%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL942_2 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.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 07:53:23 AM UTC 2026
% Result : Theorem 120.41s 27.85s
% Output : Refutation 123.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 92
% Syntax : Number of formulae : 1633 ( 283 unt; 0 typ; 71 def)
% Number of atoms : 7948 (2133 equ; 0 cnn)
% Maximal formula atoms : 205 ( 4 avg)
% Number of connectives : 27782 (3611 ~;3122 |; 610 &;19439 @)
% ( 0 <=>;1000 =>; 0 <=; 0 <~>)
% Maximal formula depth : 150 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 96 ( 93 usr; 12 con; 0-3 aty)
% Number of variables : 1804 ( 70 ^;1661 !; 2 ?;1804 :)
% ( 0 !>; 0 ?*; 0 @-; 71 @+)
% Comments :
%------------------------------------------------------------------------------
thf('$ki_world_type',type,
'$ki_world': $tType ).
thf('$ki_local_world_decl',type,
'$ki_local_world': '$ki_world' ).
thf('$ki_accessible_decl',type,
'$ki_accessible': '$ki_world' > '$ki_world' > $o ).
thf(unit_decl,type,
unit: $i ).
thf(e0_decl,type,
e0: $i ).
thf(e1_decl,type,
e1: $i ).
thf(e2_decl,type,
e2: $i ).
thf(e3_decl,type,
e3: $i ).
thf(qmltpeq_decl,type,
qmltpeq: '$ki_world' > $i > $i > $o ).
thf(inv_decl,type,
inv: $i > $i ).
thf(op_decl,type,
op: $i > $i > $i ).
thf('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': '$ki_world' > $i > $o ).
thf(sk1_decl,type,
sk1: '$ki_world' ).
thf(sk2_decl,type,
sk2: $o ).
thf(sk3_decl,type,
sk3: $o ).
thf(sk4_decl,type,
sk4: $o ).
thf(sk5_decl,type,
sk5: '$ki_world' > $o ).
thf(sk6_decl,type,
sk6: '$ki_world' > '$ki_world' ).
thf(sk7_decl,type,
sk7: '$ki_world' > $o ).
thf(sk8_decl,type,
sk8: '$ki_world' > '$ki_world' ).
thf(sk9_decl,type,
sk9: '$ki_world' > '$ki_world' ).
thf(sk10_decl,type,
sk10: '$ki_world' > '$ki_world' ).
thf(sk11_decl,type,
sk11: '$ki_world' > $o ).
thf(sk12_decl,type,
sk12: '$ki_world' > '$ki_world' ).
thf(sk13_decl,type,
sk13: '$ki_world' > $o ).
thf(sk14_decl,type,
sk14: '$ki_world' > '$ki_world' ).
thf(sk15_decl,type,
sk15: '$ki_world' > '$ki_world' ).
thf(sk16_decl,type,
sk16: '$ki_world' > '$ki_world' ).
thf(sk17_decl,type,
sk17: '$ki_world' > $o ).
thf(sk18_decl,type,
sk18: '$ki_world' > '$ki_world' ).
thf(sk19_decl,type,
sk19: '$ki_world' > $o ).
thf(sk20_decl,type,
sk20: '$ki_world' > '$ki_world' ).
thf(sk21_decl,type,
sk21: '$ki_world' > '$ki_world' ).
thf(sk22_decl,type,
sk22: '$ki_world' > '$ki_world' ).
thf(sk23_decl,type,
sk23: '$ki_world' > $o ).
thf(sk24_decl,type,
sk24: '$ki_world' > '$ki_world' ).
thf(sk25_decl,type,
sk25: '$ki_world' > $o ).
thf(sk26_decl,type,
sk26: '$ki_world' > '$ki_world' ).
thf(sk27_decl,type,
sk27: '$ki_world' > '$ki_world' ).
thf(sk28_decl,type,
sk28: '$ki_world' > '$ki_world' ).
thf(sk34_decl,type,
sk34: '$ki_world' > '$ki_world' ).
thf(sk35_decl,type,
sk35: '$ki_world' > '$ki_world' ).
thf(sk36_decl,type,
sk36: '$ki_world' > '$ki_world' ).
thf(sk37_decl,type,
sk37: '$ki_world' > '$ki_world' ).
thf(sk38_decl,type,
sk38: '$ki_world' > '$ki_world' ).
thf(sk39_decl,type,
sk39: '$ki_world' > '$ki_world' ).
thf(sk40_decl,type,
sk40: '$ki_world' > '$ki_world' ).
thf(sk41_decl,type,
sk41: '$ki_world' > '$ki_world' ).
thf(sk42_decl,type,
sk42: '$ki_world' > '$ki_world' ).
thf(sk43_decl,type,
sk43: '$ki_world' > '$ki_world' ).
thf(sk44_decl,type,
sk44: '$ki_world' > '$ki_world' ).
thf(sk45_decl,type,
sk45: '$ki_world' > '$ki_world' ).
thf(sk46_decl,type,
sk46: '$ki_world' > '$ki_world' ).
thf(sk47_decl,type,
sk47: '$ki_world' > '$ki_world' ).
thf(sk48_decl,type,
sk48: '$ki_world' > '$ki_world' ).
thf(sk49_decl,type,
sk49: '$ki_world' > '$ki_world' ).
thf(sk50_decl,type,
sk50: '$ki_world' > '$ki_world' ).
thf(sk51_decl,type,
sk51: '$ki_world' > '$ki_world' ).
thf(sk52_decl,type,
sk52: '$ki_world' > '$ki_world' ).
thf(sk53_decl,type,
sk53: '$ki_world' > '$ki_world' ).
thf(sk54_decl,type,
sk54: '$ki_world' > '$ki_world' ).
thf(sk55_decl,type,
sk55: '$ki_world' > '$ki_world' ).
thf(sk56_decl,type,
sk56: '$ki_world' > '$ki_world' ).
thf(sk57_decl,type,
sk57: '$ki_world' > '$ki_world' ).
thf(sk58_decl,type,
sk58: '$ki_world' > '$ki_world' ).
thf(sk59_decl,type,
sk59: '$ki_world' > '$ki_world' ).
thf(sk60_decl,type,
sk60: '$ki_world' > '$ki_world' ).
thf(sk61_decl,type,
sk61: '$ki_world' > '$ki_world' ).
thf(sk62_decl,type,
sk62: '$ki_world' > '$ki_world' ).
thf(sk63_decl,type,
sk63: '$ki_world' > '$ki_world' ).
thf(sk64_decl,type,
sk64: '$ki_world' > '$ki_world' ).
thf(sk65_decl,type,
sk65: '$ki_world' > '$ki_world' ).
thf(sk66_decl,type,
sk66: '$ki_world' > '$ki_world' ).
thf(sk67_decl,type,
sk67: '$ki_world' > '$ki_world' ).
thf(sk68_decl,type,
sk68: '$ki_world' > '$ki_world' ).
thf(sk69_decl,type,
sk69: '$ki_world' > '$ki_world' ).
thf(sk70_decl,type,
sk70: '$ki_world' > '$ki_world' ).
thf(sk71_decl,type,
sk71: '$ki_world' > '$ki_world' ).
thf(sk72_decl,type,
sk72: '$ki_world' > '$ki_world' ).
thf(sk73_decl,type,
sk73: '$ki_world' > '$ki_world' ).
thf(sk74_decl,type,
sk74: '$ki_world' > '$ki_world' ).
thf(sk75_decl,type,
sk75: '$ki_world' > '$ki_world' ).
thf(sk76_decl,type,
sk76: '$ki_world' > '$ki_world' ).
thf(sk77_decl,type,
sk77: '$ki_world' > '$ki_world' ).
thf(sk78_decl,type,
sk78: '$ki_world' > '$ki_world' ).
thf(sk79_decl,type,
sk79: '$ki_world' > '$ki_world' ).
thf(sk80_decl,type,
sk80: '$ki_world' > '$ki_world' ).
thf(sk81_decl,type,
sk81: '$ki_world' > '$ki_world' ).
thf(sk94_decl,type,
sk94: '$ki_world' > '$ki_world' ).
thf(sk95_decl,type,
sk95: '$ki_world' > '$ki_world' ).
thf(sk96_decl,type,
sk96: '$ki_world' > '$ki_world' ).
thf(sk97_decl,type,
sk97: '$ki_world' > '$ki_world' ).
thf(sk98_decl,type,
sk98: '$ki_world' > '$ki_world' ).
thf(sk99_decl,type,
sk99: '$ki_world' > '$ki_world' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: '$ki_world'] :
~ ( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ~ ( ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) ) ) )
& ( ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk34_def,definition,
( sk34
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk35_def,definition,
( sk35
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk36_def,definition,
( sk36
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk38_def,definition,
( sk38
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk39_def,definition,
( sk39
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk40_def,definition,
( sk40
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk41_def,definition,
( sk41
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk42_def,definition,
( sk42
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk44_def,definition,
( sk44
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk45_def,definition,
( sk45
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e1 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk46_def,definition,
( sk46
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk47_def,definition,
( sk47
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk48_def,definition,
( sk48
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk49_def,definition,
( sk49
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e2 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk50_def,definition,
( sk50
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e2 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk51_def,definition,
( sk51
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk52_def,definition,
( sk52
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e3 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk53_def,definition,
( sk53
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e3 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk54_def,definition,
( sk54
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e3 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk55_def,definition,
( sk55
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e3 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk56_def,definition,
( sk56
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e3 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk57_def,definition,
( sk57
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e3 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk58_def,definition,
( sk58
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk59_def,definition,
( sk59
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk60_def,definition,
( sk60
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk61_def,definition,
( sk61
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk62_def,definition,
( sk62
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk63_def,definition,
( sk63
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk64_def,definition,
( sk64
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk65_def,definition,
( sk65
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk66_def,definition,
( sk66
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk67_def,definition,
( sk67
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk68_def,definition,
( sk68
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk69_def,definition,
( sk69
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e2 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk70_def,definition,
( sk70
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk71_def,definition,
( sk71
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk72_def,definition,
( sk72
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk73_def,definition,
( sk73
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e1 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk74_def,definition,
( sk74
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e1 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk75_def,definition,
( sk75
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk76_def,definition,
( sk76
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk77_def,definition,
( sk77
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk78_def,definition,
( sk78
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk79_def,definition,
( sk79
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e1 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk80_def,definition,
( sk80
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e1 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk81_def,definition,
( sk81
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e2 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk94_def,definition,
( sk94
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk95_def,definition,
( sk95
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk96_def,definition,
( sk96
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk97_def,definition,
( sk97
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk98_def,definition,
( sk98
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(sk99_def,definition,
( sk99
= ( ^ [A: '$ki_world'] :
@+[B: '$ki_world'] :
~ ( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( B @ qmltpeq ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ~ ( ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) ) ) )
& ( ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ~ ( ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) ) ) )
& ( ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ~ ( ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) )
| ( ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e3 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e1 @ op ) @ ( C @ qmltpeq ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e0 @ op ) @ ( C @ qmltpeq ) ) ) ) ) ) )
& ( ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
| ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
! [Q: '$ki_world',P: '$ki_world',O: '$ki_world',N: '$ki_world',M: '$ki_world',L: '$ki_world',K: '$ki_world',J: '$ki_world',I: '$ki_world',H: '$ki_world',G: '$ki_world',F: '$ki_world',E: '$ki_world',D: '$ki_world',C: '$ki_world',B: '$ki_world',A: '$ki_world'] :
( ( ~ ( e3 @ ( e3 @ ( e3 @ op ) @ ( Q @ sk28 @ qmltpeq ) ) )
| ~ ( e3 @ ( e2 @ ( e2 @ op ) @ ( Q @ sk27 @ qmltpeq ) ) )
| ( Q @ sk25 )
| ( Q @ sk23 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ( Q @ sk28 @ ( Q @ '$ki_accessible' ) )
| ~ ( e3 @ ( e2 @ ( e2 @ op ) @ ( Q @ sk27 @ qmltpeq ) ) )
| ( Q @ sk25 )
| ( Q @ sk23 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e3 @ ( e3 @ op ) @ ( Q @ sk28 @ qmltpeq ) ) )
| ( Q @ sk27 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk25 )
| ( Q @ sk23 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ( Q @ sk28 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk27 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk25 )
| ( Q @ sk23 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk25 )
| ~ ( e3 @ ( e1 @ ( e1 @ op ) @ ( Q @ sk26 @ qmltpeq ) ) )
| ( Q @ sk23 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk25 )
| ( Q @ sk26 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk23 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk23 )
| ~ ( e3 @ ( e0 @ ( e0 @ op ) @ ( Q @ sk24 @ qmltpeq ) ) )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk23 )
| ( Q @ sk24 @ ( Q @ '$ki_accessible' ) )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e3 @ ( e3 @ op ) @ ( Q @ sk22 @ qmltpeq ) ) )
| ~ ( e2 @ ( e2 @ ( e2 @ op ) @ ( Q @ sk21 @ qmltpeq ) ) )
| ( Q @ sk19 )
| ( Q @ sk17 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ( Q @ sk22 @ ( Q @ '$ki_accessible' ) )
| ~ ( e2 @ ( e2 @ ( e2 @ op ) @ ( Q @ sk21 @ qmltpeq ) ) )
| ( Q @ sk19 )
| ( Q @ sk17 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e3 @ ( e3 @ op ) @ ( Q @ sk22 @ qmltpeq ) ) )
| ( Q @ sk21 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk19 )
| ( Q @ sk17 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ( Q @ sk22 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk21 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk19 )
| ( Q @ sk17 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk19 )
| ~ ( e2 @ ( e1 @ ( e1 @ op ) @ ( Q @ sk20 @ qmltpeq ) ) )
| ( Q @ sk17 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk19 )
| ( Q @ sk20 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk17 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk17 )
| ~ ( e2 @ ( e0 @ ( e0 @ op ) @ ( Q @ sk18 @ qmltpeq ) ) )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk17 )
| ( Q @ sk18 @ ( Q @ '$ki_accessible' ) )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e3 @ ( e3 @ op ) @ ( Q @ sk16 @ qmltpeq ) ) )
| ~ ( e1 @ ( e2 @ ( e2 @ op ) @ ( Q @ sk15 @ qmltpeq ) ) )
| ( Q @ sk13 )
| ( Q @ sk11 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ( Q @ sk16 @ ( Q @ '$ki_accessible' ) )
| ~ ( e1 @ ( e2 @ ( e2 @ op ) @ ( Q @ sk15 @ qmltpeq ) ) )
| ( Q @ sk13 )
| ( Q @ sk11 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e3 @ ( e3 @ op ) @ ( Q @ sk16 @ qmltpeq ) ) )
| ( Q @ sk15 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk13 )
| ( Q @ sk11 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ( Q @ sk16 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk15 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk13 )
| ( Q @ sk11 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk13 )
| ~ ( e1 @ ( e1 @ ( e1 @ op ) @ ( Q @ sk14 @ qmltpeq ) ) )
| ( Q @ sk11 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk13 )
| ( Q @ sk14 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk11 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk11 )
| ~ ( e1 @ ( e0 @ ( e0 @ op ) @ ( Q @ sk12 @ qmltpeq ) ) )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk11 )
| ( Q @ sk12 @ ( Q @ '$ki_accessible' ) )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( e0 @ ( e3 @ ( e3 @ op ) @ ( Q @ sk10 @ qmltpeq ) ) )
| ~ ( e0 @ ( e2 @ ( e2 @ op ) @ ( Q @ sk9 @ qmltpeq ) ) )
| ( Q @ sk7 )
| ( Q @ sk5 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ( Q @ sk10 @ ( Q @ '$ki_accessible' ) )
| ~ ( e0 @ ( e2 @ ( e2 @ op ) @ ( Q @ sk9 @ qmltpeq ) ) )
| ( Q @ sk7 )
| ( Q @ sk5 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( e0 @ ( e3 @ ( e3 @ op ) @ ( Q @ sk10 @ qmltpeq ) ) )
| ( Q @ sk9 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk7 )
| ( Q @ sk5 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ( Q @ sk10 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk9 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk7 )
| ( Q @ sk5 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk7 )
| ~ ( e0 @ ( e1 @ ( e1 @ op ) @ ( Q @ sk8 @ qmltpeq ) ) )
| ( Q @ sk5 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk7 )
| ( Q @ sk8 @ ( Q @ '$ki_accessible' ) )
| ( Q @ sk5 )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk5 )
| ~ ( e0 @ ( e0 @ ( e0 @ op ) @ ( Q @ sk6 @ qmltpeq ) ) )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ~ ( Q @ sk5 )
| ( Q @ sk6 @ ( Q @ '$ki_accessible' ) )
| ~ ( Q @ ( sk1 @ '$ki_accessible' ) ) )
& ( ( e3 @ ( e3 @ ( e3 @ op ) @ ( P @ qmltpeq ) ) )
| ~ ( P @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 )
& ( ( e3 @ ( e2 @ ( e2 @ op ) @ ( O @ qmltpeq ) ) )
| ~ ( O @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 )
& ( ( e3 @ ( e1 @ ( e1 @ op ) @ ( N @ qmltpeq ) ) )
| ~ ( N @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 )
& ( ( e3 @ ( e0 @ ( e0 @ op ) @ ( M @ qmltpeq ) ) )
| ~ ( M @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 )
& ( sk4
| ( e2 @ ( e3 @ ( e3 @ op ) @ ( L @ qmltpeq ) ) )
| ~ ( L @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 )
& ( sk4
| ( e2 @ ( e2 @ ( e2 @ op ) @ ( K @ qmltpeq ) ) )
| ~ ( K @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 )
& ( sk4
| ( e2 @ ( e1 @ ( e1 @ op ) @ ( J @ qmltpeq ) ) )
| ~ ( J @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 )
& ( sk4
| ( e2 @ ( e0 @ ( e0 @ op ) @ ( I @ qmltpeq ) ) )
| ~ ( I @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 )
& ( sk3
| ( e1 @ ( e3 @ ( e3 @ op ) @ ( H @ qmltpeq ) ) )
| ~ ( H @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 )
& ( sk3
| ( e1 @ ( e2 @ ( e2 @ op ) @ ( G @ qmltpeq ) ) )
| ~ ( G @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 )
& ( sk3
| ( e1 @ ( e1 @ ( e1 @ op ) @ ( F @ qmltpeq ) ) )
| ~ ( F @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 )
& ( sk3
| ( e1 @ ( e0 @ ( e0 @ op ) @ ( E @ qmltpeq ) ) )
| ~ ( E @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 )
& ( sk2
| ( e0 @ ( e3 @ ( e3 @ op ) @ ( D @ qmltpeq ) ) )
| ~ ( D @ ( sk1 @ '$ki_accessible' ) ) )
& ( sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( C @ qmltpeq ) ) )
| ~ ( C @ ( sk1 @ '$ki_accessible' ) ) )
& ( sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) )
| ~ ( B @ ( sk1 @ '$ki_accessible' ) ) )
& ( sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) )
& ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(29,plain,
sk1 @ ( '$ki_local_world' @ '$ki_accessible' ),
inference(cnfConj,[status(thm)],[24]) ).
thf(20,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(651,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(652,plain,
! [A: '$ki_world'] :
( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnf,[status(esa)],[651]) ).
thf(14,axiom,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(541,plain,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(542,plain,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
inference(cnf,[status(esa)],[541]) ).
thf(15,axiom,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( B @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
thf(543,plain,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( B @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(544,plain,
! [F: '$ki_world',E: '$ki_world',D: '$ki_world',C: '$ki_world',B: '$ki_world',A: '$ki_world'] :
( ( ~ ( e3 @ ( e2 @ ( F @ sk99 @ qmltpeq ) ) )
| ~ ( F @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( F @ sk99 @ ( F @ '$ki_accessible' ) )
| ~ ( F @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e1 @ ( E @ sk98 @ qmltpeq ) ) )
| ~ ( E @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( E @ sk98 @ ( E @ '$ki_accessible' ) )
| ~ ( E @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e1 @ ( D @ sk97 @ qmltpeq ) ) )
| ~ ( D @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( D @ sk97 @ ( D @ '$ki_accessible' ) )
| ~ ( D @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e0 @ ( C @ sk96 @ qmltpeq ) ) )
| ~ ( C @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( C @ sk96 @ ( C @ '$ki_accessible' ) )
| ~ ( C @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e0 @ ( B @ sk95 @ qmltpeq ) ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( B @ sk95 @ ( B @ '$ki_accessible' ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e0 @ ( A @ sk94 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( A @ sk94 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ),
inference(cnf,[status(esa)],[543]) ).
thf(550,plain,
! [A: '$ki_world'] :
( ~ ( e3 @ ( e2 @ ( A @ sk99 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[544]) ).
thf(558,plain,
! [A: '$ki_world'] :
( ~ ( e3 @ ( e2 @ ( A @ sk99 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[550]) ).
thf(769,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e2 @ ( B @ sk99 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,558]) ).
thf(770,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e2 @ ( B @ sk99 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[769]) ).
thf(771,plain,
~ ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[770:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(1253,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[652,771]) ).
thf(1254,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1253]) ).
thf(1262,plain,
! [A: '$ki_world'] :
( ( e3 != unit )
| ( ( unit @ inv )
!= e2 )
| ( A
!= ( '$ki_local_world' @ sk99 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1254]) ).
thf(1283,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e2 )
| ~ ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1262]) ).
thf(1309,plain,
( ( ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 != unit )
| ( ( unit @ inv )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,1283]) ).
thf(1310,plain,
( ( ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 != unit )
| ( ( unit @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[1309]) ).
thf(1315,plain,
( ( ( '$ki_local_world' @ sk99 )
!= sk1 )
| ( '$ki_local_world' != '$ki_local_world' )
| ( e3 != unit )
| ( ( unit @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[1310]) ).
thf(1322,plain,
( ( ( '$ki_local_world' @ sk99 )
!= sk1 )
| ( e3 != unit )
| ( ( unit @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[1315]) ).
