105 ) @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZR @ sk104 )
| ( ZJ @ ( ZR @ ( ZZI @ sk107 ) ) @ ( ZZI @ '$accessible_world' ) )
| ~ ( ZZI @ sk106 )
| ~ ( ZZI @ p0 )
| ~ ( ZZI @ ( ZJ @ ( ZR @ sk105 ) @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZR @ sk104 )
| ~ ( ZZI @ z0 )
| ~ ( ZZI @ sk106 )
| ~ ( ZZI @ p0 )
| ~ ( ZZI @ ( ZJ @ ( ZR @ sk105 ) @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZR @ sk104 )
| ( ZZI @ sk106 )
| ( ZZJ @ y0 )
| ~ ( ZZJ @ ( ZZI @ '$accessible_world' ) )
| ~ ( ZZI @ p0 )
| ~ ( ZZI @ ( ZJ @ ( ZR @ sk105 ) @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZR @ sk104 )
| ( ZZI @ sk106 )
| ~ ( ZZI @ y0 )
| ~ ( ZZI @ p0 )
| ~ ( ZZI @ ( ZJ @ ( ZR @ sk105 ) @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZR @ sk104 )
| ( ZJ @ ( ZR @ sk105 ) @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZH @ z0 )
| ~ ( ZZH @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZF @ sk103 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZF @ sk100 )
| ~ ( ZZF @ p0 )
| ~ ( ZZF @ ( ZJ @ ( ZR @ ( ZZ @ sk99 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ sk87 )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZ @ ( ZZF @ sk103 ) ) ) @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZF @ sk102 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZF @ sk100 )
| ~ ( ZZF @ p0 )
| ~ ( ZZF @ ( ZJ @ ( ZR @ ( ZZ @ sk99 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ sk87 )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZ @ ( ZZF @ sk102 ) ) ) @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZF @ sk101 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZF @ sk100 )
| ~ ( ZZF @ p0 )
| ~ ( ZZF @ ( ZJ @ ( ZR @ ( ZZ @ sk99 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ sk87 )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZ @ ( ZZF @ sk101 ) ) ) @ ( ZZF @ '$accessible_world' ) )
| ~ ( ZZF @ sk100 )
| ~ ( ZZF @ p0 )
| ~ ( ZZF @ ( ZJ @ ( ZR @ ( ZZ @ sk99 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ sk87 )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( ZZF @ z0 )
| ~ ( ZZF @ sk100 )
| ~ ( ZZF @ p0 )
| ~ ( ZZF @ ( ZJ @ ( ZR @ ( ZZ @ sk99 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ sk87 )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZF @ sk100 )
| ( ZZG @ y0 )
| ~ ( ZZG @ ( ZZF @ '$accessible_world' ) )
| ~ ( ZZF @ p0 )
| ~ ( ZZF @ ( ZJ @ ( ZR @ ( ZZ @ sk99 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ sk87 )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZF @ sk100 )
| ~ ( ZZF @ y0 )
| ~ ( ZZF @ p0 )
| ~ ( ZZF @ ( ZJ @ ( ZR @ ( ZZ @ sk99 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ sk87 )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ ( ZZ @ sk99 ) ) @ ( ZZ @ '$accessible_world' ) )
| ~ ( ZZ @ sk87 )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZZE @ z3 )
| ~ ( ZZE @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk98 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk95 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ p3 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk98 ) ) ) @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk97 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk95 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ p3 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk97 ) ) ) @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk96 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk95 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ p3 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk96 ) ) ) @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk95 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ p3 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ z3 )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk95 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ p3 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk95 ) ) ) )
| ( ZZD @ y3 )
| ~ ( ZZD @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ p3 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk95 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ y3 )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ p3 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk94 ) ) ) @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ '$accessible_world' ) )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZZC @ z0 )
| ~ ( ZZC @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk93 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk90 ) ) ) )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ p0 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk93 ) ) ) @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk92 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk90 ) ) ) )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ p0 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk92 ) ) ) @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk91 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk90 ) ) ) )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ p0 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk91 ) ) ) @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk90 ) ) ) )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ p0 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ z0 )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk90 ) ) ) )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ p0 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk90 ) ) ) )
| ( ZZB @ y0 )
| ~ ( ZZB @ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ '$accessible_world' ) )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ p0 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk90 ) ) ) )
| ~ ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ y0 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ p0 )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ ( ZZA @ sk89 ) ) ) @ ( ZZA @ '$accessible_world' ) )
| ~ ( ZZA @ ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZZ @ sk87 )
| ( ZJ @ ( ZR @ ( ZZ @ sk88 ) ) @ ( ZZ @ '$accessible_world' ) )
| ~ ( ZZ @ ( ZR @ '$accessible_world' ) )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZY @ z3 )
| ~ ( ZY @ ( ZJ @ ( ZR @ sk86 ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ sk83 ) )
| ~ ( ZJ @ ( ZR @ sk82 ) @ p3 )
| ~ ( ZR @ sk71 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ sk86 ) @ ( ZJ @ ( ZR @ sk85 ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ sk83 ) )
| ~ ( ZJ @ ( ZR @ sk82 ) @ p3 )
| ~ ( ZR @ sk71 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ sk85 ) @ ( ZJ @ ( ZR @ sk84 ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ sk83 ) )
| ~ ( ZJ @ ( ZR @ sk82 ) @ p3 )
| ~ ( ZR @ sk71 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ sk84 ) @ ( ZJ @ ( ZR @ sk82 ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ sk83 ) )
| ~ ( ZJ @ ( ZR @ sk82 ) @ p3 )
| ~ ( ZR @ sk71 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( ZJ @ ( ZR @ sk82 ) @ z3 )
| ~ ( ZJ @ ( ZR @ sk83 ) )
| ~ ( ZJ @ ( ZR @ sk82 ) @ p3 )
| ~ ( ZR @ sk71 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ sk83 ) )
| ( ZX @ y3 )
| ~ ( ZX @ ( ZJ @ ( ZR @ sk82 ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ sk82 ) @ p3 )
| ~ ( ZR @ sk71 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ sk83 ) )
| ~ ( ZJ @ ( ZR @ sk82 ) @ y3 )
| ~ ( ZJ @ ( ZR @ sk82 ) @ p3 )
| ~ ( ZR @ sk71 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZJ @ ( ZR @ sk82 ) @ ( ZJ @ ( ZR @ sk77 ) @ '$accessible_world' ) )