thf(27,plain,
! [A: '$ki_world'] :
( ~ ( e1 @ ( e3 @ ( e3 @ op ) @ ( A @ sk16 @ qmltpeq ) ) )
| ~ ( e1 @ ( e2 @ ( e2 @ op ) @ ( A @ sk15 @ qmltpeq ) ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(101,plain,
! [A: '$ki_world'] :
( ~ ( e1 @ ( e3 @ ( e3 @ op ) @ ( A @ sk16 @ qmltpeq ) ) )
| ~ ( e1 @ ( e2 @ ( e2 @ op ) @ ( A @ sk15 @ qmltpeq ) ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(12,axiom,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
thf(407,plain,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(408,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) @ ( e1 @ ( B @ qmltpeq ) ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ),
inference(cnf,[status(esa)],[407]) ).
thf(410,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[408]) ).
thf(411,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[410]) ).
thf(549,plain,
! [A: '$ki_world'] :
( ~ ( e3 @ ( e1 @ ( A @ sk98 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[544]) ).
thf(563,plain,
! [A: '$ki_world'] :
( ~ ( e3 @ ( e1 @ ( A @ sk98 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[549]) ).
thf(1153,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e1 @ ( A @ sk98 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,563]) ).
thf(1154,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e1 @ ( A @ sk98 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1153]) ).
thf(1155,plain,
~ ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[1154:[bind(A,$thf( sk1 ))]]) ).
thf(17825,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[411,1155]) ).
thf(17826,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17825]) ).
thf(17905,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ( e1 != e1 )
| ( A
!= ( sk1 @ sk98 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17826]) ).
thf(17986,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ~ ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17905]) ).
thf(10,axiom,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e2 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e1 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e1 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e1 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e1 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e2 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e3 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e3 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e3 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e3 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e3 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e3 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e2 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e2 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e1 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).
thf(167,plain,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e2 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e1 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e1 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e1 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e1 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e2 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e3 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e3 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e3 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e3 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e3 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e3 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e2 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e2 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e2 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e1 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e1 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e0 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e0 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(168,plain,
! [ZV: '$ki_world',ZU: '$ki_world',ZT: '$ki_world',ZS: '$ki_world',ZR: '$ki_world',ZQ: '$ki_world',ZP: '$ki_world',ZO: '$ki_world',ZN: '$ki_world',ZM: '$ki_world',ZL: '$ki_world',ZK: '$ki_world',ZJ: '$ki_world',ZI: '$ki_world',ZH: '$ki_world',ZG: '$ki_world',ZF: '$ki_world',ZE: '$ki_world',ZD: '$ki_world',ZC: '$ki_world',ZB: '$ki_world',ZA: '$ki_world',Z: '$ki_world',Y: '$ki_world',X: '$ki_world',W: '$ki_world',V: '$ki_world',U: '$ki_world',T: '$ki_world',S: '$ki_world',R: '$ki_world',Q: '$ki_world',P: '$ki_world',O: '$ki_world',N: '$ki_world',M: '$ki_world',L: '$ki_world',K: '$ki_world',J: '$ki_world',I: '$ki_world',H: '$ki_world',G: '$ki_world',F: '$ki_world',E: '$ki_world',D: '$ki_world',C: '$ki_world',B: '$ki_world',A: '$ki_world'] :
( ( ~ ( e3 @ ( e3 @ op ) @ ( e2 @ ( e3 @ op ) @ ( ZV @ sk81 @ qmltpeq ) ) )
| ~ ( ZV @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZV @ sk81 @ ( ZV @ '$ki_accessible' ) )
| ~ ( ZV @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e3 @ op ) @ ( e1 @ ( e3 @ op ) @ ( ZU @ sk80 @ qmltpeq ) ) )
| ~ ( ZU @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZU @ sk80 @ ( ZU @ '$ki_accessible' ) )
| ~ ( ZU @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e3 @ op ) @ ( e1 @ ( e3 @ op ) @ ( ZT @ sk79 @ qmltpeq ) ) )
| ~ ( ZT @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZT @ sk79 @ ( ZT @ '$ki_accessible' ) )
| ~ ( ZT @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( ZS @ sk78 @ qmltpeq ) ) )
| ~ ( ZS @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZS @ sk78 @ ( ZS @ '$ki_accessible' ) )
| ~ ( ZS @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( ZR @ sk77 @ qmltpeq ) ) )
| ~ ( ZR @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZR @ sk77 @ ( ZR @ '$ki_accessible' ) )
| ~ ( ZR @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e3 @ op ) @ ( e0 @ ( e3 @ op ) @ ( ZQ @ sk76 @ qmltpeq ) ) )
| ~ ( ZQ @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZQ @ sk76 @ ( ZQ @ '$ki_accessible' ) )
| ~ ( ZQ @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e2 @ op ) @ ( e2 @ ( e2 @ op ) @ ( ZP @ sk75 @ qmltpeq ) ) )
| ~ ( ZP @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZP @ sk75 @ ( ZP @ '$ki_accessible' ) )
| ~ ( ZP @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e2 @ op ) @ ( e1 @ ( e2 @ op ) @ ( ZO @ sk74 @ qmltpeq ) ) )
| ~ ( ZO @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZO @ sk74 @ ( ZO @ '$ki_accessible' ) )
| ~ ( ZO @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e2 @ op ) @ ( e1 @ ( e2 @ op ) @ ( ZN @ sk73 @ qmltpeq ) ) )
| ~ ( ZN @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZN @ sk73 @ ( ZN @ '$ki_accessible' ) )
| ~ ( ZN @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( ZM @ sk72 @ qmltpeq ) ) )
| ~ ( ZM @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZM @ sk72 @ ( ZM @ '$ki_accessible' ) )
| ~ ( ZM @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( ZL @ sk71 @ qmltpeq ) ) )
| ~ ( ZL @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZL @ sk71 @ ( ZL @ '$ki_accessible' ) )
| ~ ( ZL @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e2 @ op ) @ ( e0 @ ( e2 @ op ) @ ( ZK @ sk70 @ qmltpeq ) ) )
| ~ ( ZK @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZK @ sk70 @ ( ZK @ '$ki_accessible' ) )
| ~ ( ZK @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e1 @ op ) @ ( e2 @ ( e1 @ op ) @ ( ZJ @ sk69 @ qmltpeq ) ) )
| ~ ( ZJ @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZJ @ sk69 @ ( ZJ @ '$ki_accessible' ) )
| ~ ( ZJ @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e1 @ op ) @ ( e1 @ ( e1 @ op ) @ ( ZI @ sk68 @ qmltpeq ) ) )
| ~ ( ZI @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZI @ sk68 @ ( ZI @ '$ki_accessible' ) )
| ~ ( ZI @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e1 @ op ) @ ( e1 @ ( e1 @ op ) @ ( ZH @ sk67 @ qmltpeq ) ) )
| ~ ( ZH @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZH @ sk67 @ ( ZH @ '$ki_accessible' ) )
| ~ ( ZH @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( ZG @ sk66 @ qmltpeq ) ) )
| ~ ( ZG @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZG @ sk66 @ ( ZG @ '$ki_accessible' ) )
| ~ ( ZG @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( ZF @ sk65 @ qmltpeq ) ) )
| ~ ( ZF @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZF @ sk65 @ ( ZF @ '$ki_accessible' ) )
| ~ ( ZF @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e1 @ op ) @ ( e0 @ ( e1 @ op ) @ ( ZE @ sk64 @ qmltpeq ) ) )
| ~ ( ZE @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZE @ sk64 @ ( ZE @ '$ki_accessible' ) )
| ~ ( ZE @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e0 @ op ) @ ( e2 @ ( e0 @ op ) @ ( ZD @ sk63 @ qmltpeq ) ) )
| ~ ( ZD @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZD @ sk63 @ ( ZD @ '$ki_accessible' ) )
| ~ ( ZD @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e0 @ op ) @ ( e1 @ ( e0 @ op ) @ ( ZC @ sk62 @ qmltpeq ) ) )
| ~ ( ZC @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZC @ sk62 @ ( ZC @ '$ki_accessible' ) )
| ~ ( ZC @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e0 @ op ) @ ( e1 @ ( e0 @ op ) @ ( ZB @ sk61 @ qmltpeq ) ) )
| ~ ( ZB @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZB @ sk61 @ ( ZB @ '$ki_accessible' ) )
| ~ ( ZB @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( ZA @ sk60 @ qmltpeq ) ) )
| ~ ( ZA @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( ZA @ sk60 @ ( ZA @ '$ki_accessible' ) )
| ~ ( ZA @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( Z @ sk59 @ qmltpeq ) ) )
| ~ ( Z @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( Z @ sk59 @ ( Z @ '$ki_accessible' ) )
| ~ ( Z @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e0 @ op ) @ ( e0 @ ( e0 @ op ) @ ( Y @ sk58 @ qmltpeq ) ) )
| ~ ( Y @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( Y @ sk58 @ ( Y @ '$ki_accessible' ) )
| ~ ( Y @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e3 @ op ) @ ( e3 @ ( e2 @ op ) @ ( X @ sk57 @ qmltpeq ) ) )
| ~ ( X @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( X @ sk57 @ ( X @ '$ki_accessible' ) )
| ~ ( X @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e3 @ op ) @ ( e3 @ ( e1 @ op ) @ ( W @ sk56 @ qmltpeq ) ) )
| ~ ( W @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( W @ sk56 @ ( W @ '$ki_accessible' ) )
| ~ ( W @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e2 @ op ) @ ( e3 @ ( e1 @ op ) @ ( V @ sk55 @ qmltpeq ) ) )
| ~ ( V @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( V @ sk55 @ ( V @ '$ki_accessible' ) )
| ~ ( V @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e3 @ op ) @ ( e3 @ ( e0 @ op ) @ ( U @ sk54 @ qmltpeq ) ) )
| ~ ( U @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( U @ sk54 @ ( U @ '$ki_accessible' ) )
| ~ ( U @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e2 @ op ) @ ( e3 @ ( e0 @ op ) @ ( T @ sk53 @ qmltpeq ) ) )
| ~ ( T @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( T @ sk53 @ ( T @ '$ki_accessible' ) )
| ~ ( T @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e3 @ ( e1 @ op ) @ ( e3 @ ( e0 @ op ) @ ( S @ sk52 @ qmltpeq ) ) )
| ~ ( S @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( S @ sk52 @ ( S @ '$ki_accessible' ) )
| ~ ( S @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e3 @ op ) @ ( e2 @ ( e2 @ op ) @ ( R @ sk51 @ qmltpeq ) ) )
| ~ ( R @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( R @ sk51 @ ( R @ '$ki_accessible' ) )
| ~ ( R @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e3 @ op ) @ ( e2 @ ( e1 @ op ) @ ( Q @ sk50 @ qmltpeq ) ) )
| ~ ( Q @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( Q @ sk50 @ ( Q @ '$ki_accessible' ) )
| ~ ( Q @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e2 @ op ) @ ( e2 @ ( e1 @ op ) @ ( P @ sk49 @ qmltpeq ) ) )
| ~ ( P @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( P @ sk49 @ ( P @ '$ki_accessible' ) )
| ~ ( P @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e3 @ op ) @ ( e2 @ ( e0 @ op ) @ ( O @ sk48 @ qmltpeq ) ) )
| ~ ( O @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( O @ sk48 @ ( O @ '$ki_accessible' ) )
| ~ ( O @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e2 @ op ) @ ( e2 @ ( e0 @ op ) @ ( N @ sk47 @ qmltpeq ) ) )
| ~ ( N @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( N @ sk47 @ ( N @ '$ki_accessible' ) )
| ~ ( N @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e2 @ ( e1 @ op ) @ ( e2 @ ( e0 @ op ) @ ( M @ sk46 @ qmltpeq ) ) )
| ~ ( M @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( M @ sk46 @ ( M @ '$ki_accessible' ) )
| ~ ( M @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e3 @ op ) @ ( e1 @ ( e2 @ op ) @ ( L @ sk45 @ qmltpeq ) ) )
| ~ ( L @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( L @ sk45 @ ( L @ '$ki_accessible' ) )
| ~ ( L @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e3 @ op ) @ ( e1 @ ( e1 @ op ) @ ( K @ sk44 @ qmltpeq ) ) )
| ~ ( K @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( K @ sk44 @ ( K @ '$ki_accessible' ) )
| ~ ( K @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e2 @ op ) @ ( e1 @ ( e1 @ op ) @ ( J @ sk43 @ qmltpeq ) ) )
| ~ ( J @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( J @ sk43 @ ( J @ '$ki_accessible' ) )
| ~ ( J @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e3 @ op ) @ ( e1 @ ( e0 @ op ) @ ( I @ sk42 @ qmltpeq ) ) )
| ~ ( I @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( I @ sk42 @ ( I @ '$ki_accessible' ) )
| ~ ( I @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e2 @ op ) @ ( e1 @ ( e0 @ op ) @ ( H @ sk41 @ qmltpeq ) ) )
| ~ ( H @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( H @ sk41 @ ( H @ '$ki_accessible' ) )
| ~ ( H @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e1 @ ( e1 @ op ) @ ( e1 @ ( e0 @ op ) @ ( G @ sk40 @ qmltpeq ) ) )
| ~ ( G @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( G @ sk40 @ ( G @ '$ki_accessible' ) )
| ~ ( G @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e0 @ ( e3 @ op ) @ ( e0 @ ( e2 @ op ) @ ( F @ sk39 @ qmltpeq ) ) )
| ~ ( F @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( F @ sk39 @ ( F @ '$ki_accessible' ) )
| ~ ( F @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e0 @ ( e3 @ op ) @ ( e0 @ ( e1 @ op ) @ ( E @ sk38 @ qmltpeq ) ) )
| ~ ( E @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( E @ sk38 @ ( E @ '$ki_accessible' ) )
| ~ ( E @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e0 @ ( e2 @ op ) @ ( e0 @ ( e1 @ op ) @ ( D @ sk37 @ qmltpeq ) ) )
| ~ ( D @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( D @ sk37 @ ( D @ '$ki_accessible' ) )
| ~ ( D @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e0 @ ( e3 @ op ) @ ( e0 @ ( e0 @ op ) @ ( C @ sk36 @ qmltpeq ) ) )
| ~ ( C @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( C @ sk36 @ ( C @ '$ki_accessible' ) )
| ~ ( C @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e0 @ ( e2 @ op ) @ ( e0 @ ( e0 @ op ) @ ( B @ sk35 @ qmltpeq ) ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( B @ sk35 @ ( B @ '$ki_accessible' ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ~ ( e0 @ ( e1 @ op ) @ ( e0 @ ( e0 @ op ) @ ( A @ sk34 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( A @ sk34 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ),
inference(cnf,[status(esa)],[167]) ).
thf(232,plain,
! [A: '$ki_world'] :
( ( A @ sk34 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(21632,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( A @ sk34 @ ( A @ '$ki_accessible' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,232]) ).
thf(21633,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( A @ sk34 @ ( A @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[21632]) ).
thf(21634,plain,
sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ),
inference(pattern_uni,[status(thm)],[21633:[bind(A,$thf( sk1 ))]]) ).
thf(22636,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e2 @ ( A @ sk99 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,558]) ).
thf(22637,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e2 @ ( A @ sk99 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22636]) ).
thf(22811,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 )
!= A )
| ( sk1 != '$ki_local_world' )
| ~ ( e3 @ ( e2 @ ( A @ sk99 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22637]) ).
thf(22861,plain,
( ( sk1 != '$ki_local_world' )
| ~ ( e3 @ ( e2 @ ( sk1 @ sk34 @ sk99 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22811]) ).
thf(5,axiom,
( ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( unit @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( unit @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( unit @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( unit @ ( A @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( unit @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(125,plain,
( ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( unit @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( unit @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( unit @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( unit @ ( A @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( unit @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(126,plain,
! [L: '$ki_world',K: '$ki_world',J: '$ki_world',I: '$ki_world',H: '$ki_world',G: '$ki_world',F: '$ki_world',E: '$ki_world',D: '$ki_world',C: '$ki_world',B: '$ki_world',A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( L @ qmltpeq ) ) )
| ~ ( L @ ( '$ki_local_world' @ '$ki_accessible' ) )
| ( e2 @ ( unit @ ( K @ qmltpeq ) ) )
| ~ ( K @ ( '$ki_local_world' @ '$ki_accessible' ) )
| ( e1 @ ( unit @ ( J @ qmltpeq ) ) )
| ~ ( J @ ( '$ki_local_world' @ '$ki_accessible' ) )
| ( e0 @ ( unit @ ( I @ qmltpeq ) ) )
| ~ ( I @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e3 @ ( unit @ ( e3 @ op ) @ ( H @ qmltpeq ) ) )
| ~ ( H @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e3 @ ( e3 @ ( unit @ op ) @ ( G @ qmltpeq ) ) )
| ~ ( G @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e2 @ ( unit @ ( e2 @ op ) @ ( F @ qmltpeq ) ) )
| ~ ( F @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e2 @ ( e2 @ ( unit @ op ) @ ( E @ qmltpeq ) ) )
| ~ ( E @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e1 @ ( unit @ ( e1 @ op ) @ ( D @ qmltpeq ) ) )
| ~ ( D @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e1 @ ( e1 @ ( unit @ op ) @ ( C @ qmltpeq ) ) )
| ~ ( C @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e0 @ ( unit @ ( e0 @ op ) @ ( B @ qmltpeq ) ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e0 @ ( e0 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ),
inference(cnf,[status(esa)],[125]) ).
thf(127,plain,
! [A: '$ki_world'] :
( ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(137,plain,
! [A: '$ki_world'] :
( ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(2497,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( unit @ ( e1 @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,137]) ).
thf(2498,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( unit @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2497]) ).
thf(2499,plain,
e1 @ ( unit @ ( e1 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[2498:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(554,plain,
! [A: '$ki_world'] :
( ~ ( e1 @ ( e0 @ ( A @ sk94 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[544]) ).
thf(662,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e1 @ ( e0 @ ( A @ sk94 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,554]) ).
thf(663,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e1 @ ( e0 @ ( A @ sk94 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[662]) ).
thf(664,plain,
~ ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[663:[bind(A,$thf( sk1 ))]]) ).
thf(1222,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[652,664]) ).
thf(1223,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1222]) ).
thf(1274,plain,
! [A: '$ki_world'] :
( ( e1 != unit )
| ( ( unit @ inv )
!= e0 )
| ( A
!= ( sk1 @ sk94 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1223]) ).
thf(1295,plain,
( ( e1 != unit )
| ( ( unit @ inv )
!= e0 )
| ~ ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1274]) ).
thf(37,plain,
! [A: '$ki_world'] :
( ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(88,plain,
! [A: '$ki_world'] :
( ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(134,plain,
! [A: '$ki_world'] :
( ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(140,plain,
! [A: '$ki_world'] :
( ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(3938,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,140]) ).
thf(3939,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3938]) ).
thf(3940,plain,
e2 @ ( unit @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[3939:[bind(A,$thf( sk1 ))]]) ).
thf(546,plain,
! [A: '$ki_world'] :
( ~ ( e2 @ ( e1 @ ( A @ sk97 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[544]) ).
thf(559,plain,
! [A: '$ki_world'] :
( ~ ( e2 @ ( e1 @ ( A @ sk97 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[546]) ).
thf(901,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e1 @ ( B @ sk97 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,559]) ).
thf(902,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e1 @ ( B @ sk97 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[901]) ).
thf(903,plain,
~ ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[902:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(4132,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3940,903]) ).
thf(4133,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[4132]) ).
thf(4159,plain,
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[4133]) ).
thf(4166,plain,
( ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[4159]) ).
thf(21612,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( B @ sk34 @ ( B @ '$ki_accessible' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,232]) ).
thf(21613,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( B @ sk34 @ ( B @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[21612]) ).
thf(21614,plain,
'$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ),
inference(pattern_uni,[status(thm)],[21613:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(128,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(141,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(1140,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e1 @ ( B @ sk98 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,563]) ).
thf(1141,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e1 @ ( B @ sk98 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1140]) ).
thf(1142,plain,
~ ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[1141:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(4957,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[141,1142]) ).
thf(4958,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[4957]) ).
thf(5035,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e1 )
| ( A
!= ( '$ki_local_world' @ sk98 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[4958]) ).
thf(5063,plain,
( ( ( e3 @ ( unit @ op ) )
!= e1 )
| ~ ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5035]) ).
thf(22181,plain,
( ( ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,5063]) ).
thf(22182,plain,
( ( ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22181]) ).
thf(22331,plain,
( ( ( '$ki_local_world' @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22182]) ).
thf(22424,plain,
( ( ( '$ki_local_world' @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22331]) ).
thf(8,axiom,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ inv @ inv @ ( A @ qmltpeq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(154,plain,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ inv @ inv @ ( A @ qmltpeq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(155,plain,
! [D: '$ki_world',C: '$ki_world',B: '$ki_world',A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( D @ qmltpeq ) ) )
| ~ ( D @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e2 @ ( e2 @ inv @ inv @ ( C @ qmltpeq ) ) )
| ~ ( C @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e1 @ ( e1 @ inv @ inv @ ( B @ qmltpeq ) ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( e0 @ ( e0 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ),
inference(cnf,[status(esa)],[154]) ).
thf(159,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[155]) ).
thf(162,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(12664,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ inv @ inv @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,162]) ).
thf(12665,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ inv @ inv @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[12664]) ).
thf(12666,plain,
e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[12665:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(12902,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12666,771]) ).
thf(12903,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[12902]) ).
thf(12928,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12903]) ).
thf(12949,plain,
( ( ( e3 @ inv @ inv )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12928]) ).
thf(132,plain,
! [A: '$ki_world'] :
( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(139,plain,
! [A: '$ki_world'] :
( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(2907,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( unit @ ( e3 @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,139]) ).
thf(2908,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( unit @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2907]) ).
thf(2909,plain,
e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[2908:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(3009,plain,
( ( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2909,1142]) ).
thf(3010,plain,
( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3009]) ).
thf(3062,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3010]) ).
thf(3072,plain,
( ( ( unit @ ( e3 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3062]) ).
thf(910,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e1 @ ( A @ sk97 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,559]) ).
thf(911,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e1 @ ( A @ sk97 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[910]) ).
thf(912,plain,
~ ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[911:[bind(A,$thf( sk1 ))]]) ).
thf(1243,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[652,912]) ).
thf(1244,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1243]) ).
thf(1269,plain,
! [A: '$ki_world'] :
( ( e2 != unit )
| ( ( unit @ inv )
!= e1 )
| ( A
!= ( sk1 @ sk97 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1244]) ).