| ~ ( ZR @ sk71 )
| ~ ( ZR @ ( ZJ @ '$accessible_world' ) )
| ~ ( ZJ @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( ZW @ z0 )
| ~ ( ZW @ ( ZJ @ ( ZR @ sk81 ) @ '$accessible_world' ) )
| ~ ( ZJ @ ( ZR @ sk78 ) )
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| ~ ( M @ p1 )
| ~ ( M @ ( L @ '$accessible_world' ) )
| ~ ( L @ ( I @ '$accessible_world' ) )
| ~ ( I @ sk13 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( I @ ( L @ ( M @ sk20 ) ) @ ( M @ '$accessible_world' ) )
| ~ ( M @ sk19 )
| ~ ( M @ p1 )
| ~ ( M @ ( L @ '$accessible_world' ) )
| ~ ( L @ ( I @ '$accessible_world' ) )
| ~ ( I @ sk13 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( M @ z1 )
| ~ ( M @ sk19 )
| ~ ( M @ p1 )
| ~ ( M @ ( L @ '$accessible_world' ) )
| ~ ( L @ ( I @ '$accessible_world' ) )
| ~ ( I @ sk13 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( M @ sk19 )
| ( N @ y1 )
| ~ ( N @ ( M @ '$accessible_world' ) )
| ~ ( M @ p1 )
| ~ ( M @ ( L @ '$accessible_world' ) )
| ~ ( L @ ( I @ '$accessible_world' ) )
| ~ ( I @ sk13 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( M @ sk19 )
| ~ ( M @ y1 )
| ~ ( M @ p1 )
| ~ ( M @ ( L @ '$accessible_world' ) )
| ~ ( L @ ( I @ '$accessible_world' ) )
| ~ ( I @ sk13 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( I @ sk13 )
| ( K @ z1 )
| ~ ( K @ ( I @ sk18 @ '$accessible_world' ) )
| ~ ( I @ sk15 )
| ( I @ sk14 @ p1 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( I @ sk13 )
| ( I @ sk18 @ ( I @ sk17 @ '$accessible_world' ) )
| ~ ( I @ sk15 )
| ( I @ sk14 @ p1 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( I @ sk13 )
| ( I @ sk17 @ ( I @ sk16 @ '$accessible_world' ) )
| ~ ( I @ sk15 )
| ( I @ sk14 @ p1 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( I @ sk13 )
| ( I @ sk16 @ ( I @ sk14 @ '$accessible_world' ) )
| ~ ( I @ sk15 )
| ( I @ sk14 @ p1 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( I @ sk13 )
| ~ ( I @ sk14 @ z1 )
| ~ ( I @ sk15 )
| ( I @ sk14 @ p1 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( I @ sk13 )
| ( I @ sk15 )
| ( J @ y1 )
| ~ ( J @ ( I @ sk14 @ '$accessible_world' ) )
| ( I @ sk14 @ p1 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( I @ sk13 )
| ( I @ sk15 )
| ~ ( I @ sk14 @ y1 )
| ( I @ sk14 @ p1 )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( I @ sk13 )
| ( I @ sk14 @ ( I @ '$accessible_world' ) )
| ~ ( I @ ( sk12 @ '$accessible_world' ) )
| ~ sk1 )
& ( ( sk12 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( H @ z1 )
| ~ ( H @ ( B @ ( E @ ( F @ sk11 ) ) @ '$accessible_world' ) )
| ~ ( F @ sk8 )
| ~ ( F @ p1 )
| ~ ( F @ ( E @ '$accessible_world' ) )
| ~ ( E @ ( B @ '$accessible_world' ) )
| ~ ( B @ sk2 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( B @ ( E @ ( F @ sk11 ) ) @ ( B @ ( E @ ( F @ sk10 ) ) @ '$accessible_world' ) )
| ~ ( F @ sk8 )
| ~ ( F @ p1 )
| ~ ( F @ ( E @ '$accessible_world' ) )
| ~ ( E @ ( B @ '$accessible_world' ) )
| ~ ( B @ sk2 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( B @ ( E @ ( F @ sk10 ) ) @ ( B @ ( E @ ( F @ sk9 ) ) @ '$accessible_world' ) )
| ~ ( F @ sk8 )
| ~ ( F @ p1 )
| ~ ( F @ ( E @ '$accessible_world' ) )
| ~ ( E @ ( B @ '$accessible_world' ) )
| ~ ( B @ sk2 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( B @ ( E @ ( F @ sk9 ) ) @ ( F @ '$accessible_world' ) )
| ~ ( F @ sk8 )
| ~ ( F @ p1 )
| ~ ( F @ ( E @ '$accessible_world' ) )
| ~ ( E @ ( B @ '$accessible_world' ) )
| ~ ( B @ sk2 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ~ ( F @ z1 )
| ~ ( F @ sk8 )
| ~ ( F @ p1 )
| ~ ( F @ ( E @ '$accessible_world' ) )
| ~ ( E @ ( B @ '$accessible_world' ) )
| ~ ( B @ sk2 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( F @ sk8 )
| ( G @ y1 )