thf(1290,plain,
( ( e2 != unit )
| ( ( unit @ inv )
!= e1 )
| ~ ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1269]) ).
thf(556,plain,
! [A: '$ki_world'] :
( ~ ( e3 @ ( e0 @ ( A @ sk96 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[544]) ).
thf(562,plain,
! [A: '$ki_world'] :
( ~ ( e3 @ ( e0 @ ( A @ sk96 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[556]) ).
thf(961,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e0 @ ( A @ sk96 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,562]) ).
thf(962,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e0 @ ( A @ sk96 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[961]) ).
thf(963,plain,
~ ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[962:[bind(A,$thf( sk1 ))]]) ).
thf(12746,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[162,963]) ).
thf(12747,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12746]) ).
thf(12787,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e0 )
| ( A
!= ( sk1 @ sk96 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12747]) ).
thf(12837,plain,
( ( ( e3 @ inv @ inv )
!= e0 )
| ~ ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12787]) ).
thf(22108,plain,
( ( ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,12837]) ).
thf(22109,plain,
( ( ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22108]) ).
thf(22364,plain,
( ( ( sk1 @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22109]) ).
thf(22457,plain,
( ( ( sk1 @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22364]) ).
thf(130,plain,
! [A: '$ki_world'] :
( ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(142,plain,
! [A: '$ki_world'] :
( ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(555,plain,
! [A: '$ki_world'] :
( ~ ( e2 @ ( e0 @ ( A @ sk95 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[544]) ).
thf(557,plain,
! [A: '$ki_world'] :
( ~ ( e2 @ ( e0 @ ( A @ sk95 @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[555]) ).
thf(738,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e0 @ ( B @ sk95 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,557]) ).
thf(739,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e0 @ ( B @ sk95 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[738]) ).
thf(740,plain,
~ ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[739:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(6412,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[142,740]) ).
thf(6413,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6412]) ).
thf(6432,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk95 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6413]) ).
thf(6463,plain,
( ( ( e2 @ ( unit @ op ) )
!= e0 )
| ~ ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6432]) ).
thf(665,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e1 @ ( e0 @ ( B @ sk94 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,554]) ).
thf(666,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e1 @ ( e0 @ ( B @ sk94 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[665]) ).
thf(667,plain,
~ ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[666:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(2541,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[137,667]) ).
thf(2542,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2541]) ).
thf(2557,plain,
! [A: '$ki_world'] :
( ( e1 != e1 )
| ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk94 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2542]) ).
thf(2590,plain,
( ( ( unit @ ( e1 @ op ) )
!= e0 )
| ~ ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2557]) ).
thf(1228,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,652]) ).
thf(1229,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1228]) ).
thf(1230,plain,
unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[1229:[bind(A,$thf( sk1 ))]]) ).
thf(1401,plain,
( ( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,912]) ).
thf(1402,plain,
( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1401]) ).
thf(1422,plain,
( ( e2 != unit )
| ( ( unit @ inv )
!= e1 )
| ( ( sk1 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[1402]) ).
thf(772,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e2 @ ( A @ sk99 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,558]) ).
thf(773,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e2 @ ( A @ sk99 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[772]) ).
thf(774,plain,
~ ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[773:[bind(A,$thf( sk1 ))]]) ).
thf(12678,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[162,774]) ).
thf(12679,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12678]) ).
thf(12802,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e2 )
| ( A
!= ( sk1 @ sk99 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12679]) ).
thf(12809,plain,
( ( ( e3 @ inv @ inv )
!= e2 )
| ~ ( sk1 @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12802]) ).
thf(22141,plain,
( ( ( sk1 @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,12809]) ).
thf(22142,plain,
( ( ( sk1 @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[22141]) ).
thf(22387,plain,
( ( ( sk1 @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ inv @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[22142]) ).
thf(22480,plain,
( ( ( sk1 @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ inv @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[22387]) ).
thf(62,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk5 )
| ( A @ sk6 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(120,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk5 )
| ( A @ sk6 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(129,plain,
! [A: '$ki_world'] :
( ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(136,plain,
! [A: '$ki_world'] :
( ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(2042,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ ( unit @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,136]) ).
thf(2043,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ ( unit @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2042]) ).
thf(2044,plain,
e1 @ ( e1 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[2043:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(22168,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e1 @ ( e0 @ ( A @ sk94 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,554]) ).
thf(22169,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e1 @ ( e0 @ ( A @ sk94 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22168]) ).
thf(22170,plain,
~ ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[22169:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(23247,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2044,22170]) ).
thf(23248,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23247]) ).
thf(23302,plain,
( ( e1 != e1 )
| ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23248]) ).
thf(23369,plain,
( ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23302]) ).
thf(64,plain,
! [A: '$ki_world'] :
( ( A @ sk22 @ ( A @ '$ki_accessible' ) )
| ( A @ sk21 @ ( A @ '$ki_accessible' ) )
| ( A @ sk19 )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(96,plain,
! [A: '$ki_world'] :
( ( A @ sk22 @ ( A @ '$ki_accessible' ) )
| ( A @ sk21 @ ( A @ '$ki_accessible' ) )
| ( A @ sk19 )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(10656,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ sk22 @ ( B @ '$ki_accessible' ) )
| ( B @ sk21 @ ( B @ '$ki_accessible' ) )
| ( B @ sk19 )
| ( B @ sk17 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,96]) ).
thf(10657,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ sk22 @ ( B @ '$ki_accessible' ) )
| ( B @ sk21 @ ( B @ '$ki_accessible' ) )
| ( B @ sk19 )
| ( B @ sk17 ) ),
inference(simp,[status(thm)],[10656]) ).
thf(10658,plain,
( ( sk1 @ sk22 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk21 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk19 )
| ( sk1 @ sk17 ) ),
inference(pattern_uni,[status(thm)],[10657:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(36,plain,
! [A: '$ki_world'] :
( sk4
| ( e2 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(115,plain,
! [A: '$ki_world'] :
( sk4
| ( e2 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 ),
inference(simp,[status(thm)],[36]) ).
thf(4964,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,141]) ).
thf(4965,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[4964]) ).
thf(4966,plain,
e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[4965:[bind(A,$thf( sk1 ))]]) ).
thf(5197,plain,
( ( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4966,963]) ).
thf(5198,plain,
( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5197]) ).
thf(5216,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[5198]) ).
thf(5225,plain,
( ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[5216]) ).
thf(952,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e0 @ ( B @ sk96 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,562]) ).
thf(953,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e0 @ ( B @ sk96 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[952]) ).
thf(954,plain,
~ ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[953:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(1407,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,954]) ).
thf(1408,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1407]) ).
thf(1426,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[1408]) ).
thf(409,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[408]) ).
thf(15044,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ op ) @ ( e0 @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,409]) ).
thf(15045,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ op ) @ ( e0 @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15044]) ).
thf(15046,plain,
e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[15045:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(15302,plain,
( ( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15046,963]) ).
thf(15303,plain,
( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15302]) ).
thf(15326,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ( e0 != e0 )
| ( ( sk1 @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15303]) ).
thf(15357,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ( ( sk1 @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15326]) ).
thf(135,plain,
! [A: '$ki_world'] :
( ( e0 @ ( unit @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(143,plain,
! [A: '$ki_world'] :
( ( e0 @ ( unit @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(8099,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( unit @ ( e0 @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,143]) ).
thf(8100,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( unit @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[8099]) ).
thf(8101,plain,
e0 @ ( unit @ ( e0 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[8100:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(2943,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[139,954]) ).
thf(2944,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2943]) ).
thf(2980,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk96 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2944]) ).
thf(3004,plain,
( ( ( unit @ ( e3 @ op ) )
!= e0 )
| ~ ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2980]) ).
thf(15138,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[409,664]) ).
thf(15139,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15138]) ).
thf(15160,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( e0 != e0 )
| ( A
!= ( sk1 @ sk94 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15139]) ).
thf(15207,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ~ ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15160]) ).
thf(2912,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,139]) ).
thf(2913,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2912]) ).
thf(2914,plain,
e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[2913:[bind(A,$thf( sk1 ))]]) ).
thf(3079,plain,
( ( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2914,774]) ).
thf(3080,plain,
( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3079]) ).
thf(3120,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( sk1 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[3080]) ).
thf(3135,plain,
( ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( sk1 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[3120]) ).
thf(22076,plain,
( ( ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ ( unit @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,6463]) ).
thf(22077,plain,
( ( ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22076]) ).
thf(22355,plain,
( ( ( '$ki_local_world' @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e2 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22077]) ).
thf(22448,plain,
( ( ( '$ki_local_world' @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e2 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22355]) ).
thf(60,plain,
! [A: '$ki_world'] :
( sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(78,plain,
! [A: '$ki_world'] :
( sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(22545,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,78]) ).
thf(22546,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22545]) ).
thf(22547,plain,
( sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( sk1 @ sk34 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[22546:[bind(A,$thf( sk1 @ sk34 ))]]) ).
thf(5195,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4966,771]) ).
thf(5196,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5195]) ).
thf(5219,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[5196]) ).
thf(5227,plain,
( ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[5219]) ).
thf(2949,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[139,771]) ).
thf(2950,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2949]) ).
thf(2961,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( A
!= ( '$ki_local_world' @ sk99 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2950]) ).
thf(2985,plain,
( ( ( unit @ ( e3 @ op ) )
!= e2 )
| ~ ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2961]) ).
thf(17794,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,411]) ).
thf(17795,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[17794]) ).
thf(17796,plain,
e3 @ ( e2 @ op ) @ ( e1 @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[17795:[bind(A,$thf( sk1 ))]]) ).
thf(18187,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17796,903]) ).
thf(18188,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[18187]) ).
thf(18234,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( e1 != e1 )
| ( ( '$ki_local_world' @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[18188]) ).
thf(18252,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[18234]) ).
thf(158,plain,
! [A: '$ki_world'] :
( ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[155]) ).
thf(161,plain,
! [A: '$ki_world'] :
( ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(10939,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,161]) ).
thf(10940,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[10939]) ).
thf(10941,plain,
e2 @ ( e2 @ inv @ inv @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[10940:[bind(A,$thf( sk1 ))]]) ).
thf(22097,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e1 @ ( A @ sk97 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,559]) ).
thf(22098,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e1 @ ( A @ sk97 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22097]) ).
thf(22099,plain,
~ ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[22098:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(23016,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10941,22099]) ).
thf(23017,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23016]) ).
thf(23068,plain,
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[23017]) ).
thf(23112,plain,
( ( ( e2 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[23068]) ).
thf(157,plain,
! [A: '$ki_world'] :
( ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[155]) ).
thf(160,plain,
! [A: '$ki_world'] :
( ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(22138,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,160]) ).
thf(22139,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22138]) ).
thf(22140,plain,
e1 @ ( e1 @ inv @ inv @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22139:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(156,plain,
! [A: '$ki_world'] :
( ( e0 @ ( e0 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[155]) ).
thf(22163,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,156]) ).
thf(22164,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ inv @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22163]) ).
thf(22165,plain,
e0 @ ( e0 @ inv @ inv @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22164:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(9602,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[160,667]) ).
thf(9603,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[9602]) ).
thf(9623,plain,
! [A: '$ki_world'] :
( ( e1 != e1 )
| ( ( e1 @ inv @ inv )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk94 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[9603]) ).
thf(9661,plain,
( ( ( e1 @ inv @ inv )
!= e0 )
| ~ ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[9623]) ).
thf(9700,plain,
( ( ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ inv @ inv )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,9661]) ).
thf(9701,plain,
( ( ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[9700]) ).
thf(9735,plain,
( ( ( '$ki_local_world' @ sk94 )
!= sk1 )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[9701]) ).
thf(9746,plain,
( ( ( '$ki_local_world' @ sk94 )
!= sk1 )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[9735]) ).
thf(18157,plain,
( ( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17796,1155]) ).
thf(18158,plain,
( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[18157]) ).
thf(18209,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ( e1 != e1 )
| ( ( sk1 @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[18158]) ).
thf(18247,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ( ( sk1 @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[18209]) ).
thf(22066,plain,
( ( ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,17986]) ).
thf(22067,plain,
( ( ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e2 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22066]) ).
thf(22383,plain,
( ( ( sk1 @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( e2 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22067]) ).
thf(22476,plain,
( ( ( sk1 @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( e2 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22383]) ).
thf(1213,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( unit @ ( unit @ inv @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,652]) ).
thf(1214,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( unit @ ( unit @ inv @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1213]) ).
thf(1215,plain,
unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[1214:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(1337,plain,
( ( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1215,774]) ).
thf(1338,plain,
( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1337]) ).
thf(1366,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e2 )
| ( ( sk1 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[1338]) ).
thf(741,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e0 @ ( A @ sk95 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,557]) ).
thf(742,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e0 @ ( A @ sk95 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[741]) ).
thf(743,plain,
~ ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[742:[bind(A,$thf( sk1 ))]]) ).
thf(10980,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[161,743]) ).
thf(10981,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[10980]) ).
thf(11063,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e0 )
| ( A
!= ( sk1 @ sk95 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[10981]) ).
thf(11102,plain,
( ( ( e2 @ inv @ inv )
!= e0 )
| ~ ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[11063]) ).
thf(22234,plain,
( ( ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ inv @ inv )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,11102]) ).
thf(22235,plain,
( ( ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22234]) ).
thf(22401,plain,
( ( ( sk1 @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e2 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22235]) ).
thf(22493,plain,
( ( ( sk1 @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e2 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22401]) ).
thf(1255,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[652,963]) ).
thf(1256,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1255]) ).
thf(1266,plain,
! [A: '$ki_world'] :
( ( e3 != unit )
| ( ( unit @ inv )
!= e0 )
| ( A
!= ( sk1 @ sk96 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1256]) ).
thf(1287,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e0 )
| ~ ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1266]) ).
thf(15310,plain,
( ( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15046,740]) ).
thf(15311,plain,
( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15310]) ).
thf(15317,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ( e0 != e0 )
| ( ( '$ki_local_world' @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15311]) ).
thf(15353,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15317]) ).
thf(1409,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,903]) ).
thf(1410,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1409]) ).
thf(1430,plain,
( ( e2 != unit )
| ( ( unit @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[1410]) ).
thf(1869,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,78]) ).
thf(1870,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1869]) ).
thf(1871,plain,
( sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[1870:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(22538,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e1 @ ( A @ sk97 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,559]) ).
thf(22539,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e1 @ ( A @ sk97 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22538]) ).
thf(22827,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 )
!= A )
| ( sk1 != '$ki_local_world' )
| ~ ( e2 @ ( e1 @ ( A @ sk97 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22539]) ).
thf(22866,plain,
( ( sk1 != '$ki_local_world' )
| ~ ( e2 @ ( e1 @ ( sk1 @ sk34 @ sk97 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22827]) ).
thf(22227,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e1 @ ( A @ sk98 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,563]) ).
thf(22228,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e1 @ ( A @ sk98 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22227]) ).
thf(22229,plain,
~ ( e3 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk98 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[22228:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(9610,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[160,664]) ).
thf(9611,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[9610]) ).
thf(9630,plain,
! [A: '$ki_world'] :
( ( e1 != e1 )
| ( ( e1 @ inv @ inv )
!= e0 )
| ( A
!= ( sk1 @ sk94 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[9611]) ).
thf(9668,plain,
( ( ( e1 @ inv @ inv )
!= e0 )
| ~ ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[9630]) ).
thf(12671,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,162]) ).
thf(12672,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[12671]) ).
thf(12673,plain,
e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[12672:[bind(A,$thf( sk1 ))]]) ).
thf(12961,plain,
( ( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12673,1142]) ).
thf(12962,plain,
( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[12961]) ).
thf(13044,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[12962]) ).
thf(13067,plain,
( ( ( e3 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[13044]) ).
thf(45,plain,
! [A: '$ki_world'] :
( ( A @ sk28 @ ( A @ '$ki_accessible' ) )
| ( A @ sk27 @ ( A @ '$ki_accessible' ) )
| ( A @ sk25 )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(95,plain,
! [A: '$ki_world'] :
( ( A @ sk28 @ ( A @ '$ki_accessible' ) )
| ( A @ sk27 @ ( A @ '$ki_accessible' ) )
| ( A @ sk25 )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(9958,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ sk28 @ ( B @ '$ki_accessible' ) )
| ( B @ sk27 @ ( B @ '$ki_accessible' ) )
| ( B @ sk25 )
| ( B @ sk23 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,95]) ).
thf(9959,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ sk28 @ ( B @ '$ki_accessible' ) )
| ( B @ sk27 @ ( B @ '$ki_accessible' ) )
| ( B @ sk25 )
| ( B @ sk23 ) ),
inference(simp,[status(thm)],[9958]) ).
thf(9960,plain,
( ( sk1 @ sk28 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk27 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk25 )
| ( sk1 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[9959:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(12700,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[162,1155]) ).
thf(12701,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12700]) ).
thf(12796,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e1 )
| ( A
!= ( sk1 @ sk98 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12701]) ).
thf(12846,plain,
( ( ( e3 @ inv @ inv )
!= e1 )
| ~ ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12796]) ).
thf(22143,plain,
( ( ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,12846]) ).
thf(22144,plain,
( ( ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22143]) ).
thf(22318,plain,
( ( ( sk1 @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22144]) ).
thf(22412,plain,
( ( ( sk1 @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22318]) ).
thf(1224,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[652,740]) ).
thf(1225,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1224]) ).
thf(1277,plain,
! [A: '$ki_world'] :
( ( e2 != unit )
| ( ( unit @ inv )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk95 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1225]) ).
thf(1298,plain,
( ( e2 != unit )
| ( ( unit @ inv )
!= e0 )
| ~ ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1277]) ).
thf(3083,plain,
( ( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2914,1155]) ).
thf(3084,plain,
( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3083]) ).
thf(3112,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e1 )
| ( ( sk1 @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[3084]) ).
thf(3131,plain,
( ( ( unit @ ( e3 @ op ) )
!= e1 )
| ( ( sk1 @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[3112]) ).
thf(10932,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ inv @ inv @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,161]) ).
thf(10933,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ inv @ inv @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[10932]) ).
thf(10934,plain,
e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[10933:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(11148,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10934,903]) ).
thf(11149,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[11148]) ).
thf(11189,plain,
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[11149]) ).
thf(11203,plain,
( ( ( e2 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[11189]) ).
thf(4969,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[141,774]) ).
thf(4970,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[4969]) ).
thf(5033,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( A
!= ( sk1 @ sk99 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[4970]) ).
thf(5061,plain,
( ( ( e3 @ ( unit @ op ) )
!= e2 )
| ~ ( sk1 @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5033]) ).
thf(22305,plain,
( ( ( sk1 @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,5061]) ).
thf(22306,plain,
( ( ( sk1 @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22305]) ).
thf(22351,plain,
( ( ( sk1 @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( unit @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22306]) ).
thf(22444,plain,
( ( ( sk1 @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( unit @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22351]) ).
thf(12874,plain,
( ( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12666,1155]) ).
thf(12875,plain,
( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[12874]) ).
thf(12919,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e1 )
| ( ( sk1 @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12875]) ).
thf(12956,plain,
( ( ( e3 @ inv @ inv )
!= e1 )
| ( ( sk1 @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12919]) ).
thf(3933,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( unit @ ( e2 @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,140]) ).
thf(3934,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( unit @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3933]) ).
thf(3935,plain,
e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[3934:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(22928,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3935,22099]) ).
thf(22929,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22928]) ).
thf(23088,plain,
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[22929]) ).
thf(23123,plain,
( ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23088]) ).
thf(11022,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[161,740]) ).
thf(11023,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[11022]) ).
thf(11048,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk95 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[11023]) ).
thf(11087,plain,
( ( ( e2 @ inv @ inv )
!= e0 )
| ~ ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[11048]) ).
thf(72,plain,
! [A: '$ki_world'] :
( sk3
| ( e1 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(110,plain,
! [A: '$ki_world'] :
( sk3
| ( e1 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 ),
inference(simp,[status(thm)],[72]) ).
thf(22689,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e0 @ ( A @ sk95 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,557]) ).
thf(22690,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e0 @ ( A @ sk95 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22689]) ).
thf(22808,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 )
!= A )
| ( sk1 != '$ki_local_world' )
| ~ ( e2 @ ( e0 @ ( A @ sk95 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22690]) ).
thf(22859,plain,
( ( sk1 != '$ki_local_world' )
| ~ ( e2 @ ( e0 @ ( sk1 @ sk34 @ sk95 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22808]) ).
thf(4959,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ ( unit @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,141]) ).
thf(4960,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ ( unit @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[4959]) ).
thf(4961,plain,
e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[4960:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(5095,plain,
( ( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4961,1155]) ).
thf(5096,plain,
( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5095]) ).
thf(5128,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e1 )
| ( ( sk1 @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5096]) ).
thf(5150,plain,
( ( ( e3 @ ( unit @ op ) )
!= e1 )
| ( ( sk1 @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5128]) ).
thf(5173,plain,
( ( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4966,1155]) ).
thf(5174,plain,
( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5173]) ).
thf(5204,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e1 )
| ( ( sk1 @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[5174]) ).
thf(5231,plain,
( ( ( e3 @ ( unit @ op ) )
!= e1 )
| ( ( sk1 @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[5204]) ).
thf(12744,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[162,771]) ).
thf(12745,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12744]) ).
thf(12785,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e2 )
| ( A
!= ( '$ki_local_world' @ sk99 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12745]) ).
thf(12835,plain,
( ( ( e3 @ inv @ inv )
!= e2 )
| ~ ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12785]) ).
thf(22200,plain,
( ( ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,12835]) ).
thf(22201,plain,
( ( ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[22200]) ).
thf(22356,plain,
( ( ( '$ki_local_world' @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ inv @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[22201]) ).
thf(22449,plain,
( ( ( '$ki_local_world' @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ inv @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[22356]) ).
thf(11004,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[161,903]) ).
thf(11005,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[11004]) ).
thf(11061,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e1 )
| ( A
!= ( '$ki_local_world' @ sk97 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[11005]) ).
thf(11100,plain,
( ( ( e2 @ inv @ inv )
!= e1 )
| ~ ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[11061]) ).
thf(28,plain,
! [A: '$ki_world'] :
( ( A @ sk16 @ ( A @ '$ki_accessible' ) )
| ( A @ sk15 @ ( A @ '$ki_accessible' ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(93,plain,
! [A: '$ki_world'] :
( ( A @ sk16 @ ( A @ '$ki_accessible' ) )
| ( A @ sk15 @ ( A @ '$ki_accessible' ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(12660,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[162,1142]) ).
thf(12661,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12660]) ).
thf(12784,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e1 )
| ( A
!= ( '$ki_local_world' @ sk98 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12661]) ).
thf(12834,plain,
( ( ( e3 @ inv @ inv )
!= e1 )
| ~ ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12784]) ).
thf(22161,plain,
( ( ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,12834]) ).
thf(22162,plain,
( ( ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22161]) ).
thf(22406,plain,
( ( ( '$ki_local_world' @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22162]) ).
thf(22498,plain,
( ( ( '$ki_local_world' @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22406]) ).
thf(5007,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[141,954]) ).
thf(5008,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5007]) ).
thf(5049,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk96 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5008]) ).
thf(5077,plain,
( ( ( e3 @ ( unit @ op ) )
!= e0 )
| ~ ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5049]) ).
thf(1331,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1215,664]) ).
thf(1332,plain,
( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1331]) ).
thf(1379,plain,
( ( e1 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( sk1 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[1332]) ).
thf(15051,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,409]) ).
thf(15052,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15051]) ).
thf(15053,plain,
e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[15052:[bind(A,$thf( sk1 ))]]) ).
thf(15425,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15053,667]) ).
thf(15426,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15425]) ).
thf(15451,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( e0 != e0 )
| ( ( '$ki_local_world' @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[15426]) ).
thf(15477,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[15451]) ).
thf(2047,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,136]) ).
thf(2048,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2047]) ).
thf(2049,plain,
e1 @ ( e1 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[2048:[bind(A,$thf( sk1 ))]]) ).
thf(54,plain,
! [A: '$ki_world'] :
( sk3
| ( e1 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(103,plain,
! [A: '$ki_world'] :
( sk3
| ( e1 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 ),
inference(simp,[status(thm)],[54]) ).
thf(16112,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk3
| ( e1 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true
| ~ sk2 ),
inference(paramod_ordered,[status(thm)],[542,103]) ).
thf(16113,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk3
| ( e1 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) )
| ~ sk2 ),
inference(simp,[status(thm)],[16112]) ).
thf(16114,plain,
( sk3
| ( e1 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ qmltpeq ) ) )
| ~ sk2 ),
inference(pattern_uni,[status(thm)],[16113:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(15116,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[409,954]) ).
thf(15117,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15116]) ).
thf(15183,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ( e0 != e0 )
| ( A
!= ( '$ki_local_world' @ sk96 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15117]) ).
thf(15230,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ~ ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15183]) ).
thf(22286,plain,
( ( ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,15230]) ).
thf(22287,plain,
( ( ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22286]) ).
thf(22332,plain,
( ( ( '$ki_local_world' @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( e3 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22287]) ).
thf(22425,plain,
( ( ( '$ki_local_world' @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( e3 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22332]) ).
thf(33,plain,
! [A: '$ki_world'] :
( sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(11361,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk22 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk21 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk19 )
| ( sk1 @ sk17 ) ),
inference(paramod_ordered,[status(thm)],[10658,33]) ).
thf(11362,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk22 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk21 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk19 )
| ( sk1 @ sk17 ) ),
inference(simp,[status(thm)],[11361]) ).
thf(11363,plain,
( sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk22 @ qmltpeq ) ) )
| ( sk1 @ sk21 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk19 )
| ( sk1 @ sk17 ) ),
inference(pattern_uni,[status(thm)],[11362:[bind(A,$thf( sk1 @ sk22 ))]]) ).
thf(6382,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[142,912]) ).
thf(6383,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6382]) ).
thf(6446,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( A
!= ( sk1 @ sk97 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6383]) ).
thf(6477,plain,
( ( ( e2 @ ( unit @ op ) )
!= e1 )
| ~ ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6446]) ).
thf(22166,plain,
( ( ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ ( unit @ op ) )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,6477]) ).
thf(22167,plain,
( ( ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22166]) ).
thf(22388,plain,
( ( ( sk1 @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e2 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22167]) ).
thf(22481,plain,
( ( ( sk1 @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e2 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22388]) ).
thf(10986,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[161,912]) ).
thf(10987,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[10986]) ).
thf(11026,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e1 )
| ( A
!= ( sk1 @ sk97 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[10987]) ).
thf(11065,plain,
( ( ( e2 @ inv @ inv )
!= e1 )
| ~ ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[11026]) ).
thf(22192,plain,
( ( ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ inv @ inv )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,11065]) ).
thf(22193,plain,
( ( ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22192]) ).
thf(22323,plain,
( ( ( sk1 @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e2 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22193]) ).
thf(22416,plain,
( ( ( sk1 @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e2 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22323]) ).
thf(57,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk11 )
| ~ ( e1 @ ( e0 @ ( e0 @ op ) @ ( A @ sk12 @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(91,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk11 )
| ~ ( e1 @ ( e0 @ ( e0 @ op ) @ ( A @ sk12 @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(6655,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk11 )
| ~ ( e1 @ ( e0 @ ( e0 @ op ) @ ( B @ sk12 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,91]) ).
thf(6656,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk11 )
| ~ ( e1 @ ( e0 @ ( e0 @ op ) @ ( B @ sk12 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[6655]) ).
thf(6657,plain,
( ~ ( sk1 @ sk11 )
| ~ ( e1 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk12 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[6656:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(22717,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,652]) ).
thf(22718,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22717]) ).
thf(22795,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 )
!= A )
| ( sk1 != '$ki_local_world' )
| ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22718]) ).
thf(22855,plain,
( ( sk1 != '$ki_local_world' )
| ( unit @ ( unit @ inv @ ( sk1 @ sk34 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22795]) ).
thf(1385,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,664]) ).
thf(1386,plain,
( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1385]) ).
thf(1418,plain,
( ( e1 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( sk1 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[1386]) ).
thf(5117,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4961,771]) ).
thf(5118,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5117]) ).
thf(5141,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5118]) ).
thf(5156,plain,
( ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5141]) ).
thf(4120,plain,
( ( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3940,743]) ).
thf(4121,plain,
( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[4120]) ).
thf(4150,plain,
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e0 )
| ( ( sk1 @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[4121]) ).
thf(4162,plain,
( ( ( unit @ ( e2 @ op ) )
!= e0 )
| ( ( sk1 @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[4150]) ).
thf(671,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ sk10 @ ( B @ '$ki_accessible' ) )
| ( B @ sk9 @ ( B @ '$ki_accessible' ) )
| ( B @ sk7 )
| ( B @ sk5 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,88]) ).
thf(672,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ sk10 @ ( B @ '$ki_accessible' ) )
| ( B @ sk9 @ ( B @ '$ki_accessible' ) )
| ( B @ sk7 )
| ( B @ sk5 ) ),
inference(simp,[status(thm)],[671]) ).
thf(673,plain,
( ( sk1 @ sk10 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[672:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(791,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ $true
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[673,88]) ).
thf(792,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[791]) ).
thf(793,plain,
( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[792:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(133,plain,
! [A: '$ki_world'] :
( ( e0 @ ( e0 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(1813,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[793,133]) ).
thf(1814,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1813]) ).
thf(1841,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= '$ki_local_world' )
| ( e0 @ ( e0 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1814]) ).
thf(1858,plain,
( ( ( sk1 @ sk10 )
!= '$ki_local_world' )
| ( e0 @ ( e0 @ ( unit @ op ) @ ( sk1 @ sk10 @ sk10 @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1841]) ).
thf(63,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk17 )
| ( A @ sk18 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(106,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk17 )
| ( A @ sk18 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(17787,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e2 @ op ) @ ( e1 @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,411]) ).
thf(17788,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e2 @ op ) @ ( e1 @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[17787]) ).
thf(17789,plain,
e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[17788:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(18047,plain,
( ( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17789,912]) ).
thf(18048,plain,
( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[18047]) ).
thf(18110,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( e1 != e1 )
| ( ( sk1 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[18048]) ).
thf(18126,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( ( sk1 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[18110]) ).
thf(3,axiom,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(121,plain,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2915,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[139,774]) ).
thf(2916,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2915]) ).
thf(2960,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( A
!= ( sk1 @ sk99 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2916]) ).
thf(2984,plain,
( ( ( unit @ ( e3 @ op ) )
!= e2 )
| ~ ( sk1 @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2960]) ).
thf(22232,plain,
( ( ( sk1 @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,2984]) ).
thf(22233,plain,
( ( ( sk1 @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22232]) ).
thf(22363,plain,
( ( ( sk1 @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22233]) ).
thf(22456,plain,
( ( ( sk1 @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22363]) ).
thf(1872,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[793,78]) ).
thf(1873,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1872]) ).
thf(1940,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= sk1 )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1873]) ).
thf(1960,plain,
( ( ( sk1 @ sk10 )
!= sk1 )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( sk1 @ sk10 @ sk10 @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1940]) ).
thf(66,plain,
! [A: '$ki_world'] :
( ~ ( e3 @ ( e3 @ ( e3 @ op ) @ ( A @ sk28 @ qmltpeq ) ) )
| ( A @ sk27 @ ( A @ '$ki_accessible' ) )
| ( A @ sk25 )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(84,plain,
! [A: '$ki_world'] :
( ~ ( e3 @ ( e3 @ ( e3 @ op ) @ ( A @ sk28 @ qmltpeq ) ) )
| ( A @ sk27 @ ( A @ '$ki_accessible' ) )
| ( A @ sk25 )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(22197,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e0 @ ( A @ sk96 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,562]) ).
thf(22198,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e0 @ ( A @ sk96 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22197]) ).
thf(22199,plain,
~ ( e3 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk96 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[22198:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(24264,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2914,22199]) ).
thf(24265,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[24264]) ).
thf(24331,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[24265]) ).
thf(24401,plain,
( ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[24331]) ).
thf(22100,plain,
( ( ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ inv @ inv )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,11100]) ).
thf(22101,plain,
( ( ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22100]) ).
thf(22327,plain,
( ( ( '$ki_local_world' @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e2 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22101]) ).
thf(22420,plain,
( ( ( '$ki_local_world' @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e2 @ inv @ inv )
!= e1 ) ),
inference(simp,[status(thm)],[22327]) ).
thf(2168,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2044,664]) ).
thf(2169,plain,
( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2168]) ).
thf(2172,plain,
( ( e1 != e1 )
| ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[2169]) ).
thf(2190,plain,
( ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[2172]) ).
thf(15278,plain,
( ( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15046,743]) ).
thf(15279,plain,
( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15278]) ).
thf(15334,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ( e0 != e0 )
| ( ( sk1 @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15279]) ).
thf(15360,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ( ( sk1 @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15334]) ).
thf(23233,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15053,22170]) ).
thf(23234,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23233]) ).
thf(23291,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( e0 != e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[23234]) ).
thf(23400,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[23291]) ).
thf(30,plain,
! [A: '$ki_world'] :
( sk4
| ( e2 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(116,plain,
! [A: '$ki_world'] :
( sk4
| ( e2 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 ),
inference(simp,[status(thm)],[30]) ).
thf(9528,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ inv @ inv @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,160]) ).
thf(9529,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ inv @ inv @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[9528]) ).
thf(9530,plain,
e1 @ ( e1 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[9529:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(23183,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9530,22170]) ).
thf(23184,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23183]) ).
thf(23300,plain,
( ( e1 != e1 )
| ( ( e1 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23184]) ).
thf(23368,plain,
( ( ( e1 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23300]) ).
thf(56,plain,
! [A: '$ki_world'] :
( sk3
| ( e1 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(75,plain,
! [A: '$ki_world'] :
( sk3
| ( e1 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 ),
inference(simp,[status(thm)],[56]) ).
thf(847,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk3
| ( e1 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true
| ~ sk2 ),
inference(paramod_ordered,[status(thm)],[542,75]) ).
thf(848,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk3
| ( e1 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) )
| ~ sk2 ),
inference(simp,[status(thm)],[847]) ).
thf(849,plain,
( sk3
| ( e1 @ ( e3 @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) )
| ~ sk2 ),
inference(pattern_uni,[status(thm)],[848:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(69,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk13 )
| ( A @ sk14 @ ( A @ '$ki_accessible' ) )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(74,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk13 )
| ( A @ sk14 @ ( A @ '$ki_accessible' ) )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(2545,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[137,664]) ).
thf(2546,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2545]) ).
thf(2553,plain,
! [A: '$ki_world'] :
( ( e1 != e1 )
| ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( A
!= ( sk1 @ sk94 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2546]) ).
thf(2586,plain,
( ( ( unit @ ( e1 @ op ) )
!= e0 )
| ~ ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2553]) ).
thf(6398,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[142,903]) ).
thf(6399,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6398]) ).
thf(6420,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( A
!= ( '$ki_local_world' @ sk97 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6399]) ).
thf(6451,plain,
( ( ( e2 @ ( unit @ op ) )
!= e1 )
| ~ ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6420]) ).
thf(18005,plain,
( ( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17789,1142]) ).
thf(18006,plain,
( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[18005]) ).
thf(18088,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ( e1 != e1 )
| ( ( '$ki_local_world' @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[18006]) ).
thf(18123,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ( ( '$ki_local_world' @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[18088]) ).
thf(3037,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2909,771]) ).
thf(3038,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3037]) ).
thf(3053,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3038]) ).
thf(3068,plain,
( ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3053]) ).
thf(1359,plain,
( ( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1215,963]) ).
thf(1360,plain,
( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1359]) ).
thf(1377,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( sk1 @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[1360]) ).
thf(25,plain,
! [A: '$ki_world'] :
( ~ ( e2 @ ( e3 @ ( e3 @ op ) @ ( A @ sk22 @ qmltpeq ) ) )
| ( A @ sk21 @ ( A @ '$ki_accessible' ) )
| ( A @ sk19 )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(89,plain,
! [A: '$ki_world'] :
( ~ ( e2 @ ( e3 @ ( e3 @ op ) @ ( A @ sk22 @ qmltpeq ) ) )
| ( A @ sk21 @ ( A @ '$ki_accessible' ) )
| ( A @ sk19 )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(50,plain,
! [A: '$ki_world'] :
( sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(107,plain,
! [A: '$ki_world'] :
( sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(21198,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk22 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk21 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk19 )
| ( sk1 @ sk17 ) ),
inference(paramod_ordered,[status(thm)],[10658,107]) ).
thf(21199,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk22 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk21 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk19 )
| ( sk1 @ sk17 ) ),
inference(simp,[status(thm)],[21198]) ).
thf(21200,plain,
( sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( sk1 @ sk22 @ qmltpeq ) ) )
| ( sk1 @ sk21 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk19 )
| ( sk1 @ sk17 ) ),
inference(pattern_uni,[status(thm)],[21199:[bind(A,$thf( sk1 @ sk22 ))]]) ).
thf(5113,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4961,954]) ).
thf(5114,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5113]) ).
thf(5143,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5114]) ).
thf(5157,plain,
( ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5143]) ).
thf(51,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk11 )
| ( A @ sk12 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(117,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk11 )
| ( A @ sk12 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(6342,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ ( unit @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,142]) ).
thf(6343,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ ( unit @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[6342]) ).
thf(6344,plain,
e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[6343:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(6502,plain,
( ( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6344,912]) ).
thf(6503,plain,
( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[6502]) ).
thf(6546,plain,
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( sk1 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[6503]) ).
thf(6560,plain,
( ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( sk1 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[6546]) ).
thf(35,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk23 )
| ~ ( e3 @ ( e0 @ ( e0 @ op ) @ ( A @ sk24 @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(85,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk23 )
| ~ ( e3 @ ( e0 @ ( e0 @ op ) @ ( A @ sk24 @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(4981,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[141,1155]) ).
thf(4982,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[4981]) ).
thf(5039,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e1 )
| ( A
!= ( sk1 @ sk98 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[4982]) ).
thf(5067,plain,
( ( ( e3 @ ( unit @ op ) )
!= e1 )
| ~ ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5039]) ).
thf(22202,plain,
( ( ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,5067]) ).
thf(22203,plain,
( ( ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22202]) ).
thf(22404,plain,
( ( ( sk1 @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22203]) ).
thf(22496,plain,
( ( ( sk1 @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22404]) ).
thf(71,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk5 )
| ~ ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ sk6 @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(102,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk5 )
| ~ ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ sk6 @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[71]) ).
thf(4059,plain,
( ( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3935,912]) ).
thf(4060,plain,
( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[4059]) ).
thf(4087,plain,
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( sk1 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[4060]) ).
thf(4100,plain,
( ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( sk1 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[4087]) ).
thf(22613,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e1 @ ( e0 @ ( A @ sk94 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,554]) ).
thf(22614,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e1 @ ( e0 @ ( A @ sk94 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22613]) ).
thf(22774,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 )
!= A )
| ( sk1 != '$ki_local_world' )
| ~ ( e1 @ ( e0 @ ( A @ sk94 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22614]) ).
thf(22874,plain,
( ( sk1 != '$ki_local_world' )
| ~ ( e1 @ ( e0 @ ( sk1 @ sk34 @ sk94 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22774]) ).
thf(2502,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,137]) ).
thf(2503,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2502]) ).
thf(2504,plain,
e1 @ ( unit @ ( e1 @ op ) @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[2503:[bind(A,$thf( sk1 ))]]) ).
thf(2682,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2504,667]) ).
thf(2683,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2682]) ).
thf(2695,plain,
( ( e1 != e1 )
| ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[2683]) ).
thf(2705,plain,
( ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[2695]) ).
thf(22763,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( A @ sk34 @ ( A @ '$ki_accessible' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,232]) ).
thf(22764,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( A @ sk34 @ ( A @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[22763]) ).
thf(22829,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 )
!= A )
| ( sk1 != '$ki_local_world' )
| ( A @ sk34 @ ( A @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[22764]) ).
thf(22867,plain,
( ( sk1 != '$ki_local_world' )
| ( sk1 @ sk34 @ sk34 @ ( sk1 @ sk34 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[22829]) ).
thf(18131,plain,
( ( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17796,1142]) ).
thf(18132,plain,
( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[18131]) ).
thf(18233,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ( e1 != e1 )
| ( ( '$ki_local_world' @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[18132]) ).
thf(18251,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ( ( '$ki_local_world' @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[18233]) ).
thf(1074,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e3 @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true
| sk3
| ~ sk2 ),
inference(paramod_ordered,[status(thm)],[849,667]) ).
thf(1075,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e3 @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| sk3
| ~ sk2 ),
inference(simp,[status(thm)],[1074]) ).
thf(1079,plain,
( ( e1 != e1 )
| ( ( e3 @ ( e3 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= sk1 )
| ~ sk2
| sk3 ),
inference(simp,[status(thm)],[1075]) ).
thf(1091,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= sk1 )
| ~ sk2
| sk3 ),
inference(simp,[status(thm)],[1079]) ).
thf(7708,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ sk16 @ ( B @ '$ki_accessible' ) )
| ( B @ sk15 @ ( B @ '$ki_accessible' ) )
| ( B @ sk13 )
| ( B @ sk11 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,93]) ).
thf(7709,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ sk16 @ ( B @ '$ki_accessible' ) )
| ( B @ sk15 @ ( B @ '$ki_accessible' ) )
| ( B @ sk13 )
| ( B @ sk11 ) ),
inference(simp,[status(thm)],[7708]) ).
thf(7710,plain,
( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[7709:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(21236,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(paramod_ordered,[status(thm)],[7710,107]) ).
thf(21237,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(simp,[status(thm)],[21236]) ).
thf(21238,plain,
( sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( sk1 @ sk16 @ qmltpeq ) ) )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[21237:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(2086,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[136,664]) ).
thf(2087,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2086]) ).
thf(2110,plain,
! [A: '$ki_world'] :
( ( e1 != e1 )
| ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( A
!= ( sk1 @ sk94 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2087]) ).
thf(2133,plain,
( ( ( e1 @ ( unit @ op ) )
!= e0 )
| ~ ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2110]) ).
thf(3033,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2909,954]) ).
thf(3034,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3033]) ).
thf(3054,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3034]) ).
thf(3069,plain,
( ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3054]) ).
thf(22189,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e2 @ ( A @ sk99 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,558]) ).
thf(22190,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e2 @ ( A @ sk99 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22189]) ).
thf(22191,plain,
~ ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[22190:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(23961,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4966,22191]) ).
thf(23962,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23961]) ).
thf(24112,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[23962]) ).
thf(24157,plain,
( ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[24112]) ).
thf(3105,plain,
( ( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2914,963]) ).
thf(3106,plain,
( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3105]) ).
thf(3117,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( ( sk1 @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[3106]) ).
thf(3134,plain,
( ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( ( sk1 @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[3117]) ).
thf(37202,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk5 )
| ( B @ sk6 @ ( B @ '$ki_accessible' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,120]) ).
thf(37203,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk5 )
| ( B @ sk6 @ ( B @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[37202]) ).
thf(37204,plain,
( ~ ( sk1 @ sk5 )
| ( sk1 @ sk6 @ ( sk1 @ '$ki_accessible' ) ) ),
inference(pattern_uni,[status(thm)],[37203:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1333,plain,
( ( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1215,740]) ).
thf(1334,plain,
( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1333]) ).
thf(1365,plain,
( ( e2 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[1334]) ).
thf(18,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(625,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8533,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ $true
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(paramod_ordered,[status(thm)],[7710,88]) ).
thf(8534,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(simp,[status(thm)],[8533]) ).
thf(8535,plain,
( ( sk1 @ sk16 @ sk10 @ ( sk1 @ sk16 @ '$ki_accessible' ) )
| ( sk1 @ sk16 @ sk9 @ ( sk1 @ sk16 @ '$ki_accessible' ) )
| ( sk1 @ sk16 @ sk7 )
| ( sk1 @ sk16 @ sk5 )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[8534:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(1211,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[652,1142]) ).
thf(1212,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1211]) ).
thf(1270,plain,
! [A: '$ki_world'] :
( ( e3 != unit )
| ( ( unit @ inv )
!= e1 )
| ( A
!= ( '$ki_local_world' @ sk98 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1212]) ).
thf(1291,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e1 )
| ~ ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1270]) ).
thf(13015,plain,
( ( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12673,963]) ).