| ~ ( G @ ( F @ '$accessible_world' ) )
| ~ ( F @ p1 )
| ~ ( F @ ( E @ '$accessible_world' ) )
| ~ ( E @ ( B @ '$accessible_world' ) )
| ~ ( B @ sk2 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( F @ sk8 )
| ~ ( F @ y1 )
| ~ ( F @ p1 )
| ~ ( F @ ( E @ '$accessible_world' ) )
| ~ ( E @ ( B @ '$accessible_world' ) )
| ~ ( B @ sk2 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( B @ sk2 )
| ( D @ z1 )
| ~ ( D @ ( B @ sk7 @ '$accessible_world' ) )
| ~ ( B @ sk4 )
| ( B @ sk3 @ p1 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( B @ sk2 )
| ( B @ sk7 @ ( B @ sk6 @ '$accessible_world' ) )
| ~ ( B @ sk4 )
| ( B @ sk3 @ p1 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( B @ sk2 )
| ( B @ sk6 @ ( B @ sk5 @ '$accessible_world' ) )
| ~ ( B @ sk4 )
| ( B @ sk3 @ p1 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( B @ sk2 )
| ( B @ sk5 @ ( B @ sk3 @ '$accessible_world' ) )
| ~ ( B @ sk4 )
| ( B @ sk3 @ p1 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( B @ sk2 )
| ~ ( B @ sk3 @ z1 )
| ~ ( B @ sk4 )
| ( B @ sk3 @ p1 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( B @ sk2 )
| ( B @ sk4 )
| ( C @ y1 )
| ~ ( C @ ( B @ sk3 @ '$accessible_world' ) )
| ( B @ sk3 @ p1 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( B @ sk2 )
| ( B @ sk4 )
| ~ ( B @ sk3 @ y1 )
| ( B @ sk3 @ p1 )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( ( B @ sk2 )
| ( B @ sk3 @ ( B @ '$accessible_world' ) )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 )
& ( sk1
| ~ ( A @ x0 )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) )
& ( sk1
| ( '$local_world' @ x0 ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(267,plain,
! [A: '$world'] :
( ( A @ z1 )
| ~ ( A @ ( sk45 @ '$accessible_world' ) )
| ~ sk42
| ~ ( sk41 @ p1 )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(425,plain,
! [A: '$world'] :
( ( A @ z1 )
| ~ ( A @ ( sk45 @ '$accessible_world' ) )
| ~ sk42
| ~ ( sk41 @ p1 )
| ~ sk1 ),
inference(simp,[status(thm)],[267]) ).
thf(45,plain,
( sk1
| ( '$local_world' @ x0 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(121,plain,
! [A: '$world'] :
( sk1
| ~ ( A @ x0 )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(3,axiom,
! [A: '$world',B: '$world'] : ( B @ ( A @ '$accessible_world' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
thf(515,plain,
! [A: '$world',B: '$world'] : ( B @ ( A @ '$accessible_world' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(516,plain,
! [B: '$world',A: '$world'] : ( B @ ( A @ '$accessible_world' ) ),
inference(cnf,[status(esa)],[515]) ).
thf(542,plain,
! [A: '$world'] :
( sk1
| ~ ( A @ x0 )
| ~ $true ),
inference(rewrite,[status(thm)],[121,516]) ).
thf(543,plain,
! [A: '$world'] :
( sk1
| ~ ( A @ x0 ) ),
inference(simp,[status(thm)],[542]) ).
thf(544,plain,
! [A: '$world'] :
( ( ( '$local_world' @ x0 )
!= ( A @ x0 ) )
| sk1
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[45,543]) ).
thf(545,plain,
! [A: '$world'] :
( ( ( '$local_world' @ x0 )
!= ( A @ x0 ) )
| sk1 ),
inference(simp,[status(thm)],[544]) ).
thf(546,plain,
sk1,
inference(pattern_uni,[status(thm)],[545:[bind(A,$thf( '$local_world' ))]]) ).
thf(609,plain,
! [A: '$world'] :
( ( A @ z1 )
| ~ $true
| ~ sk42
| ~ ( sk41 @ p1 )
| ~ $true ),
inference(rewrite,[status(thm)],[425,546,516]) ).
thf(610,plain,
! [A: '$world'] :
( ( A @ z1 )
| ~ sk42
| ~ ( sk41 @ p1 ) ),
inference(simp,[status(thm)],[609]) ).
thf(34,plain,
( ~ ( sk41 @ z1 )
| ~ sk42
| ~ ( sk41 @ p1 )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(555,plain,
( ~ ( sk41 @ z1 )
| ~ sk42
| ~ ( sk41 @ p1 )
| ~ $true ),
inference(rewrite,[status(thm)],[34,546]) ).
thf(556,plain,
( ~ ( sk41 @ z1 )
| ~ sk42
| ~ ( sk41 @ p1 ) ),
inference(simp,[status(thm)],[555]) ).
thf(617,plain,
! [A: '$world'] :
( ( ( A @ z1 )
!= ( sk41 @ z1 ) )
| ~ $true
| ~ sk42
| ~ ( sk41 @ p1 )
| ~ sk42
| ~ ( sk41 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[610,556]) ).
thf(618,plain,
! [A: '$world'] :
( ( ( A @ z1 )
!= ( sk41 @ z1 ) )
| ~ sk42
| ~ ( sk41 @ p1 ) ),
inference(simp,[status(thm)],[617]) ).
thf(619,plain,
( ~ sk42
| ~ ( sk41 @ p1 ) ),
inference(pattern_uni,[status(thm)],[618:[bind(A,$thf( sk41 ))]]) ).
thf(20,plain,
! [B: '$world',A: '$world'] :
( ( A @ sk36 )
| ( B @ y1 )
| ~ ( B @ ( A @ '$accessible_world' ) )
| ( A @ p1 )
| ~ ( A @ ( sk35 @ '$accessible_world' ) )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(300,plain,
! [B: '$world',A: '$world'] :
( ( A @ sk36 )
| ( B @ y1 )
| ~ ( B @ ( A @ '$accessible_world' ) )
| ( A @ p1 )
| ~ ( A @ ( sk35 @ '$accessible_world' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[20]) ).
thf(931,plain,
! [B: '$world',A: '$world'] :
( ( A @ sk36 )
| ( B @ y1 )
| ~ $true
| ( A @ p1 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[300,546,516]) ).
thf(932,plain,
! [B: '$world',A: '$world'] :
( ( A @ sk36 )
| ( B @ y1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[931]) ).
thf(64,plain,
! [A: '$world'] :
( ( A @ sk36 )
| ~ ( A @ y1 )
| ( A @ p1 )
| ~ ( A @ ( sk35 @ '$accessible_world' ) )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(379,plain,
! [A: '$world'] :
( ( A @ sk36 )
| ~ ( A @ y1 )
| ( A @ p1 )
| ~ ( A @ ( sk35 @ '$accessible_world' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[64]) ).
thf(661,plain,
! [A: '$world'] :
( ( A @ sk36 )
| ~ ( A @ y1 )
| ( A @ p1 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[379,546,516]) ).
thf(662,plain,
! [A: '$world'] :
( ( A @ sk36 )
| ~ ( A @ y1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[661]) ).
thf(942,plain,
! [C: '$world',B: '$world',A: '$world'] :
( ( ( B @ y1 )
!= ( C @ y1 ) )
| ( C @ sk36 )
| ~ $true
| ( C @ p1 )
| ( A @ sk36 )
| ( A @ p1 ) ),
inference(paramod_ordered,[status(thm)],[932,662]) ).
thf(943,plain,
! [C: '$world',B: '$world',A: '$world'] :
( ( ( B @ y1 )
!= ( C @ y1 ) )
| ( C @ sk36 )
| ( C @ p1 )
| ( A @ sk36 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[942]) ).
thf(944,plain,
! [B: '$world',A: '$world'] :
( ( B @ sk36 )
| ( B @ p1 )
| ( A @ sk36 )
| ( A @ p1 ) ),
inference(pattern_uni,[status(thm)],[943:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(983,plain,
! [B: '$world',A: '$world'] :
( ~ $true
| ( ( B @ sk36 )
!= ( A @ sk36 ) )
| ( B @ p1 )
| ( A @ sk36 )
| ( A @ p1 ) ),
inference(eqfactor_ordered,[status(thm)],[944]) ).
thf(984,plain,
! [A: '$world'] :
( ( A @ p1 )
| ( A @ sk36 )
| ( A @ p1 ) ),
inference(pattern_uni,[status(thm)],[983:[bind(A,$thf( B ))]]) ).
thf(987,plain,
! [A: '$world'] :
( ( A @ sk36 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[984]) ).
thf(7,plain,
! [B: '$world',A: '$world'] :
( ( B @ z1 )
| ~ ( B @ ( A @ sk39 @ '$accessible_world' ) )
| ~ ( A @ sk36 )
| ( A @ p1 )
| ~ ( A @ ( sk35 @ '$accessible_world' ) )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(408,plain,
! [B: '$world',A: '$world'] :
( ( B @ z1 )
| ~ ( B @ ( A @ sk39 @ '$accessible_world' ) )
| ~ ( A @ sk36 )
| ( A @ p1 )
| ~ ( A @ ( sk35 @ '$accessible_world' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[7]) ).