thf(13016,plain,
( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[13015]) ).
thf(13036,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[13016]) ).
thf(13063,plain,
( ( ( e3 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[13036]) ).
thf(70,plain,
! [A: '$ki_world'] :
( ~ ( e0 @ ( e3 @ ( e3 @ op ) @ ( A @ sk10 @ qmltpeq ) ) )
| ~ ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ sk9 @ qmltpeq ) ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(92,plain,
! [A: '$ki_world'] :
( ~ ( e0 @ ( e3 @ ( e3 @ op ) @ ( A @ sk10 @ qmltpeq ) ) )
| ~ ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ sk9 @ qmltpeq ) ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(1413,plain,
( ( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,963]) ).
thf(1414,plain,
( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1413]) ).
thf(1423,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( sk1 @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[1414]) ).
thf(3099,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2914,954]) ).
thf(3100,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3099]) ).
thf(3123,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[3100]) ).
thf(3137,plain,
( ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[3123]) ).
thf(22087,plain,
( ( ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,2985]) ).
thf(22088,plain,
( ( ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22087]) ).
thf(22378,plain,
( ( ( '$ki_local_world' @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22088]) ).
thf(22471,plain,
( ( ( '$ki_local_world' @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22378]) ).
thf(32,plain,
! [A: '$ki_world'] :
( ~ ( e2 @ ( e3 @ ( e3 @ op ) @ ( A @ sk22 @ qmltpeq ) ) )
| ~ ( e2 @ ( e2 @ ( e2 @ op ) @ ( A @ sk21 @ qmltpeq ) ) )
| ( A @ sk19 )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(97,plain,
! [A: '$ki_world'] :
( ~ ( e2 @ ( e3 @ ( e3 @ op ) @ ( A @ sk22 @ qmltpeq ) ) )
| ~ ( e2 @ ( e2 @ ( e2 @ op ) @ ( A @ sk21 @ qmltpeq ) ) )
| ( A @ sk19 )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(6500,plain,
( ( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6344,743]) ).
thf(6501,plain,
( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[6500]) ).
thf(6536,plain,
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[6501]) ).
thf(6556,plain,
( ( ( e2 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[6536]) ).
thf(22106,plain,
( ( ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,5077]) ).
thf(22107,plain,
( ( ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22106]) ).
thf(22411,plain,
( ( ( '$ki_local_world' @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22107]) ).
thf(22503,plain,
( ( ( '$ki_local_world' @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22411]) ).
thf(15134,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[409,667]) ).
thf(15135,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15134]) ).
thf(15164,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( e0 != e0 )
| ( A
!= ( '$ki_local_world' @ sk94 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15135]) ).
thf(15211,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ~ ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15164]) ).
thf(1803,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[793,33]) ).
thf(1804,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1803]) ).
thf(1837,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= sk1 )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1804]) ).
thf(1856,plain,
( ( ( sk1 @ sk10 )
!= sk1 )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk10 @ sk10 @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1837]) ).
thf(23905,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12666,22191]) ).
thf(23906,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23905]) ).
thf(24088,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23906]) ).
thf(24145,plain,
( ( ( e3 @ inv @ inv )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[24088]) ).
thf(1387,plain,
( ( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,740]) ).
thf(1388,plain,
( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1387]) ).
thf(1425,plain,
( ( e2 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[1388]) ).
thf(9535,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,160]) ).
thf(9536,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ inv @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[9535]) ).
thf(9537,plain,
e1 @ ( e1 @ inv @ inv @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[9536:[bind(A,$thf( sk1 ))]]) ).
thf(9897,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9537,664]) ).
thf(9898,plain,
( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[9897]) ).
thf(9931,plain,
( ( e1 != e1 )
| ( ( e1 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[9898]) ).
thf(9936,plain,
( ( ( e1 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[9931]) ).
thf(2225,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2049,664]) ).
thf(2226,plain,
( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2225]) ).
thf(2244,plain,
( ( e1 != e1 )
| ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[2226]) ).
thf(2245,plain,
( ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[2244]) ).
thf(12858,plain,
( ( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12666,774]) ).
thf(12859,plain,
( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[12858]) ).
thf(12924,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e2 )
| ( ( sk1 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12859]) ).
thf(12959,plain,
( ( ( e3 @ inv @ inv )
!= e2 )
| ( ( sk1 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12924]) ).
thf(2082,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[136,667]) ).
thf(2083,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2082]) ).
thf(2102,plain,
! [A: '$ki_world'] :
( ( e1 != e1 )
| ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk94 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2083]) ).
thf(2125,plain,
( ( ( e1 @ ( unit @ op ) )
!= e0 )
| ~ ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2102]) ).
thf(22177,plain,
( ( ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ ( unit @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,2125]) ).
thf(22178,plain,
( ( ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22177]) ).
thf(22335,plain,
( ( ( '$ki_local_world' @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e1 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22178]) ).
thf(22428,plain,
( ( ( '$ki_local_world' @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e1 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22335]) ).
thf(3959,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[140,743]) ).
thf(3960,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[3959]) ).
thf(4014,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e0 )
| ( A
!= ( sk1 @ sk95 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[3960]) ).
thf(4039,plain,
( ( ( unit @ ( e2 @ op ) )
!= e0 )
| ~ ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[4014]) ).
thf(22282,plain,
( ( ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e2 @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,4039]) ).
thf(22283,plain,
( ( ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e2 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22282]) ).
thf(22380,plain,
( ( ( sk1 @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e2 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22283]) ).
thf(22473,plain,
( ( ( sk1 @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e2 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22380]) ).
thf(15399,plain,
( ( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15053,743]) ).
thf(15400,plain,
( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15399]) ).
thf(15468,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ( e0 != e0 )
| ( ( sk1 @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[15400]) ).
thf(15481,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ( ( sk1 @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[15468]) ).
thf(1353,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1215,954]) ).
thf(1354,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1353]) ).
thf(1375,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[1354]) ).
thf(4,axiom,
! [A: '$ki_world',B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
thf(123,plain,
! [A: '$ki_world',B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(124,plain,
! [B: $i,A: '$ki_world'] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(cnf,[status(esa)],[123]) ).
thf(8553,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(paramod_ordered,[status(thm)],[7710,78]) ).
thf(8554,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(simp,[status(thm)],[8553]) ).
thf(8555,plain,
( sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( sk1 @ sk16 @ qmltpeq ) ) )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[8554:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(31,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(109,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 ),
inference(simp,[status(thm)],[31]) ).
thf(5013,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[141,771]) ).
thf(5014,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5013]) ).
thf(5052,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( A
!= ( '$ki_local_world' @ sk99 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5014]) ).
thf(5080,plain,
( ( ( e3 @ ( unit @ op ) )
!= e2 )
| ~ ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5052]) ).
thf(61,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk23 )
| ( A @ sk24 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(77,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk23 )
| ( A @ sk24 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(1381,plain,
( ( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,1142]) ).
thf(1382,plain,
( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1381]) ).
thf(1424,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[1382]) ).
thf(15617,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk5 )
| ~ ( e0 @ ( e0 @ ( e0 @ op ) @ ( B @ sk6 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,102]) ).
thf(15618,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk5 )
| ~ ( e0 @ ( e0 @ ( e0 @ op ) @ ( B @ sk6 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15617]) ).
thf(15619,plain,
( ~ ( sk1 @ sk5 )
| ~ ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk6 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[15618:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1610,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,133]) ).
thf(1611,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1610]) ).
thf(1612,plain,
e0 @ ( e0 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[1611:[bind(A,$thf( sk1 ))]]) ).
thf(2625,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2499,667]) ).
thf(2626,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2625]) ).
thf(2640,plain,
( ( e1 != e1 )
| ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[2626]) ).
thf(2649,plain,
( ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[2640]) ).
thf(22194,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,161]) ).
thf(22195,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ inv @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22194]) ).
thf(22196,plain,
e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22195:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(4382,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk23 )
| ~ ( e3 @ ( e0 @ ( e0 @ op ) @ ( B @ sk24 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,85]) ).
thf(4383,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk23 )
| ~ ( e3 @ ( e0 @ ( e0 @ op ) @ ( B @ sk24 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[4382]) ).
thf(4384,plain,
( ~ ( sk1 @ sk23 )
| ~ ( e3 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk24 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[4383:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(687,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,33]) ).
thf(688,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[687]) ).
thf(689,plain,
( sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[688:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(42,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk17 )
| ~ ( e2 @ ( e0 @ ( e0 @ op ) @ ( A @ sk18 @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(87,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk17 )
| ~ ( e2 @ ( e0 @ ( e0 @ op ) @ ( A @ sk18 @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(5310,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk17 )
| ~ ( e2 @ ( e0 @ ( e0 @ op ) @ ( B @ sk18 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,87]) ).
thf(5311,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk17 )
| ~ ( e2 @ ( e0 @ ( e0 @ op ) @ ( B @ sk18 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5310]) ).
thf(5312,plain,
( ~ ( sk1 @ sk17 )
| ~ ( e2 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk18 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[5311:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(6239,plain,
( ( ( e2 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk18 @ qmltpeq ) ) )
!= ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ ( sk1 @ sk17 )
| ~ $true
| sk2 ),
inference(paramod_ordered,[status(thm)],[689,5312]) ).
thf(6240,plain,
( ( ( e2 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk18 @ qmltpeq ) ) )
!= ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ ( sk1 @ sk17 )
| sk2 ),
inference(simp,[status(thm)],[6239]) ).
thf(6304,plain,
( ( e2 != e0 )
| ( ( e0 @ ( e0 @ op ) )
!= ( e0 @ ( e0 @ op ) ) )
| ( ( sk1 @ sk18 )
!= sk1 )
| ~ ( sk1 @ sk17 )
| sk2 ),
inference(simp,[status(thm)],[6240]) ).
thf(6331,plain,
( ( e2 != e0 )
| ( ( sk1 @ sk18 )
!= sk1 )
| ~ ( sk1 @ sk17 )
| sk2 ),
inference(simp,[status(thm)],[6304]) ).
thf(15096,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[409,743]) ).
thf(15097,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15096]) ).
thf(15153,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ( e0 != e0 )
| ( A
!= ( sk1 @ sk95 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15097]) ).
thf(15200,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ~ ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15153]) ).
thf(6378,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[142,743]) ).
thf(6379,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6378]) ).
thf(6430,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e0 )
| ( A
!= ( sk1 @ sk95 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6379]) ).
thf(6461,plain,
( ( ( e2 @ ( unit @ op ) )
!= e0 )
| ~ ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[6430]) ).
thf(22208,plain,
( ( ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ ( unit @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,6461]) ).
thf(22209,plain,
( ( ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22208]) ).
thf(22348,plain,
( ( ( sk1 @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e2 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22209]) ).
thf(22441,plain,
( ( ( sk1 @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e2 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22348]) ).
thf(3013,plain,
( ( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2909,774]) ).
thf(3014,plain,
( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3013]) ).
thf(3047,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( sk1 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3014]) ).
thf(3064,plain,
( ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( sk1 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3047]) ).
thf(7824,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk16 @ ( A @ '$ki_accessible' ) )
| ( A @ sk15 @ ( A @ '$ki_accessible' ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ~ $true
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[673,93]) ).
thf(7825,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk16 @ ( A @ '$ki_accessible' ) )
| ( A @ sk15 @ ( A @ '$ki_accessible' ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[7824]) ).
thf(7826,plain,
( ( sk1 @ sk10 @ sk16 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk15 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk13 )
| ( sk1 @ sk10 @ sk11 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[7825:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(22248,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,409]) ).
thf(22249,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22248]) ).
thf(22250,plain,
e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22249:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(6347,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,142]) ).
thf(6348,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[6347]) ).
thf(6349,plain,
e2 @ ( e2 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[6348:[bind(A,$thf( sk1 ))]]) ).
thf(7977,plain,
( ( ( e1 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk12 @ qmltpeq ) ) )
!= ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ ( sk1 @ sk11 )
| ~ $true
| sk2 ),
inference(paramod_ordered,[status(thm)],[689,6657]) ).
thf(7978,plain,
( ( ( e1 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk12 @ qmltpeq ) ) )
!= ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ ( sk1 @ sk11 )
| sk2 ),
inference(simp,[status(thm)],[7977]) ).
thf(8028,plain,
( ( e1 != e0 )
| ( ( e0 @ ( e0 @ op ) )
!= ( e0 @ ( e0 @ op ) ) )
| ( ( sk1 @ sk12 )
!= sk1 )
| ~ ( sk1 @ sk11 )
| sk2 ),
inference(simp,[status(thm)],[7978]) ).
thf(8072,plain,
( ( e1 != e0 )
| ( ( sk1 @ sk12 )
!= sk1 )
| ~ ( sk1 @ sk11 )
| sk2 ),
inference(simp,[status(thm)],[8028]) ).
thf(1237,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[652,1155]) ).
thf(1238,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1237]) ).
thf(1276,plain,
! [A: '$ki_world'] :
( ( e3 != unit )
| ( ( unit @ inv )
!= e1 )
| ( A
!= ( sk1 @ sk98 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1238]) ).
thf(1297,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e1 )
| ~ ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1276]) ).
thf(2951,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[139,963]) ).
thf(2952,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2951]) ).
thf(2979,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( A
!= ( sk1 @ sk96 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2952]) ).
thf(3003,plain,
( ( ( unit @ ( e3 @ op ) )
!= e0 )
| ~ ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2979]) ).
thf(22274,plain,
( ( ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,3003]) ).
thf(22275,plain,
( ( ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22274]) ).
thf(22339,plain,
( ( ( sk1 @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e3 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22275]) ).
thf(22432,plain,
( ( ( sk1 @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e3 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22339]) ).
thf(5083,plain,
( ( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4961,1142]) ).
thf(5084,plain,
( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5083]) ).
thf(5127,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5084]) ).
thf(5149,plain,
( ( ( e3 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5127]) ).
thf(22976,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17796,22099]) ).
thf(22977,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22976]) ).
thf(23077,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( e1 != e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[22977]) ).
thf(23118,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[23077]) ).
thf(22930,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6349,22099]) ).
thf(22931,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22930]) ).
thf(23052,plain,
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[22931]) ).
thf(23107,plain,
( ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[23052]) ).
thf(15306,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15046,664]) ).
thf(15307,plain,
( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15306]) ).
thf(15319,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( e0 != e0 )
| ( ( sk1 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15307]) ).
thf(15354,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( ( sk1 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15319]) ).
thf(12736,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[162,954]) ).
thf(12737,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12736]) ).
thf(12788,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk96 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12737]) ).
thf(12838,plain,
( ( ( e3 @ inv @ inv )
!= e0 )
| ~ ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[12788]) ).
thf(23151,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2049,22170]) ).
thf(23152,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23151]) ).
thf(23361,plain,
( ( e1 != e1 )
| ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[23152]) ).
thf(23397,plain,
( ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[23361]) ).
thf(1809,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ $true
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[793,88]) ).
thf(1810,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1809]) ).
thf(1838,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= sk1 )
| ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1810]) ).
thf(1857,plain,
( ( ( sk1 @ sk10 )
!= sk1 )
| ( sk1 @ sk10 @ sk10 @ sk10 @ ( sk1 @ sk10 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk10 @ sk9 @ ( sk1 @ sk10 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk10 @ sk5 )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1838]) ).
thf(48,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk13 )
| ~ ( e1 @ ( e1 @ ( e1 @ op ) @ ( A @ sk14 @ qmltpeq ) ) )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(105,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk13 )
| ~ ( e1 @ ( e1 @ ( e1 @ op ) @ ( A @ sk14 @ qmltpeq ) ) )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(11132,plain,
( ( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10934,743]) ).
thf(11133,plain,
( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[11132]) ).
thf(11169,plain,
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[11133]) ).
thf(11197,plain,
( ( ( e2 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[11169]) ).
thf(22,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ op ) @ ( B @ ( F @ op ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_substitution_2) ).
thf(657,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ op ) @ ( B @ ( F @ op ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24005,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4961,22191]) ).
thf(24006,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[24005]) ).
thf(24083,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[24006]) ).
thf(24142,plain,
( ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[24083]) ).
thf(22592,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,33]) ).
thf(22593,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22592]) ).
thf(22594,plain,
( sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk34 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[22593:[bind(A,$thf( sk1 @ sk34 ))]]) ).
thf(2166,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2044,667]) ).
thf(2167,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2166]) ).
thf(2186,plain,
( ( e1 != e1 )
| ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[2167]) ).
thf(2189,plain,
( ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[2186]) ).
thf(11248,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10941,903]) ).
thf(11249,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[11248]) ).
thf(11266,plain,
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[11249]) ).
thf(11296,plain,
( ( ( e2 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[11266]) ).
thf(15142,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[409,740]) ).
thf(15143,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15142]) ).
thf(15149,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ( e0 != e0 )
| ( A
!= ( '$ki_local_world' @ sk95 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15143]) ).
thf(15196,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ~ ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15149]) ).
thf(22255,plain,
( ( ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,15196]) ).
thf(22256,plain,
( ( ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22255]) ).
thf(22389,plain,
( ( ( '$ki_local_world' @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22256]) ).
thf(22482,plain,
( ( ( '$ki_local_world' @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22389]) ).
thf(13007,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12673,954]) ).
thf(13008,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[13007]) ).
thf(13055,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[13008]) ).
thf(13071,plain,
( ( ( e3 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[13055]) ).
thf(13,axiom,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e3 @ op ) @ ( e3 @ ( e3 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e3 @ op ) @ ( e2 @ ( e3 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e3 @ op ) @ ( e1 @ ( e3 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e3 @ op ) @ ( e0 @ ( e3 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e3 @ op ) @ ( e3 @ ( e2 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e3 @ op ) @ ( e2 @ ( e2 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e3 @ op ) @ ( e1 @ ( e2 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e3 @ op ) @ ( e0 @ ( e2 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e3 @ op ) @ ( e3 @ ( e1 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e3 @ op ) @ ( e2 @ ( e1 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e3 @ op ) @ ( e1 @ ( e1 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ op ) @ ( e3 @ op ) @ ( e0 @ ( e1 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e3 @ op ) @ ( e3 @ ( e0 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e3 @ op ) @ ( e2 @ ( e0 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ op ) @ ( e3 @ op ) @ ( e1 @ ( e0 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ op ) @ ( e3 @ op ) @ ( e0 @ ( e0 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e2 @ op ) @ ( e3 @ ( e3 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e2 @ op ) @ ( e2 @ ( e3 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e2 @ op ) @ ( e1 @ ( e3 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e2 @ op ) @ ( e0 @ ( e3 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e2 @ op ) @ ( e3 @ ( e2 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e2 @ op ) @ ( e2 @ ( e2 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e2 @ op ) @ ( e1 @ ( e2 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e2 @ op ) @ ( e0 @ ( e2 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e2 @ op ) @ ( e3 @ ( e1 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e2 @ op ) @ ( e2 @ ( e1 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e2 @ op ) @ ( e1 @ ( e1 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ op ) @ ( e2 @ op ) @ ( e0 @ ( e1 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e2 @ op ) @ ( e3 @ ( e0 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e2 @ op ) @ ( e2 @ ( e0 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ op ) @ ( e2 @ op ) @ ( e1 @ ( e0 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ op ) @ ( e2 @ op ) @ ( e0 @ ( e0 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e1 @ op ) @ ( e3 @ ( e3 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e1 @ op ) @ ( e2 @ ( e3 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e1 @ op ) @ ( e1 @ ( e3 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e1 @ op ) @ ( e0 @ ( e3 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e1 @ op ) @ ( e3 @ ( e2 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e1 @ op ) @ ( e2 @ ( e2 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e1 @ op ) @ ( e1 @ ( e2 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e1 @ op ) @ ( e0 @ ( e2 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e1 @ op ) @ ( e3 @ ( e1 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e1 @ op ) @ ( e2 @ ( e1 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e1 @ op ) @ ( e1 @ ( e1 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ op ) @ ( e1 @ op ) @ ( e0 @ ( e1 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e1 @ op ) @ ( e3 @ ( e0 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e1 @ op ) @ ( e2 @ ( e0 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ op ) @ ( e1 @ op ) @ ( e1 @ ( e0 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ op ) @ ( e1 @ op ) @ ( e0 @ ( e0 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e0 @ op ) @ ( e3 @ ( e3 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e0 @ op ) @ ( e2 @ ( e3 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e0 @ op ) @ ( e1 @ ( e3 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e0 @ op ) @ ( e0 @ ( e3 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e0 @ op ) @ ( e3 @ ( e2 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e0 @ op ) @ ( e2 @ ( e2 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e0 @ op ) @ ( e1 @ ( e2 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e0 @ op ) @ ( e0 @ ( e2 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e0 @ op ) @ ( e3 @ ( e1 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e0 @ op ) @ ( e2 @ ( e1 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e0 @ op ) @ ( e1 @ ( e1 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ op ) @ ( e0 @ op ) @ ( e0 @ ( e1 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e0 @ op ) @ ( e3 @ ( e0 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e0 @ op ) @ ( e2 @ ( e0 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ op ) @ ( e0 @ op ) @ ( e1 @ ( e0 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ op ) @ ( e0 @ op ) @ ( e0 @ ( e0 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(412,plain,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e3 @ op ) @ ( e3 @ ( e3 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e3 @ op ) @ ( e2 @ ( e3 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e3 @ op ) @ ( e1 @ ( e3 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e3 @ op ) @ ( e0 @ ( e3 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e3 @ op ) @ ( e3 @ ( e2 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e3 @ op ) @ ( e2 @ ( e2 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e3 @ op ) @ ( e1 @ ( e2 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e3 @ op ) @ ( e0 @ ( e2 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e3 @ op ) @ ( e3 @ ( e1 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e3 @ op ) @ ( e2 @ ( e1 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e3 @ op ) @ ( e1 @ ( e1 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ op ) @ ( e3 @ op ) @ ( e0 @ ( e1 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e3 @ op ) @ ( e3 @ ( e0 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e3 @ op ) @ ( e2 @ ( e0 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ op ) @ ( e3 @ op ) @ ( e1 @ ( e0 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ op ) @ ( e3 @ op ) @ ( e0 @ ( e0 @ ( e3 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e2 @ op ) @ ( e3 @ ( e3 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e2 @ op ) @ ( e2 @ ( e3 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e2 @ op ) @ ( e1 @ ( e3 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e2 @ op ) @ ( e0 @ ( e3 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e2 @ op ) @ ( e3 @ ( e2 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e2 @ op ) @ ( e2 @ ( e2 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e2 @ op ) @ ( e1 @ ( e2 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e2 @ op ) @ ( e0 @ ( e2 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e2 @ op ) @ ( e3 @ ( e1 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e2 @ op ) @ ( e2 @ ( e1 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e2 @ op ) @ ( e1 @ ( e1 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ op ) @ ( e2 @ op ) @ ( e0 @ ( e1 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e2 @ op ) @ ( e3 @ ( e0 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e2 @ op ) @ ( e2 @ ( e0 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ op ) @ ( e2 @ op ) @ ( e1 @ ( e0 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ op ) @ ( e2 @ op ) @ ( e0 @ ( e0 @ ( e2 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e1 @ op ) @ ( e3 @ ( e3 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e1 @ op ) @ ( e2 @ ( e3 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e1 @ op ) @ ( e1 @ ( e3 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e1 @ op ) @ ( e0 @ ( e3 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e1 @ op ) @ ( e3 @ ( e2 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e1 @ op ) @ ( e2 @ ( e2 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e1 @ op ) @ ( e1 @ ( e2 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e1 @ op ) @ ( e0 @ ( e2 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e1 @ op ) @ ( e3 @ ( e1 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e1 @ op ) @ ( e2 @ ( e1 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e1 @ op ) @ ( e1 @ ( e1 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ op ) @ ( e1 @ op ) @ ( e0 @ ( e1 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e1 @ op ) @ ( e3 @ ( e0 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e1 @ op ) @ ( e2 @ ( e0 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ op ) @ ( e1 @ op ) @ ( e1 @ ( e0 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ op ) @ ( e1 @ op ) @ ( e0 @ ( e0 @ ( e1 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ op ) @ ( e0 @ op ) @ ( e3 @ ( e3 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ op ) @ ( e0 @ op ) @ ( e2 @ ( e3 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ op ) @ ( e0 @ op ) @ ( e1 @ ( e3 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ op ) @ ( e0 @ op ) @ ( e0 @ ( e3 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ op ) @ ( e0 @ op ) @ ( e3 @ ( e2 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ op ) @ ( e0 @ op ) @ ( e2 @ ( e2 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ op ) @ ( e0 @ op ) @ ( e1 @ ( e2 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ op ) @ ( e0 @ op ) @ ( e0 @ ( e2 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ op ) @ ( e0 @ op ) @ ( e3 @ ( e1 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ op ) @ ( e0 @ op ) @ ( e2 @ ( e1 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ op ) @ ( e0 @ op ) @ ( e1 @ ( e1 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ op ) @ ( e0 @ op ) @ ( e0 @ ( e1 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ op ) @ ( e0 @ op ) @ ( e3 @ ( e0 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ op ) @ ( e0 @ op ) @ ( e2 @ ( e0 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ op ) @ ( e0 @ op ) @ ( e1 @ ( e0 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ op ) @ ( e0 @ op ) @ ( e0 @ ( e0 @ ( e0 @ op ) @ op ) @ ( A @ qmltpeq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6586,plain,
( ( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6349,912]) ).
thf(6587,plain,
( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[6586]) ).
thf(6612,plain,
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( sk1 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[6587]) ).
thf(6637,plain,
( ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( sk1 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[6612]) ).
thf(22642,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e0 @ ( A @ sk96 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,562]) ).
thf(22643,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e0 @ ( A @ sk96 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22642]) ).
thf(22846,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 )
!= A )
| ( sk1 != '$ki_local_world' )
| ~ ( e3 @ ( e0 @ ( A @ sk96 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22643]) ).
thf(22871,plain,
( ( sk1 != '$ki_local_world' )
| ~ ( e3 @ ( e0 @ ( sk1 @ sk34 @ sk96 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22846]) ).
thf(17783,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[411,1142]) ).
thf(17784,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17783]) ).
thf(17926,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ( e1 != e1 )
| ( A
!= ( '$ki_local_world' @ sk98 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17784]) ).
thf(17956,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ~ ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17926]) ).
thf(22284,plain,
( ( ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,17956]) ).
thf(22285,plain,
( ( ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e2 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22284]) ).
thf(22386,plain,
( ( ( '$ki_local_world' @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( e2 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22285]) ).
thf(22479,plain,
( ( ( '$ki_local_world' @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( e2 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22386]) ).
thf(1481,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk23 )
| ( B @ sk24 @ ( B @ '$ki_accessible' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,77]) ).
thf(1482,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk23 )
| ( B @ sk24 @ ( B @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1481]) ).
thf(1483,plain,
( ~ ( sk1 @ sk23 )
| ( sk1 @ sk24 @ ( sk1 @ '$ki_accessible' ) ) ),
inference(pattern_uni,[status(thm)],[1482:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(5167,plain,
( ( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4966,774]) ).
thf(5168,plain,
( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5167]) ).
thf(5203,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( sk1 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[5168]) ).
thf(5230,plain,
( ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( sk1 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[5203]) ).
thf(2489,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[793,137]) ).
thf(2490,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[2489]) ).
thf(2560,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= '$ki_local_world' )
| ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[2490]) ).
thf(2570,plain,
( ( ( sk1 @ sk10 )
!= '$ki_local_world' )
| ( e1 @ ( unit @ ( e1 @ op ) @ ( sk1 @ sk10 @ sk10 @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[2560]) ).
thf(9179,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,156]) ).
thf(9180,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ inv @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[9179]) ).
thf(9181,plain,
e0 @ ( e0 @ inv @ inv @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[9180:[bind(A,$thf( sk1 ))]]) ).
thf(10418,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk28 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk27 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk25 )
| ( sk1 @ sk23 ) ),
inference(paramod_ordered,[status(thm)],[9960,78]) ).
thf(10419,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk28 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk27 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk25 )
| ( sk1 @ sk23 ) ),
inference(simp,[status(thm)],[10418]) ).
thf(10420,plain,
( sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( sk1 @ sk28 @ qmltpeq ) ) )
| ( sk1 @ sk27 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk25 )
| ( sk1 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[10419:[bind(A,$thf( sk1 @ sk28 ))]]) ).
thf(1593,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ ( unit @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,133]) ).
thf(1594,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ ( unit @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1593]) ).
thf(1595,plain,
e0 @ ( e0 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[1594:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(1341,plain,
( ( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1215,1155]) ).
thf(1342,plain,
( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1341]) ).
thf(1374,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e1 )
| ( ( sk1 @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[1342]) ).
thf(6514,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6344,903]) ).
thf(6515,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[6514]) ).
thf(6548,plain,
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[6515]) ).
thf(6561,plain,
( ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[6548]) ).
thf(23193,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2504,22170]) ).
thf(23194,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23193]) ).
thf(23296,plain,
( ( e1 != e1 )
| ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[23194]) ).
thf(23365,plain,
( ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[23296]) ).
thf(12904,plain,
( ( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12666,963]) ).
thf(12905,plain,
( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[12904]) ).
thf(12939,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12905]) ).
thf(12951,plain,
( ( ( e3 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12939]) ).
thf(17853,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[411,912]) ).
thf(17854,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17853]) ).
thf(17931,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( e1 != e1 )
| ( A
!= ( sk1 @ sk97 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17854]) ).
thf(17961,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ~ ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17931]) ).
thf(22297,plain,
( ( ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,17961]) ).
thf(22298,plain,
( ( ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e2 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22297]) ).
thf(22370,plain,
( ( ( sk1 @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( e2 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22298]) ).
thf(22463,plain,
( ( ( sk1 @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( e2 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22370]) ).
thf(2905,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[139,1142]) ).
thf(2906,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2905]) ).
thf(2967,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e1 )
| ( A
!= ( '$ki_local_world' @ sk98 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2906]) ).
thf(2991,plain,
( ( ( unit @ ( e3 @ op ) )
!= e1 )
| ~ ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2967]) ).
thf(47,plain,
! [A: '$ki_world'] :
( ~ ( e0 @ ( e3 @ ( e3 @ op ) @ ( A @ sk10 @ qmltpeq ) ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(118,plain,
! [A: '$ki_world'] :
( ~ ( e0 @ ( e3 @ ( e3 @ op ) @ ( A @ sk10 @ qmltpeq ) ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(1399,plain,
( ( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,743]) ).
thf(1400,plain,
( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1399]) ).
thf(1428,plain,
( ( e2 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( sk1 @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[1400]) ).
thf(1347,plain,
( ( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1215,912]) ).
thf(1348,plain,
( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1371,plain,
( ( e2 != unit )
| ( ( unit @ inv )
!= e1 )
| ( ( sk1 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[1348]) ).
thf(23935,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12673,22191]) ).
thf(23936,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23935]) ).
thf(24072,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[23936]) ).
thf(24136,plain,
( ( ( e3 @ inv @ inv )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[24072]) ).
thf(4069,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3935,903]) ).
thf(4070,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[4069]) ).
thf(4081,plain,
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[4070]) ).
thf(4099,plain,
( ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[4081]) ).
thf(6,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ qmltpeq ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(144,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ qmltpeq ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(58,plain,
! [A: '$ki_world'] :
( sk4
| ( e2 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(86,plain,
! [A: '$ki_world'] :
( sk4
| ( e2 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 ),
inference(simp,[status(thm)],[58]) ).
thf(22085,plain,
( ( ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,15207]) ).
thf(22086,plain,
( ( ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22085]) ).
thf(22329,plain,
( ( ( sk1 @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22086]) ).
thf(22422,plain,
( ( ( sk1 @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22329]) ).
thf(22257,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( unit @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,143]) ).
thf(22258,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( unit @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22257]) ).
thf(22259,plain,
e0 @ ( unit @ ( e0 @ op ) @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22258:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(22158,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,141]) ).
thf(22159,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22158]) ).
thf(22160,plain,
e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22159:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(26,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk19 )
| ~ ( e2 @ ( e1 @ ( e1 @ op ) @ ( A @ sk20 @ qmltpeq ) ) )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(113,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk19 )
| ~ ( e2 @ ( e1 @ ( e1 @ op ) @ ( A @ sk20 @ qmltpeq ) ) )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(41,plain,
! [A: '$ki_world'] :
( sk3
| ( e1 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(81,plain,
! [A: '$ki_world'] :
( sk3
| ( e1 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 ),
inference(simp,[status(thm)],[41]) ).
thf(21203,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk28 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk27 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk25 )
| ( sk1 @ sk23 ) ),
inference(paramod_ordered,[status(thm)],[9960,107]) ).
thf(21204,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk28 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk27 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk25 )
| ( sk1 @ sk23 ) ),
inference(simp,[status(thm)],[21203]) ).
thf(21205,plain,
( sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( sk1 @ sk28 @ qmltpeq ) ) )
| ( sk1 @ sk27 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk25 )
| ( sk1 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[21204:[bind(A,$thf( sk1 @ sk28 ))]]) ).
thf(18173,plain,
( ( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17796,912]) ).
thf(18174,plain,
( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[18173]) ).
thf(18222,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( e1 != e1 )
| ( ( sk1 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[18174]) ).
thf(18250,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( ( sk1 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[18222]) ).
thf(68,plain,
! [A: '$ki_world'] :
( sk2
| ( e0 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(119,plain,
! [A: '$ki_world'] :
( sk2
| ( e0 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(36637,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,119]) ).
thf(36638,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[36637]) ).
thf(36639,plain,
( sk2
| ( e0 @ ( e3 @ ( e3 @ op ) @ ( sk1 @ sk34 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[36638:[bind(A,$thf( sk1 @ sk34 ))]]) ).
thf(3075,plain,
( ( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2914,1142]) ).
thf(3076,plain,
( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3075]) ).
thf(3124,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[3076]) ).
thf(3138,plain,
( ( ( unit @ ( e3 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[3124]) ).
thf(34,plain,
! [A: '$ki_world'] :
( ~ ( e1 @ ( e3 @ ( e3 @ op ) @ ( A @ sk16 @ qmltpeq ) ) )
| ( A @ sk15 @ ( A @ '$ki_accessible' ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(98,plain,
! [A: '$ki_world'] :
( ~ ( e1 @ ( e3 @ ( e3 @ op ) @ ( A @ sk16 @ qmltpeq ) ) )
| ( A @ sk15 @ ( A @ '$ki_accessible' ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(22271,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,139]) ).
thf(22272,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22271]) ).
thf(22273,plain,
e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22272:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(22171,plain,
( ( ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,5080]) ).
thf(22172,plain,
( ( ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22171]) ).
thf(22366,plain,
( ( ( '$ki_local_world' @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( unit @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22172]) ).
thf(22459,plain,
( ( ( '$ki_local_world' @ sk99 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( unit @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22366]) ).
thf(52,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk25 )
| ( A @ sk26 @ ( A @ '$ki_accessible' ) )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(76,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk25 )
| ( A @ sk26 @ ( A @ '$ki_accessible' ) )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(16,axiom,
( ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(567,plain,
( ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22118,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,411]) ).
thf(22119,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22118]) ).
thf(22120,plain,
e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22119:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(1327,plain,
( ( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1215,1142]) ).
thf(1328,plain,
( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1327]) ).
thf(1376,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[1328]) ).
thf(2923,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[139,1155]) ).
thf(2924,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2923]) ).
thf(2970,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e1 )
| ( A
!= ( sk1 @ sk98 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2924]) ).
thf(2994,plain,
( ( ( unit @ ( e3 @ op ) )
!= e1 )
| ~ ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[2970]) ).
thf(22239,plain,
( ( ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,2994]) ).
thf(22240,plain,
( ( ( sk1 @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22239]) ).
thf(22353,plain,
( ( ( sk1 @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22240]) ).
thf(22446,plain,
( ( ( sk1 @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22353]) ).
thf(3927,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[140,740]) ).
thf(3928,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[3927]) ).
thf(4003,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk95 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[3928]) ).
thf(4028,plain,
( ( ( unit @ ( e2 @ op ) )
!= e0 )
| ~ ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[4003]) ).
thf(797,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[673,33]) ).
thf(798,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[797]) ).
thf(799,plain,
( sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk10 @ qmltpeq ) ) )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[798:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(23024,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10934,22099]) ).
thf(23025,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23024]) ).
thf(23092,plain,
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23025]) ).
thf(23125,plain,
( ( ( e2 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23092]) ).
thf(2627,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2499,664]) ).
thf(2628,plain,
( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2627]) ).
thf(2633,plain,
( ( e1 != e1 )
| ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( sk1 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[2628]) ).
thf(2647,plain,
( ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( sk1 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[2633]) ).
thf(67,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk7 )
| ~ ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ sk8 @ qmltpeq ) ) )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(108,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk7 )
| ~ ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ sk8 @ qmltpeq ) ) )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(9172,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ inv @ inv @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,156]) ).
thf(9173,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ inv @ inv @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[9172]) ).
thf(9174,plain,
e0 @ ( e0 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[9173:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(2030,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[793,136]) ).
thf(2031,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[2030]) ).
thf(2088,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= '$ki_local_world' )
| ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[2031]) ).
thf(2111,plain,
( ( ( sk1 @ sk10 )
!= '$ki_local_world' )
| ( e1 @ ( e1 @ ( unit @ op ) @ ( sk1 @ sk10 @ sk10 @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[2088]) ).
thf(3148,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk3
| ( e1 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true
| ~ sk2 ),
inference(paramod_ordered,[status(thm)],[542,81]) ).
thf(3149,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk3
| ( e1 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) )
| ~ sk2 ),
inference(simp,[status(thm)],[3148]) ).
thf(3150,plain,
( sk3
| ( e1 @ ( e2 @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) )
| ~ sk2 ),
inference(pattern_uni,[status(thm)],[3149:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(12985,plain,
( ( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12673,1155]) ).
thf(12986,plain,
( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[12985]) ).
thf(13047,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e1 )
| ( ( sk1 @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[12986]) ).
thf(13069,plain,
( ( ( e3 @ inv @ inv )
!= e1 )
| ( ( sk1 @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[13047]) ).
thf(18031,plain,
( ( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17789,1155]) ).
thf(18032,plain,
( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[18031]) ).
thf(18114,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ( e1 != e1 )
| ( ( sk1 @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[18032]) ).
thf(18121,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e3 )
| ( ( sk1 @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[18114]) ).
thf(15413,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15053,954]) ).
thf(15414,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15413]) ).
thf(15441,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ( e0 != e0 )
| ( ( '$ki_local_world' @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[15414]) ).
thf(15475,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ( ( '$ki_local_world' @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[15441]) ).
thf(15128,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[409,963]) ).
thf(15129,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) @ ( e0 @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15128]) ).
thf(15169,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ( e0 != e0 )
| ( A
!= ( sk1 @ sk96 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15129]) ).
thf(15216,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ~ ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[15169]) ).
thf(3963,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[140,912]) ).
thf(3964,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[3963]) ).
thf(3999,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( A
!= ( sk1 @ sk97 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[3964]) ).
thf(4024,plain,
( ( ( unit @ ( e2 @ op ) )
!= e1 )
| ~ ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[3999]) ).
thf(22303,plain,
( ( ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e2 @ op ) )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,4024]) ).
thf(22304,plain,
( ( ( sk1 @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e2 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22303]) ).
thf(22334,plain,
( ( ( sk1 @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e2 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22304]) ).
thf(22427,plain,
( ( ( sk1 @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e2 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22334]) ).
thf(1361,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1215,667]) ).
thf(1362,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1361]) ).
thf(1364,plain,
( ( e1 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[1362]) ).
thf(9802,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9530,664]) ).
thf(9803,plain,
( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[9802]) ).
thf(9817,plain,
( ( e1 != e1 )
| ( ( e1 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[9803]) ).
thf(9841,plain,
( ( ( e1 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[9817]) ).
thf(24268,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4961,22199]) ).
thf(24269,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[24268]) ).
thf(24320,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[24269]) ).
thf(24397,plain,
( ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[24320]) ).
thf(1100,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk25 )
| ( B @ sk26 @ ( B @ '$ki_accessible' ) )
| ( B @ sk23 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,76]) ).
thf(1101,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk25 )
| ( B @ sk26 @ ( B @ '$ki_accessible' ) )
| ( B @ sk23 ) ),
inference(simp,[status(thm)],[1100]) ).
thf(1102,plain,
( ~ ( sk1 @ sk25 )
| ( sk1 @ sk26 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[1101:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(22082,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,142]) ).
thf(22083,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( e2 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22082]) ).
thf(22084,plain,
e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22083:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(53,plain,
! [A: '$ki_world'] :
( ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ~ ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ sk9 @ qmltpeq ) ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(80,plain,
! [A: '$ki_world'] :
( ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ~ ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ sk9 @ qmltpeq ) ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(21,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ inv @ ( B @ inv @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inv_substitution_1) ).
thf(653,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ inv @ ( B @ inv @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(22952,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17789,22099]) ).
thf(22953,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22952]) ).
thf(23079,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( e1 != e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[22953]) ).
thf(23119,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23079]) ).
thf(22984,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3940,22099]) ).
thf(22985,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22984]) ).
thf(23070,plain,
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[22985]) ).
thf(23113,plain,
( ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[23070]) ).
thf(40,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk19 )
| ( A @ sk20 @ ( A @ '$ki_accessible' ) )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(112,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk19 )
| ( A @ sk20 @ ( A @ '$ki_accessible' ) )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(22204,plain,
( ( ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,2991]) ).
thf(22205,plain,
( ( ( '$ki_local_world' @ sk98 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22204]) ).
thf(22390,plain,
( ( ( '$ki_local_world' @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22205]) ).
thf(22483,plain,
( ( ( '$ki_local_world' @ sk98 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22390]) ).
thf(22290,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,136]) ).
thf(22291,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( e1 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22290]) ).
thf(22292,plain,
e1 @ ( e1 @ ( unit @ op ) @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22291:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(12969,plain,
( ( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12673,774]) ).
thf(12970,plain,
( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[12969]) ).
thf(13040,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e2 )
| ( ( sk1 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[12970]) ).
thf(13065,plain,
( ( ( e3 @ inv @ inv )
!= e2 )
| ( ( sk1 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[13040]) ).
thf(6524,plain,
( ( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6344,740]) ).
thf(6525,plain,
( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[6524]) ).
thf(6540,plain,
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[6525]) ).
thf(6557,plain,
( ( ( e2 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[6540]) ).
thf(6598,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6349,903]) ).
thf(6599,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[6598]) ).
thf(6626,plain,
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[6599]) ).
thf(6641,plain,
( ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[6626]) ).
thf(17873,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[411,903]) ).
thf(17874,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) @ ( e1 @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17873]) ).
thf(17938,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( e1 != e1 )
| ( A
!= ( '$ki_local_world' @ sk97 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17874]) ).
thf(17968,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ~ ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17938]) ).
thf(7,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ op ) @ ( F @ ( B @ op ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_substitution_1) ).
thf(150,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ op ) @ ( F @ ( B @ op ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(34437,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk11 )
| ( B @ sk12 @ ( B @ '$ki_accessible' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,117]) ).
thf(34438,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk11 )
| ( B @ sk12 @ ( B @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[34437]) ).
thf(34439,plain,
( ~ ( sk1 @ sk11 )
| ( sk1 @ sk12 @ ( sk1 @ '$ki_accessible' ) ) ),
inference(pattern_uni,[status(thm)],[34438:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(4871,plain,
( ( ( e3 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk24 @ qmltpeq ) ) )
!= ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ ( sk1 @ sk23 )
| ~ $true
| sk2 ),
inference(paramod_ordered,[status(thm)],[689,4384]) ).
thf(4872,plain,
( ( ( e3 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk24 @ qmltpeq ) ) )
!= ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ ( sk1 @ sk23 )
| sk2 ),
inference(simp,[status(thm)],[4871]) ).
thf(4923,plain,
( ( e3 != e0 )
| ( ( e0 @ ( e0 @ op ) )
!= ( e0 @ ( e0 @ op ) ) )
| ( ( sk1 @ sk24 )
!= sk1 )
| ~ ( sk1 @ sk23 )
| sk2 ),
inference(simp,[status(thm)],[4872]) ).
thf(4950,plain,
( ( e3 != e0 )
| ( ( sk1 @ sk24 )
!= sk1 )
| ~ ( sk1 @ sk23 )
| sk2 ),
inference(simp,[status(thm)],[4923]) ).