thf(102885,plain,
! [B: '$world',A: '$world'] :
( ( B @ z1 )
| ~ $true
| ~ ( A @ sk36 )
| ( A @ p1 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[408,546,516]) ).
thf(102886,plain,
! [B: '$world',A: '$world'] :
( ( B @ z1 )
| ~ ( A @ sk36 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[102885]) ).
thf(102920,plain,
! [C: '$world',B: '$world',A: '$world'] :
( ( ( A @ sk36 )
!= ( B @ sk36 ) )
| ( C @ z1 )
| ~ $true
| ( B @ p1 )
| ( A @ p1 ) ),
inference(paramod_ordered,[status(thm)],[987,102886]) ).
thf(102921,plain,
! [C: '$world',B: '$world',A: '$world'] :
( ( ( A @ sk36 )
!= ( B @ sk36 ) )
| ( C @ z1 )
| ( B @ p1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[102920]) ).
thf(102922,plain,
! [B: '$world',A: '$world'] :
( ( B @ z1 )
| ( A @ p1 )
| ( A @ p1 ) ),
inference(pattern_uni,[status(thm)],[102921:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(102926,plain,
! [B: '$world',A: '$world'] :
( ( B @ z1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[102922]) ).
thf(87,plain,
! [A: '$world'] :
( ~ ( A @ z1 )
| ~ ( A @ sk36 )
| ( A @ p1 )
| ~ ( A @ ( sk35 @ '$accessible_world' ) )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(458,plain,
! [A: '$world'] :
( ~ ( A @ z1 )
| ~ ( A @ sk36 )
| ( A @ p1 )
| ~ ( A @ ( sk35 @ '$accessible_world' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[87]) ).
thf(677,plain,
! [A: '$world'] :
( ~ ( A @ z1 )
| ~ ( A @ sk36 )
| ( A @ p1 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[458,546,516]) ).
thf(678,plain,
! [A: '$world'] :
( ~ ( A @ z1 )
| ~ ( A @ sk36 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[677]) ).
thf(988,plain,
! [B: '$world',A: '$world'] :
( ( ( A @ sk36 )
!= ( B @ sk36 ) )
| ~ ( B @ z1 )
| ~ $true
| ( B @ p1 )
| ( A @ p1 ) ),
inference(paramod_ordered,[status(thm)],[987,678]) ).
thf(989,plain,
! [B: '$world',A: '$world'] :
( ( ( A @ sk36 )
!= ( B @ sk36 ) )
| ~ ( B @ z1 )
| ( B @ p1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[988]) ).
thf(990,plain,
! [A: '$world'] :
( ~ ( A @ z1 )
| ( A @ p1 )
| ( A @ p1 ) ),
inference(pattern_uni,[status(thm)],[989:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(991,plain,
! [A: '$world'] :
( ~ ( A @ z1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[990]) ).
thf(103037,plain,
! [C: '$world',B: '$world',A: '$world'] :
( ( ( B @ z1 )
!= ( C @ z1 ) )
| ~ $true
| ( C @ p1 )
| ( A @ p1 ) ),
inference(paramod_ordered,[status(thm)],[102926,991]) ).
thf(103038,plain,
! [C: '$world',B: '$world',A: '$world'] :
( ( ( B @ z1 )
!= ( C @ z1 ) )
| ( C @ p1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[103037]) ).
thf(103039,plain,
! [B: '$world',A: '$world'] :
( ( B @ p1 )
| ( A @ p1 ) ),
inference(pattern_uni,[status(thm)],[103038:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(103286,plain,
! [B: '$world',A: '$world'] :
( ~ $true
| ( ( B @ p1 )
!= ( A @ p1 ) )
| ( A @ p1 ) ),
inference(eqfactor_ordered,[status(thm)],[103039]) ).
thf(103287,plain,
! [A: '$world'] : ( A @ p1 ),
inference(pattern_uni,[status(thm)],[103286:[bind(A,$thf( B ))]]) ).