thf(12850,plain,
( ( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12666,1142]) ).
thf(12851,plain,
( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[12850]) ).
thf(12948,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12851]) ).
thf(12954,plain,
( ( ( e3 @ inv @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12948]) ).
thf(17570,plain,
! [A: '$ki_world'] :
( ( ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk6 @ qmltpeq ) ) ) )
| ~ ( sk1 @ sk5 )
| ~ $true
| sk2
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[33,15619]) ).
thf(17571,plain,
! [A: '$ki_world'] :
( ( ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk6 @ qmltpeq ) ) ) )
| ~ ( sk1 @ sk5 )
| sk2
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[17570]) ).
thf(17572,plain,
( ~ ( sk1 @ sk5 )
| sk2
| ~ ( sk1 @ sk6 @ ( sk1 @ '$ki_accessible' ) ) ),
inference(pattern_uni,[status(thm)],[17571:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(37986,plain,
( ( ( sk1 @ sk6 @ ( sk1 @ '$ki_accessible' ) )
!= ( sk1 @ sk6 @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( sk1 @ sk5 )
| sk2
| ~ $true
| ~ ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[37204,17572]) ).
thf(37987,plain,
( ( ( sk1 @ sk6 @ ( sk1 @ '$ki_accessible' ) )
!= ( sk1 @ sk6 @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ~ ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[37986]) ).
thf(37988,plain,
( sk2
| ~ ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[37987:[]]) ).
thf(22950,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6344,22099]) ).
thf(22951,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk34 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22950]) ).
thf(23043,plain,
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[22951]) ).
thf(23106,plain,
( ( ( e2 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23043]) ).
thf(15423,plain,
( ( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15053,963]) ).
thf(15424,plain,
( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15423]) ).
thf(15457,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ( e0 != e0 )
| ( ( sk1 @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[15424]) ).
thf(15479,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ( ( sk1 @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[15457]) ).
thf(22513,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,88]) ).
thf(22514,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk10 @ ( A @ '$ki_accessible' ) )
| ( A @ sk9 @ ( A @ '$ki_accessible' ) )
| ( A @ sk7 )
| ( A @ sk5 ) ),
inference(simp,[status(thm)],[22513]) ).
thf(22515,plain,
( ( sk1 @ sk34 @ sk10 @ ( sk1 @ sk34 @ '$ki_accessible' ) )
| ( sk1 @ sk34 @ sk9 @ ( sk1 @ sk34 @ '$ki_accessible' ) )
| ( sk1 @ sk34 @ sk7 )
| ( sk1 @ sk34 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[22514:[bind(A,$thf( sk1 @ sk34 ))]]) ).
thf(22244,plain,
( ( ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,17968]) ).
thf(22245,plain,
( ( ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e2 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22244]) ).
thf(22358,plain,
( ( ( '$ki_local_world' @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( e2 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22245]) ).
thf(22451,plain,
( ( ( '$ki_local_world' @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( e2 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22358]) ).
thf(22078,plain,
( ( ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e1 @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,2590]) ).
thf(22079,plain,
( ( ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e1 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22078]) ).
thf(22403,plain,
( ( ( '$ki_local_world' @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e1 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22079]) ).
thf(22495,plain,
( ( ( '$ki_local_world' @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e1 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22403]) ).
thf(5191,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4966,954]) ).
thf(5192,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5191]) ).
thf(5211,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[5192]) ).
thf(5235,plain,
( ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= sk1 ) ),
inference(simp,[status(thm)],[5211]) ).
thf(1415,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,667]) ).
thf(1416,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1415]) ).
thf(1432,plain,
( ( e1 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[1416]) ).
thf(23963,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2909,22191]) ).
thf(23964,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23963]) ).
thf(24080,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23964]) ).
thf(24139,plain,
( ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[24080]) ).
thf(11260,plain,
( ( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10941,740]) ).
thf(11261,plain,
( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[11260]) ).
thf(11268,plain,
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[11261]) ).
thf(11297,plain,
( ( ( e2 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[11268]) ).
thf(22676,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e1 @ ( A @ sk98 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,563]) ).
thf(22677,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e3 @ ( e1 @ ( A @ sk98 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22676]) ).
thf(22803,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 )
!= A )
| ( sk1 != '$ki_local_world' )
| ~ ( e3 @ ( e1 @ ( A @ sk98 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22677]) ).
thf(22857,plain,
( ( sk1 != '$ki_local_world' )
| ~ ( e3 @ ( e1 @ ( sk1 @ sk34 @ sk98 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22803]) ).
thf(22156,plain,
( ( ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,15211]) ).
thf(22157,plain,
( ( ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22156]) ).
thf(22393,plain,
( ( ( '$ki_local_world' @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22157]) ).
thf(22486,plain,
( ( ( '$ki_local_world' @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( e3 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22393]) ).
thf(11160,plain,
( ( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10934,740]) ).
thf(11161,plain,
( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[11160]) ).
thf(11172,plain,
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[11161]) ).
thf(11198,plain,
( ( ( e2 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[11172]) ).
thf(5015,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[141,963]) ).
thf(5016,plain,
! [A: '$ki_world'] :
( ( ( e3 @ ( e3 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5015]) ).
thf(5034,plain,
! [A: '$ki_world'] :
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( A
!= ( sk1 @ sk96 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5016]) ).
thf(5062,plain,
( ( ( e3 @ ( unit @ op ) )
!= e0 )
| ~ ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5034]) ).
thf(4122,plain,
( ( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3940,912]) ).
thf(4123,plain,
( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[4122]) ).
thf(4155,plain,
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( sk1 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[4123]) ).
thf(4164,plain,
( ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( ( sk1 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[4155]) ).
thf(22748,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21634,107]) ).
thf(22749,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk34 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22748]) ).
thf(22750,plain,
( sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( sk1 @ sk34 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[22749:[bind(A,$thf( sk1 @ sk34 ))]]) ).
thf(21303,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[673,107]) ).
thf(21304,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[21303]) ).
thf(21305,plain,
( sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( sk1 @ sk10 @ qmltpeq ) ) )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[21304:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(11,axiom,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
thf(359,plain,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(22251,plain,
( ( ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,5062]) ).
thf(22252,plain,
( ( ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22251]) ).
thf(22361,plain,
( ( ( sk1 @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22252]) ).
thf(22454,plain,
( ( ( sk1 @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22361]) ).
thf(22129,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ ( unit @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,133]) ).
thf(22130,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( e0 @ ( unit @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22129]) ).
thf(22131,plain,
e0 @ ( e0 @ ( unit @ op ) @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22130:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(22218,plain,
( ( ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e2 @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,4028]) ).
thf(22219,plain,
( ( ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e2 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22218]) ).
thf(22382,plain,
( ( ( '$ki_local_world' @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e2 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22219]) ).
thf(22475,plain,
( ( ( '$ki_local_world' @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e2 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22382]) ).
thf(17,axiom,
( ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ inv @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ inv @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ inv @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ inv @ ( A @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e3 @ ( e3 @ inv @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e3 @ inv @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e2 @ ( e2 @ inv @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e2 @ inv @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e1 @ ( e1 @ inv @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e1 @ inv @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e0 @ ( e0 @ inv @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e0 @ inv @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(600,plain,
( ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e3 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e3 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e3 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e3 @ inv @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e2 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e2 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e2 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e2 @ inv @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e1 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e1 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e1 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e1 @ inv @ ( A @ qmltpeq ) ) ) ) )
& ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e3 @ ( e0 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e2 @ ( e0 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e1 @ ( e0 @ inv @ ( A @ qmltpeq ) ) ) )
| ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( e0 @ ( e0 @ inv @ ( A @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e3 @ ( e3 @ inv @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e3 @ inv @ ( e3 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e2 @ ( e2 @ inv @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e2 @ inv @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e1 @ ( e1 @ inv @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e1 @ inv @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e0 @ ( e0 @ inv @ op ) @ ( A @ qmltpeq ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( unit @ ( e0 @ inv @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1395,plain,
( ( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,1155]) ).
thf(1396,plain,
( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1395]) ).
thf(1427,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e1 )
| ( ( sk1 @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[1396]) ).
thf(8550,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk16 @ ( A @ '$ki_accessible' ) )
| ( A @ sk15 @ ( A @ '$ki_accessible' ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ~ $true
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(paramod_ordered,[status(thm)],[7710,93]) ).
thf(8551,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk16 @ ( A @ '$ki_accessible' ) )
| ( A @ sk15 @ ( A @ '$ki_accessible' ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(simp,[status(thm)],[8550]) ).
thf(8552,plain,
( ( sk1 @ sk16 @ sk16 @ ( sk1 @ sk16 @ '$ki_accessible' ) )
| ( sk1 @ sk16 @ sk15 @ ( sk1 @ sk16 @ '$ki_accessible' ) )
| ( sk1 @ sk16 @ sk13 )
| ( sk1 @ sk16 @ sk11 )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[8551:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(3039,plain,
( ( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2909,963]) ).
thf(3040,plain,
( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3039]) ).
thf(3060,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( ( sk1 @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3040]) ).
thf(3071,plain,
( ( ( unit @ ( e3 @ op ) )
!= e0 )
| ( ( sk1 @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3060]) ).
thf(1879,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[673,78]) ).
thf(1880,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1879]) ).
thf(1881,plain,
( sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( sk1 @ sk10 @ qmltpeq ) ) )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1880:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(11232,plain,
( ( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10941,743]) ).
thf(11233,plain,
( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[11232]) ).
thf(11285,plain,
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[11233]) ).
thf(11302,plain,
( ( ( e2 @ inv @ inv )
!= e0 )
| ( ( sk1 @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[11285]) ).
thf(2223,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2049,667]) ).
thf(2224,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2223]) ).
thf(2239,plain,
( ( e1 != e1 )
| ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[2224]) ).
thf(2247,plain,
( ( ( e1 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[2239]) ).
thf(5119,plain,
( ( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4961,963]) ).
thf(5120,plain,
( ( e3 @ ( e0 @ ( sk1 @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5119]) ).
thf(5125,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5120]) ).
thf(5147,plain,
( ( ( e3 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5125]) ).
thf(22125,plain,
( ( ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ ( unit @ op ) )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,6451]) ).
thf(22126,plain,
( ( ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22125]) ).
thf(22409,plain,
( ( ( '$ki_local_world' @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e2 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22126]) ).
thf(22501,plain,
( ( ( '$ki_local_world' @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e2 @ ( unit @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22409]) ).
thf(1231,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[652,774]) ).
thf(1232,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1231]) ).
thf(1263,plain,
! [A: '$ki_world'] :
( ( e3 != unit )
| ( ( unit @ inv )
!= e2 )
| ( A
!= ( sk1 @ sk99 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1232]) ).
thf(1284,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e2 )
| ~ ( sk1 @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1263]) ).
thf(22220,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,140]) ).
thf(22221,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22220]) ).
thf(22222,plain,
e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22221:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(8106,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( unit @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,143]) ).
thf(8107,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e0 @ ( unit @ ( e0 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[8106]) ).
thf(8108,plain,
e0 @ ( unit @ ( e0 @ op ) @ ( sk1 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[8107:[bind(A,$thf( sk1 ))]]) ).
thf(1345,plain,
( ( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1215,743]) ).
thf(1346,plain,
( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1345]) ).
thf(1372,plain,
( ( e2 != unit )
| ( ( unit @ inv )
!= e0 )
| ( ( sk1 @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[1346]) ).
thf(9696,plain,
! [A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ inv @ inv )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,9661]) ).
thf(9697,plain,
! [A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[9696]) ).
thf(9737,plain,
! [A: '$ki_world'] :
( ( A
!= ( '$ki_local_world' @ sk94 ) )
| ( A != '$ki_local_world' )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[9697]) ).
thf(9747,plain,
( ( ( '$ki_local_world' @ sk94 )
!= '$ki_local_world' )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[9737]) ).
thf(1391,plain,
( ( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,774]) ).
thf(1392,plain,
( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1391]) ).
thf(1421,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e2 )
| ( ( sk1 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[1392]) ).
thf(19,axiom,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ inv @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ inv @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ inv @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ inv @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ inv @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ inv @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
thf(627,plain,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ inv @ ( e2 @ inv @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ inv @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ inv @ ( e1 @ inv @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e3 @ inv @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e2 @ inv @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) )
& ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ '$ki_accessible' ) )
=> ( e1 @ inv @ ( e0 @ inv @ ( B @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(44,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk25 )
| ~ ( e3 @ ( e1 @ ( e1 @ op ) @ ( A @ sk26 @ qmltpeq ) ) )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(99,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk25 )
| ~ ( e3 @ ( e1 @ ( e1 @ op ) @ ( A @ sk26 @ qmltpeq ) ) )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(3017,plain,
( ( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2909,1155]) ).
thf(3018,plain,
( ( e3 @ ( e1 @ ( sk1 @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3017]) ).
thf(3051,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e1 )
| ( ( sk1 @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3018]) ).
thf(3067,plain,
( ( ( unit @ ( e3 @ op ) )
!= e1 )
| ( ( sk1 @ sk98 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[3051]) ).
thf(3977,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[140,903]) ).
thf(3978,plain,
! [A: '$ki_world'] :
( ( ( e2 @ ( unit @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[3977]) ).
thf(4004,plain,
! [A: '$ki_world'] :
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e1 )
| ( A
!= ( '$ki_local_world' @ sk97 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[3978]) ).
thf(4029,plain,
( ( ( unit @ ( e2 @ op ) )
!= e1 )
| ~ ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[4004]) ).
thf(22288,plain,
( ( ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e2 @ op ) )
!= e1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,4029]) ).
thf(22289,plain,
( ( ( '$ki_local_world' @ sk97 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e2 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22288]) ).
thf(22347,plain,
( ( ( '$ki_local_world' @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e2 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22289]) ).
thf(22440,plain,
( ( ( '$ki_local_world' @ sk97 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e2 @ op ) )
!= e1 ) ),
inference(simp,[status(thm)],[22347]) ).
thf(2897,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[793,139]) ).
thf(2898,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[2897]) ).
thf(2973,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= '$ki_local_world' )
| ( e3 @ ( unit @ ( e3 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[2898]) ).
thf(2997,plain,
( ( ( sk1 @ sk10 )
!= '$ki_local_world' )
| ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ sk10 @ sk10 @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[2973]) ).
thf(49,plain,
! [A: '$ki_world'] :
( ( A @ sk28 @ ( A @ '$ki_accessible' ) )
| ~ ( e3 @ ( e2 @ ( e2 @ op ) @ ( A @ sk27 @ qmltpeq ) ) )
| ( A @ sk25 )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(104,plain,
! [A: '$ki_world'] :
( ( A @ sk28 @ ( A @ '$ki_accessible' ) )
| ~ ( e3 @ ( e2 @ ( e2 @ op ) @ ( A @ sk27 @ qmltpeq ) ) )
| ( A @ sk25 )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(4041,plain,
( ( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3935,740]) ).
thf(4042,plain,
( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[4041]) ).
thf(4092,plain,
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[4042]) ).
thf(4102,plain,
( ( ( unit @ ( e2 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[4092]) ).
thf(1249,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[652,954]) ).
thf(1250,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1249]) ).
thf(1268,plain,
! [A: '$ki_world'] :
( ( e3 != unit )
| ( ( unit @ inv )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk96 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1250]) ).
thf(1289,plain,
( ( e3 != unit )
| ( ( unit @ inv )
!= e0 )
| ~ ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1268]) ).
thf(22091,plain,
( ( ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ inv @ inv )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,11087]) ).
thf(22092,plain,
( ( ( '$ki_local_world' @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e2 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22091]) ).
thf(22340,plain,
( ( ( '$ki_local_world' @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e2 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22092]) ).
thf(22433,plain,
( ( ( '$ki_local_world' @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e2 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22340]) ).
thf(23167,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15046,22170]) ).
thf(23168,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23167]) ).
thf(23341,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( e0 != e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23168]) ).
thf(23385,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23341]) ).
thf(12896,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12666,954]) ).
thf(12897,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[12896]) ).
thf(12920,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12897]) ).
thf(12957,plain,
( ( ( e3 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[12920]) ).
thf(6584,plain,
( ( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6349,743]) ).
thf(6585,plain,
( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[6584]) ).
thf(6618,plain,
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[6585]) ).
thf(6639,plain,
( ( ( e2 @ ( unit @ op ) )
!= e0 )
| ( ( sk1 @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[6618]) ).
thf(8582,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(paramod_ordered,[status(thm)],[7710,33]) ).
thf(8583,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(simp,[status(thm)],[8582]) ).
thf(8584,plain,
( sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk16 @ qmltpeq ) ) )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[8583:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(22241,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e0 @ ( A @ sk95 @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,557]) ).
thf(22242,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( e2 @ ( e0 @ ( A @ sk95 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22241]) ).
thf(22243,plain,
~ ( e2 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk95 @ qmltpeq ) ) ),
inference(pattern_uni,[status(thm)],[22242:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(15292,plain,
( ( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15046,954]) ).
thf(15293,plain,
( ( e3 @ ( e0 @ ( '$ki_local_world' @ sk96 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15292]) ).
thf(15328,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ( e0 != e0 )
| ( ( '$ki_local_world' @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15293]) ).
thf(15358,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ( ( '$ki_local_world' @ sk96 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15328]) ).
thf(1827,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[793,652]) ).
thf(1828,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1827]) ).
thf(1835,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= '$ki_local_world' )
| ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1828]) ).
thf(1854,plain,
( ( ( sk1 @ sk10 )
!= '$ki_local_world' )
| ( unit @ ( unit @ inv @ ( sk1 @ sk10 @ sk10 @ qmltpeq ) ) )
| ( sk1 @ sk10 @ sk9 @ ( sk1 @ sk10 @ '$ki_accessible' ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk5 )
| ( sk1 @ sk9 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk7 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[1835]) ).
thf(3103,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2914,771]) ).
thf(3104,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[3103]) ).
thf(3122,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[3104]) ).
thf(3136,plain,
( ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[3122]) ).
thf(1303,plain,
! [A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 != unit )
| ( ( unit @ inv )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,1283]) ).
thf(1304,plain,
! [A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk99 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 != unit )
| ( ( unit @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[1303]) ).
thf(1319,plain,
! [A: '$ki_world'] :
( ( A
!= ( '$ki_local_world' @ sk99 ) )
| ( A != '$ki_local_world' )
| ( e3 != unit )
| ( ( unit @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[1304]) ).
thf(1326,plain,
( ( ( '$ki_local_world' @ sk99 )
!= '$ki_local_world' )
| ( e3 != unit )
| ( ( unit @ inv )
!= e2 ) ),
inference(simp,[status(thm)],[1319]) ).
thf(24001,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2914,22191]) ).
thf(24002,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk34 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( unit @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[24001]) ).
thf(24094,plain,
( ( e3 != e3 )
| ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[24002]) ).
thf(24150,plain,
( ( ( unit @ ( e3 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk34 @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[24094]) ).
thf(15431,plain,
( ( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15053,740]) ).
thf(15432,plain,
( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15431]) ).
thf(15443,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ( e0 != e0 )
| ( ( '$ki_local_world' @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[15432]) ).
thf(15476,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[15443]) ).
thf(5161,plain,
( ( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4966,1142]) ).
thf(5162,plain,
( ( e3 @ ( e1 @ ( '$ki_local_world' @ sk98 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5161]) ).
thf(5222,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[5162]) ).
thf(5228,plain,
( ( ( e3 @ ( unit @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk98 )
!= sk1 ) ),
inference(simp,[status(thm)],[5222]) ).
thf(55,plain,
! [A: '$ki_world'] :
( ~ ( e3 @ ( e3 @ ( e3 @ op ) @ ( A @ sk28 @ qmltpeq ) ) )
| ~ ( e3 @ ( e2 @ ( e2 @ op ) @ ( A @ sk27 @ qmltpeq ) ) )
| ( A @ sk25 )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(114,plain,
! [A: '$ki_world'] :
( ~ ( e3 @ ( e3 @ ( e3 @ op ) @ ( A @ sk28 @ qmltpeq ) ) )
| ~ ( e3 @ ( e2 @ ( e2 @ op ) @ ( A @ sk27 @ qmltpeq ) ) )
| ( A @ sk25 )
| ( A @ sk23 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(15304,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15046,667]) ).
thf(15305,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15304]) ).
thf(15351,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( e0 != e0 )
| ( ( '$ki_local_world' @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15305]) ).
thf(15362,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( ( '$ki_local_world' @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[15351]) ).
thf(4057,plain,
( ( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3935,743]) ).
thf(4058,plain,
( ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[4057]) ).
thf(4080,plain,
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e0 )
| ( ( sk1 @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[4058]) ).
thf(4098,plain,
( ( ( unit @ ( e2 @ op ) )
!= e0 )
| ( ( sk1 @ sk95 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[4080]) ).
thf(73,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk7 )
| ( A @ sk8 @ ( A @ '$ki_accessible' ) )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(82,plain,
! [A: '$ki_world'] :
( ~ ( A @ sk7 )
| ( A @ sk8 @ ( A @ '$ki_accessible' ) )
| ( A @ sk5 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(714,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk13 )
| ( B @ sk14 @ ( B @ '$ki_accessible' ) )
| ( B @ sk11 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,74]) ).
thf(715,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk13 )
| ( B @ sk14 @ ( B @ '$ki_accessible' ) )
| ( B @ sk11 ) ),
inference(simp,[status(thm)],[714]) ).
thf(716,plain,
( ~ ( sk1 @ sk13 )
| ( sk1 @ sk14 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[715:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(21206,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,107]) ).
thf(21207,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[21206]) ).
thf(21208,plain,
( sk2
| ( e0 @ ( e2 @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[21207:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1241,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[652,743]) ).
thf(1242,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e2 @ ( e0 @ ( sk1 @ sk95 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1241]) ).
thf(1273,plain,
! [A: '$ki_world'] :
( ( e2 != unit )
| ( ( unit @ inv )
!= e0 )
| ( A
!= ( sk1 @ sk95 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1242]) ).
thf(1294,plain,
( ( e2 != unit )
| ( ( unit @ inv )
!= e0 )
| ~ ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1273]) ).
thf(22225,plain,
( ( ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,15216]) ).
thf(22226,plain,
( ( ( sk1 @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22225]) ).
thf(22319,plain,
( ( ( sk1 @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( e3 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22226]) ).
thf(22413,plain,
( ( ( sk1 @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( e3 @ op ) )
!= e3 ) ),
inference(simp,[status(thm)],[22319]) ).
thf(22110,plain,
( ( ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ inv @ inv )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,9661]) ).
thf(22111,plain,
( ( ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22110]) ).
thf(22402,plain,
( ( ( '$ki_local_world' @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22111]) ).
thf(22494,plain,
( ( ( '$ki_local_world' @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22402]) ).
thf(22136,plain,
( ( ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ ( unit @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,2133]) ).
thf(22137,plain,
( ( ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22136]) ).
thf(22362,plain,
( ( ( sk1 @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e1 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22137]) ).
thf(22455,plain,
( ( ( sk1 @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e1 @ ( unit @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22362]) ).
thf(22268,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,652]) ).
thf(22269,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22268]) ).
thf(22270,plain,
unit @ ( unit @ inv @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22269:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(15427,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15053,664]) ).
thf(15428,plain,
( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ op ) @ ( e0 @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[15427]) ).
thf(15464,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( e0 != e0 )
| ( ( sk1 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[15428]) ).
thf(15480,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e1 )
| ( ( sk1 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[15464]) ).
thf(10451,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk28 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk27 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk25 )
| ( sk1 @ sk23 ) ),
inference(paramod_ordered,[status(thm)],[9960,33]) ).
thf(10452,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk28 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk27 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk25 )
| ( sk1 @ sk23 ) ),
inference(simp,[status(thm)],[10451]) ).
thf(10453,plain,
( sk2
| ( e0 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk28 @ qmltpeq ) ) )
| ( sk1 @ sk27 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk25 )
| ( sk1 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[10452:[bind(A,$thf( sk1 @ sk28 ))]]) ).
thf(23137,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2499,22170]) ).
thf(23138,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23137]) ).
thf(23346,plain,
( ( e1 != e1 )
| ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23138]) ).
thf(23388,plain,
( ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[23346]) ).
thf(3371,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk7 )
| ( B @ sk8 @ ( B @ '$ki_accessible' ) )
| ( B @ sk5 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,82]) ).
thf(3372,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk7 )
| ( B @ sk8 @ ( B @ '$ki_accessible' ) )
| ( B @ sk5 ) ),
inference(simp,[status(thm)],[3371]) ).
thf(3373,plain,
( ~ ( sk1 @ sk7 )
| ( sk1 @ sk8 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[3372:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1355,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1215,903]) ).
thf(1356,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( unit @ ( unit @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[1355]) ).
thf(1380,plain,
( ( e2 != unit )
| ( ( unit @ inv )
!= e1 )
| ( ( '$ki_local_world' @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[1356]) ).
thf(22179,plain,
( ( ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,15200]) ).
thf(22180,plain,
( ( ( sk1 @ sk95 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22179]) ).
thf(22379,plain,
( ( ( sk1 @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22180]) ).
thf(22472,plain,
( ( ( sk1 @ sk95 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ ( e3 @ op ) )
!= e2 ) ),
inference(simp,[status(thm)],[22379]) ).
thf(22123,plain,
( ( ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e1 @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,2586]) ).
thf(22124,plain,
( ( ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e1 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22123]) ).
thf(22350,plain,
( ( ( sk1 @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e1 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22124]) ).
thf(22443,plain,
( ( ( sk1 @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e1 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22350]) ).
thf(22145,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,137]) ).
thf(22146,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e1 @ ( unit @ ( e1 @ op ) @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22145]) ).
thf(22147,plain,
e1 @ ( unit @ ( e1 @ op ) @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22146:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(13013,plain,
( ( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12673,771]) ).
thf(13014,plain,
( ( e3 @ ( e2 @ ( '$ki_local_world' @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[13013]) ).
thf(13045,plain,
( ( e3 != e3 )
| ( ( e3 @ inv @ inv )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[13014]) ).
thf(13068,plain,
( ( ( e3 @ inv @ inv )
!= e2 )
| ( ( '$ki_local_world' @ sk99 )
!= sk1 ) ),
inference(simp,[status(thm)],[13045]) ).
thf(2684,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2504,664]) ).
thf(2685,plain,
( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( unit @ ( e1 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[2684]) ).
thf(2688,plain,
( ( e1 != e1 )
| ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( sk1 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[2685]) ).
thf(2704,plain,
( ( ( unit @ ( e1 @ op ) )
!= e0 )
| ( ( sk1 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[2688]) ).
thf(38,plain,
! [A: '$ki_world'] :
( ( A @ sk22 @ ( A @ '$ki_accessible' ) )
| ~ ( e2 @ ( e2 @ ( e2 @ op ) @ ( A @ sk21 @ qmltpeq ) ) )
| ( A @ sk19 )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(94,plain,
! [A: '$ki_world'] :
( ( A @ sk22 @ ( A @ '$ki_accessible' ) )
| ~ ( e2 @ ( e2 @ ( e2 @ op ) @ ( A @ sk21 @ qmltpeq ) ) )
| ( A @ sk19 )
| ( A @ sk17 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(11136,plain,
( ( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10934,912]) ).
thf(11137,plain,
( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[11136]) ).
thf(11173,plain,
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e1 )
| ( ( sk1 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[11137]) ).
thf(11199,plain,
( ( ( e2 @ inv @ inv )
!= e1 )
| ( ( sk1 @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[11173]) ).
thf(65,plain,
! [A: '$ki_world'] :
( sk4
| ( e2 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(79,plain,
! [A: '$ki_world'] :
( sk4
| ( e2 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk3
| ~ sk2 ),
inference(simp,[status(thm)],[65]) ).
thf(10007,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk28 @ ( A @ '$ki_accessible' ) )
| ( A @ sk27 @ ( A @ '$ki_accessible' ) )
| ( A @ sk25 )
| ( A @ sk23 )
| ~ $true
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(paramod_ordered,[status(thm)],[7710,95]) ).
thf(10008,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk16 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ( A @ sk28 @ ( A @ '$ki_accessible' ) )
| ( A @ sk27 @ ( A @ '$ki_accessible' ) )
| ( A @ sk25 )
| ( A @ sk23 )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(simp,[status(thm)],[10007]) ).
thf(10009,plain,
( ( sk1 @ sk16 @ sk28 @ ( sk1 @ sk16 @ '$ki_accessible' ) )
| ( sk1 @ sk16 @ sk27 @ ( sk1 @ sk16 @ '$ki_accessible' ) )
| ( sk1 @ sk16 @ sk25 )
| ( sk1 @ sk16 @ sk23 )
| ( sk1 @ sk15 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk13 )
| ( sk1 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[10008:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(6608,plain,
( ( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6349,740]) ).
thf(6609,plain,
( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ ( unit @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[6608]) ).
thf(6632,plain,
( ( e2 != e2 )
| ( ( e2 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[6609]) ).
thf(6644,plain,
( ( ( e2 @ ( unit @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[6632]) ).
thf(23265,plain,
( ( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9537,22170]) ).
thf(23266,plain,
( ( e1 @ ( e0 @ ( '$ki_local_world' @ sk34 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e1 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[23265]) ).
thf(23331,plain,
( ( e1 != e1 )
| ( ( e1 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[23266]) ).
thf(23382,plain,
( ( ( e1 @ inv @ inv )
!= e0 )
| ( ( '$ki_local_world' @ sk34 @ sk94 )
!= sk1 ) ),
inference(simp,[status(thm)],[23331]) ).
thf(1257,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[652,667]) ).
thf(1258,plain,
! [A: '$ki_world'] :
( ( ( unit @ ( unit @ inv @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( '$ki_local_world' @ sk94 @ qmltpeq ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1257]) ).
thf(1267,plain,
! [A: '$ki_world'] :
( ( e1 != unit )
| ( ( unit @ inv )
!= e0 )
| ( A
!= ( '$ki_local_world' @ sk94 ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1258]) ).
thf(1288,plain,
( ( e1 != unit )
| ( ( unit @ inv )
!= e0 )
| ~ ( '$ki_local_world' @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[1267]) ).
thf(1052,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e3 @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true
| sk3
| ~ sk2 ),
inference(paramod_ordered,[status(thm)],[849,664]) ).
thf(1053,plain,
( ( ( e1 @ ( e0 @ ( sk1 @ sk94 @ qmltpeq ) ) )
!= ( e1 @ ( e3 @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| sk3
| ~ sk2 ),
inference(simp,[status(thm)],[1052]) ).
thf(1083,plain,
( ( e1 != e1 )
| ( ( e3 @ ( e3 @ op ) )
!= e0 )
| ( ( sk1 @ sk94 )
!= sk1 )
| ~ sk2
| sk3 ),
inference(simp,[status(thm)],[1053]) ).
thf(1093,plain,
( ( ( e3 @ ( e3 @ op ) )
!= e0 )
| ( ( sk1 @ sk94 )
!= sk1 )
| ~ sk2
| sk3 ),
inference(simp,[status(thm)],[1083]) ).
thf(22093,plain,
( ( ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ inv @ inv )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,9668]) ).
thf(22094,plain,
( ( ( sk1 @ sk94 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22093]) ).
thf(22405,plain,
( ( ( sk1 @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22094]) ).
thf(22497,plain,
( ( ( sk1 @ sk94 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e1 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22405]) ).
thf(18061,plain,
( ( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17789,903]) ).
thf(18062,plain,
( ( e2 @ ( e1 @ ( '$ki_local_world' @ sk97 @ qmltpeq ) ) )
!= ( e3 @ ( e2 @ op ) @ ( e1 @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[18061]) ).
thf(18100,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( e1 != e1 )
| ( ( '$ki_local_world' @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[18062]) ).
thf(18125,plain,
( ( ( e3 @ ( e2 @ op ) )
!= e2 )
| ( ( '$ki_local_world' @ sk97 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[18100]) ).
thf(36458,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,119]) ).
thf(36459,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e3 @ ( e3 @ op ) @ ( B @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[36458]) ).
thf(36460,plain,
( sk2
| ( e0 @ ( e3 @ ( e3 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(pattern_uni,[status(thm)],[36459:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(19612,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk17 )
| ( B @ sk18 @ ( B @ '$ki_accessible' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,106]) ).
thf(19613,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( B @ sk17 )
| ( B @ sk18 @ ( B @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[19612]) ).
thf(19614,plain,
( ~ ( sk1 @ sk17 )
| ( sk1 @ sk18 @ ( sk1 @ '$ki_accessible' ) ) ),
inference(pattern_uni,[status(thm)],[19613:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(16122,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk12 @ qmltpeq ) ) ) )
| ~ ( sk1 @ sk11 )
| ~ $true
| sk3
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 ),
inference(paramod_ordered,[status(thm)],[103,6657]) ).
thf(16123,plain,
! [A: '$ki_world'] :
( ( ( e1 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
!= ( e1 @ ( e0 @ ( e0 @ op ) @ ( sk1 @ sk12 @ qmltpeq ) ) ) )
| ~ ( sk1 @ sk11 )
| sk3
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 ),
inference(simp,[status(thm)],[16122]) ).
thf(16124,plain,
( ~ ( sk1 @ sk11 )
| sk3
| ~ ( sk1 @ sk12 @ ( sk1 @ '$ki_accessible' ) )
| ~ sk2 ),
inference(pattern_uni,[status(thm)],[16123:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(34923,plain,
( ( ( sk1 @ sk12 @ ( sk1 @ '$ki_accessible' ) )
!= ( sk1 @ sk12 @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( sk1 @ sk11 )
| sk3
| ~ $true
| ~ sk2
| ~ ( sk1 @ sk11 ) ),
inference(paramod_ordered,[status(thm)],[34439,16124]) ).
thf(34924,plain,
( ( ( sk1 @ sk12 @ ( sk1 @ '$ki_accessible' ) )
!= ( sk1 @ sk12 @ ( sk1 @ '$ki_accessible' ) ) )
| sk3
| ~ sk2
| ~ ( sk1 @ sk11 ) ),
inference(simp,[status(thm)],[34923]) ).
thf(34925,plain,
( sk3
| ~ sk2
| ~ ( sk1 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[34924:[]]) ).
thf(11236,plain,
( ( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10941,912]) ).
thf(11237,plain,
( ( e2 @ ( e1 @ ( sk1 @ sk97 @ qmltpeq ) ) )
!= ( e2 @ ( e2 @ inv @ inv @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[11236]) ).
thf(11269,plain,
( ( e2 != e2 )
| ( ( e2 @ inv @ inv )
!= e1 )
| ( ( sk1 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[11237]) ).
thf(11298,plain,
( ( ( e2 @ inv @ inv )
!= e1 )
| ( ( sk1 @ sk97 )
!= sk1 ) ),
inference(simp,[status(thm)],[11269]) ).
thf(11328,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk22 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ $true
| ( sk1 @ sk21 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk19 )
| ( sk1 @ sk17 ) ),
inference(paramod_ordered,[status(thm)],[10658,78]) ).
thf(11329,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ sk22 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ( sk1 @ sk21 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk19 )
| ( sk1 @ sk17 ) ),
inference(simp,[status(thm)],[11328]) ).
thf(11330,plain,
( sk2
| ( e0 @ ( e1 @ ( e1 @ op ) @ ( sk1 @ sk22 @ qmltpeq ) ) )
| ( sk1 @ sk21 @ ( sk1 @ '$ki_accessible' ) )
| ( sk1 @ sk19 )
| ( sk1 @ sk17 ) ),
inference(pattern_uni,[status(thm)],[11329:[bind(A,$thf( sk1 @ sk22 ))]]) ).
thf(9,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(163,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5089,plain,
( ( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4961,774]) ).
thf(5090,plain,
( ( e3 @ ( e2 @ ( sk1 @ sk99 @ qmltpeq ) ) )
!= ( e3 @ ( e3 @ ( unit @ op ) @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[5089]) ).
thf(5140,plain,
( ( e3 != e3 )
| ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( sk1 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5090]) ).
thf(5155,plain,
( ( ( e3 @ ( unit @ op ) )
!= e2 )
| ( ( sk1 @ sk99 )
!= '$ki_local_world' ) ),
inference(simp,[status(thm)],[5140]) ).
thf(22236,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,162]) ).
thf(22237,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( e3 @ ( e3 @ inv @ inv @ ( A @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[22236]) ).
thf(22238,plain,
e3 @ ( e3 @ inv @ inv @ ( '$ki_local_world' @ sk34 @ qmltpeq ) ),
inference(pattern_uni,[status(thm)],[22237:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(22080,plain,
( ( ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,3004]) ).
thf(22081,plain,
( ( ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( unit @ ( e3 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22080]) ).
thf(22372,plain,
( ( ( '$ki_local_world' @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( unit @ ( e3 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22081]) ).
thf(22465,plain,
( ( ( '$ki_local_world' @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( unit @ ( e3 @ op ) )
!= e0 ) ),
inference(simp,[status(thm)],[22372]) ).
thf(22311,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( A @ sk34 @ ( A @ '$ki_accessible' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,232]) ).
thf(22312,plain,
! [A: '$ki_world'] :
( ( ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( A @ sk34 @ ( A @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[22311]) ).
thf(22313,plain,
'$ki_local_world' @ sk34 @ sk34 @ ( '$ki_local_world' @ sk34 @ '$ki_accessible' ),
inference(pattern_uni,[status(thm)],[22312:[bind(A,$thf( '$ki_local_world' @ sk34 ))]]) ).
thf(22185,plain,
( ( ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21614,12838]) ).
thf(22186,plain,
( ( ( '$ki_local_world' @ sk96 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( '$ki_local_world' @ sk34 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( ( e3 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22185]) ).
thf(22344,plain,
( ( ( '$ki_local_world' @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( '$ki_local_world' != '$ki_local_world' )
| ( ( e3 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22186]) ).
thf(22437,plain,
( ( ( '$ki_local_world' @ sk96 )
!= ( '$ki_local_world' @ sk34 ) )
| ( ( e3 @ inv @ inv )
!= e0 ) ),
inference(simp,[status(thm)],[22344]) ).
thf(59,plain,
! [A: '$ki_world'] :
( ( A @ sk16 @ ( A @ '$ki_accessible' ) )
| ~ ( e1 @ ( e2 @ ( e2 @ op ) @ ( A @ sk15 @ qmltpeq ) ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(100,plain,
! [A: '$ki_world'] :
( ( A @ sk16 @ ( A @ '$ki_accessible' ) )
| ~ ( e1 @ ( e2 @ ( e2 @ op ) @ ( A @ sk15 @ qmltpeq ) ) )
| ( A @ sk13 )
| ( A @ sk11 )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(46,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(90,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e1 @ ( e1 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 ),
inference(simp,[status(thm)],[46]) ).
thf(43,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(111,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e0 @ ( e0 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 ),
inference(simp,[status(thm)],[43]) ).
thf(39,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(83,plain,
! [A: '$ki_world'] :
( ( e3 @ ( e2 @ ( e2 @ op ) @ ( A @ qmltpeq ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ sk4
| ~ sk3
| ~ sk2 ),
inference(simp,[status(thm)],[39]) ).
thf(4104,plain,
( ( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3940,740]) ).
thf(4105,plain,
( ( e2 @ ( e0 @ ( '$ki_local_world' @ sk95 @ qmltpeq ) ) )
!= ( e2 @ ( unit @ ( e2 @ op ) @ ( sk1 @ qmltpeq ) ) ) ),
inference(simp,[status(thm)],[4104]) ).
thf(4142,plain,
( ( e2 != e2 )
| ( ( unit @ ( e2 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[4105]) ).
thf(4161,plain,
( ( ( unit @ ( e2 @ op ) )
!= e0 )
| ( ( '$ki_local_world' @ sk95 )
!= sk1 ) ),
inference(simp,[status(thm)],[4142]) ).
thf(62806,plain,
$false,
inference(e,[status(thm)],[1322,101,17986,22861,2499,1295,88,4166,22424,12949,3072,1290,12666,22457,6463,2590,1422,22480,120,1142,23369,10658,115,5225,1426,15357,8101,3004,142,15207,3135,22448,22547,5227,2985,18252,23112,651,22140,22165,9746,18247,22476,1366,22493,1287,15353,1430,1871,22866,125,22229,9668,13067,542,9960,22412,1298,3131,11203,22444,12956,23123,11087,110,22859,5150,5231,559,22449,11100,93,22498,78,5077,29,1379,12837,15477,2049,16114,22425,11363,9661,22481,22416,6657,22855,1418,5156,1283,4162,1858,106,18126,121,22456,21614,1960,84,24401,22420,1215,2190,774,15360,23400,116,23368,849,74,2586,6451,18123,3068,1377,89,133,411,21200,15046,5157,117,6560,793,85,22496,102,4100,22874,12673,2705,22867,18251,1091,21238,2133,160,7710,12809,3069,137,407,12846,24157,3134,37204,33,1365,625,8535,1291,13063,92,1423,3137,22471,97,6556,22503,15211,1856,24145,1425,9936,141,12834,2245,12959,22428,22473,15481,156,1375,6477,22191,124,8555,554,1155,109,9530,5080,77,1424,15619,1612,2649,3935,96,22196,2125,4384,6331,15200,22441,3064,7826,22250,6349,5063,2504,8072,1297,22432,5149,23118,23107,15354,12838,23397,1857,105,11197,4966,657,24142,558,11065,22594,2189,11296,22482,541,2909,13071,412,6637,22871,22479,1483,5230,2570,9181,161,10420,1595,689,1374,6561,23365,562,12951,22463,5067,743,2991,22199,12835,118,6344,1428,1371,17789,24136,4099,144,86,22422,22259,22160,113,81,21205,18250,36639,3138,98,22273,22459,6461,22170,76,567,22120,1376,22446,103,4028,140,799,91,23125,2647,108,9174,2111,3150,13069,912,18121,15475,15216,563,22427,1364,167,2984,11102,9841,24397,1102,22084,80,653,23119,23113,162,2994,112,15053,123,22483,22292,13065,2914,6557,6641,557,17796,17968,150,34439,95,4950,12954,954,37988,4961,23106,15479,22515,22451,409,1230,22495,5235,3940,1432,24139,11297,22857,22486,11198,5062,4164,22750,673,21305,2044,359,22454,22131,22475,600,15196,1427,8552,3071,1881,143,11302,2247,5147,154,22501,1284,22222,8108,1372,9747,1421,627,99,3067,903,22440,87,2997,104,4102,1289,22433,771,23385,12957,963,6639,8584,652,22243,15358,1854,3136,23,1326,24150,15476,5228,114,139,3003,119,9537,15362,4098,22099,82,716,75,21208,667,1294,22413,22494,4039,22455,22270,17956,15480,15230,10453,23388,3373,1380,22472,22443,22147,4029,136,13068,2704,664,94,17961,107,11199,10941,79,10009,6644,4024,23382,1288,1093,740,21634,22497,18125,36460,5061,19614,34925,11298,11330,163,5155,22238,5312,22465,22313,22437,232,100,90,111,10934,83,543,4161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL942_2 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/0.41 % Computer : n014.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 23:50:02 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/1.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.26/1.42 % [INFO] Parsing done (392ms).
% 2.26/1.43 % [INFO] Running in sequential loop mode.
% 3.27/1.82 % [INFO] eprover registered as external prover.
% 3.27/1.83 % [INFO] Scanning for conjecture ...
% 3.83/2.04 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 4.12/2.18 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 4.93/2.49 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.17/2.51 % [INFO] Type checking passed.
% 5.17/2.52 % [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 ...
% 120.41/27.85 % External prover 'e' found a proof!
% 120.41/27.85 % [INFO] Killing All external provers ...
% 120.41/27.85 % Time passed: 27269ms (effective reasoning time: 26408ms)
% 120.41/27.85 % 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)>
% 120.41/27.85 % Axioms used in derivation (20): ax9, ax6, op_substitution_2, ax8, reflexivity, ax11, ax2, $ki_exists_in_world_$i_const, transitivity, inv_substitution_1, symmetry, $ki_exists_in_world_$i_nonempty, ax4, mrel_reflexive, ax10, op_substitution_1, ax1, ax7, ax3, ax5
% 120.41/27.85 % No. of inferences in proof: 1562
% 120.41/27.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 27269 ms resp. 26408 ms w/o parsing
% 123.80/28.38 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 123.80/28.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------