thf(103344,plain,
! [A: '$world'] : ( A @ p1 ),
inference(simp,[status(thm)],[103287]) ).
thf(103357,plain,
( ~ sk42
| ~ $true ),
inference(rewrite,[status(thm)],[619,103344]) ).
thf(103358,plain,
~ sk42,
inference(simp,[status(thm)],[103357]) ).
thf(114,plain,
! [A: '$world'] :
( sk42
| ( A @ y1 )
| ~ ( A @ ( sk41 @ '$accessible_world' ) )
| ~ ( sk41 @ p1 )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(471,plain,
! [A: '$world'] :
( sk42
| ( A @ y1 )
| ~ ( A @ ( sk41 @ '$accessible_world' ) )
| ~ ( sk41 @ p1 )
| ~ sk1 ),
inference(simp,[status(thm)],[114]) ).
thf(625,plain,
! [A: '$world'] :
( sk42
| ( A @ y1 )
| ~ $true
| ~ ( sk41 @ p1 )
| ~ $true ),
inference(rewrite,[status(thm)],[471,546,516]) ).
thf(626,plain,
! [A: '$world'] :
( sk42
| ( A @ y1 )
| ~ ( sk41 @ p1 ) ),
inference(simp,[status(thm)],[625]) ).
thf(152,plain,
( sk42
| ~ ( sk41 @ y1 )
| ~ ( sk41 @ p1 )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(551,plain,
( sk42
| ~ ( sk41 @ y1 )
| ~ ( sk41 @ p1 )
| ~ $true ),
inference(rewrite,[status(thm)],[152,546]) ).
thf(552,plain,
( sk42
| ~ ( sk41 @ y1 )
| ~ ( sk41 @ p1 ) ),
inference(simp,[status(thm)],[551]) ).
thf(627,plain,
! [A: '$world'] :
( ( ( A @ y1 )
!= ( sk41 @ y1 ) )
| sk42
| ~ $true
| ~ ( sk41 @ p1 )
| sk42
| ~ ( sk41 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[626,552]) ).
thf(628,plain,
! [A: '$world'] :
( ( ( A @ y1 )
!= ( sk41 @ y1 ) )
| sk42
| ~ ( sk41 @ p1 ) ),
inference(simp,[status(thm)],[627]) ).
thf(629,plain,
( sk42
| ~ ( sk41 @ p1 ) ),
inference(pattern_uni,[status(thm)],[628:[bind(A,$thf( sk41 ))]]) ).
thf(103349,plain,
( sk42
| ~ $true ),
inference(rewrite,[status(thm)],[629,103344]) ).
thf(103350,plain,
sk42,
inference(simp,[status(thm)],[103349]) ).
thf(103394,plain,
~ $true,
inference(rewrite,[status(thm)],[103358,103350]) ).
thf(103395,plain,
$false,
inference(simp,[status(thm)],[103394]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO924_1.002 : TPTP v9.3.1. Released v9.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n026.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 20:19:55 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.20 % [INFO] Parsing done (202ms).
% 1.41/1.23 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.41/1.24 %%% First-order logic specification detected, trying modal-logic-to-TXF embedding (redirected from embedding '$$modal' to embedding '$$fomlModel' version 1.3.7) ... Use flag -p FORCE_HIGHERORDER if you want to have THF output instead.
% 1.63/1.36 % [INFO] Running in sequential loop mode.
% 2.42/1.72 % [INFO] eprover registered as external prover.
% 2.42/1.73 % [INFO] Scanning for conjecture ...
% 2.84/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 3.10/2.07 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 3.10/2.07 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.10/2.09 % [INFO] Type checking passed.
% 3.10/2.09 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 74.92/44.65 % [INFO] Killing All external provers ...
% 74.92/44.65 % Time passed: 44092ms (effective reasoning time: 43287ms)
% 74.92/44.65 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 74.92/44.65 % Axioms used in derivation (1): mrel_universal
% 74.92/44.65 % No. of inferences in proof: 77
% 74.92/44.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 44092 ms resp. 43287 ms w/o parsing
% 76.38/45.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 76.81/45.15 % [INFO] Killing All external provers ...
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