%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN548+1 : TPTP v9.3.1. Released v2.2.0.
% 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:17:49 AM UTC 2026
% Result : Theorem 80.40s 23.09s
% Output : Refutation 67.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 8
% Syntax : Number of formulae : 934 ( 18 unt; 0 typ; 5 def)
% Number of atoms : 4682 ( 840 equ; 0 cnn)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 14898 (2393 ~;2569 |; 17 &;9878 @)
% ( 2 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 633 ( 5 ^; 620 !; 3 ?; 633 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(reachable_decl,type,
reachable: $i > $i > $o ).
thf(initial_world_decl,type,
initial_world: $i ).
thf(p_decl,type,
p: $i > $o ).
thf(q_decl,type,
q: $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ( A @ reachable ) )
=> ( ( ( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ q ) )
| ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ p ) ) )
=> ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ q ) )
| ( C @ p ) ) ) )
& ( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ q ) )
| ( C @ p ) ) )
=> ( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ q ) )
| ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ p ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ( A @ sk1 @ reachable ) )
=> ( B @ p ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ( A @ sk1 @ reachable ) )
=> ( B @ q ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ( A @ sk1 @ reachable ) )
=> ( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ q ) )
| ( B @ p ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ( A @ sk5 @ reachable ) )
=> ( B @ q ) ) ) ) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ reachable ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_reachable) ).
thf(19,plain,
! [A: $i] : ( A @ ( A @ reachable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,plain,
! [A: $i] : ( A @ ( A @ reachable ) ),
inference(cnf,[status(esa)],[19]) ).
thf(1,conjecture,
? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ q ) )
| ( C @ p ) ) )
<=> ( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ q ) )
| ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ p ) ) ) ) )
& ( A @ ( initial_world @ reachable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ q ) )
| ( C @ p ) ) )
<=> ( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ q ) )
| ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ p ) ) ) ) )
& ( A @ ( initial_world @ reachable ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ( ( ( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ q ) )
| ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ p ) ) )
=> ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ q ) )
| ( C @ p ) ) ) )
& ( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ q ) )
| ( C @ p ) ) )
=> ( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ q ) )
| ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ p ) ) ) ) ) )
& ( A @ ( initial_world @ reachable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) )
& ( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) )
& ( ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) )
& ( ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) )
& ( ( E @ q )
| ~ ( E @ ( A @ sk1 @ reachable ) )
| ( D @ p )
| ~ ( D @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) )
& ( ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ ( A @ ( initial_world @ reachable ) ) )
& ( ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) )
& ( ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ ( A @ ( initial_world @ reachable ) ) )
& ( ~ ( A @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) )
& ( ~ ( A @ sk2 )
| ( C @ q )
| ~ ( C @ ( B @ reachable ) )
| ( B @ p )
| ~ ( B @ ( A @ sk1 @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) )
& ( ( A @ sk1 @ ( A @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
! [A: $i] :
( ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ( B @ sk4 @ ( B @ sk1 @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,7]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ( B @ sk4 @ ( B @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
( ~ ( initial_world @ sk2 )
| ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(12,plain,
! [A: $i] :
( ( A @ sk1 @ ( A @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk1 @ ( B @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,12]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk1 @ ( B @ reachable ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
initial_world @ sk1 @ ( initial_world @ reachable ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ reachable ) )
& ( B @ ( A @ reachable ) ) )
=> ( C @ ( A @ reachable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_reachable) ).
thf(21,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ reachable ) )
& ( B @ ( A @ reachable ) ) )
=> ( C @ ( A @ reachable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ reachable ) )
| ~ ( C @ ( B @ reachable ) )
| ~ ( B @ ( A @ reachable ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(2187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( B @ ( A @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( C @ ( B @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,22]) ).
thf(2188,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( B @ ( A @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( C @ ( B @ reachable ) ) ),
inference(simp,[status(thm)],[2187]) ).
thf(2189,plain,
! [A: $i] :
( ( A @ ( initial_world @ reachable ) )
| ~ ( A @ ( initial_world @ sk1 @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[2188:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world @ sk1 )),bind(C,$thf( C ))]]) ).
thf(2368,plain,
! [A: $i] :
( ( A @ ( initial_world @ reachable ) )
| ~ ( A @ ( initial_world @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[2189]) ).
thf(2734,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[91,2368]) ).
thf(2735,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2734]) ).
thf(2736,plain,
( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2735:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(15,plain,
! [A: $i] :
( ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(3019,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2736,15]) ).
thf(3020,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3019]) ).
thf(3021,plain,
( ~ ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3020:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(3791,plain,
( ~ $true
| ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[3021]) ).
thf(3798,plain,
( ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3791]) ).
thf(29,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,12]) ).
thf(30,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(31,plain,
initial_world @ sk1 @ sk1 @ ( initial_world @ sk1 @ reachable ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( initial_world @ sk1 ))]]) ).
thf(2295,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ sk1 @ reachable ) )
!= ( B @ ( A @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( C @ ( B @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(2296,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ sk1 @ reachable ) )
!= ( B @ ( A @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( C @ ( B @ reachable ) ) ),
inference(simp,[status(thm)],[2295]) ).
thf(2297,plain,
! [A: $i] :
( ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[2296:[bind(A,$thf( initial_world @ sk1 )),bind(B,$thf( initial_world @ sk1 @ sk1 )),bind(C,$thf( C ))]]) ).
thf(2412,plain,
! [A: $i] :
( ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[2297]) ).
thf(86,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,7]) ).
thf(87,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(88,plain,
( ~ ( initial_world @ sk1 @ sk2 )
| ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( initial_world @ sk1 ))]]) ).
thf(2744,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,2368]) ).
thf(2745,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[2744]) ).
thf(2746,plain,
initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ),
inference(pattern_uni,[status(thm)],[2745:[bind(A,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(8,plain,
! [A: $i] :
( ~ ( A @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(2859,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2746,8]) ).
thf(2860,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[2859]) ).
thf(2861,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[2860:[bind(A,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(2833,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2746,12]) ).
thf(2834,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[2833]) ).
thf(2835,plain,
initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ reachable ),
inference(pattern_uni,[status(thm)],[2834:[bind(A,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(2827,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( B @ ( A @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( C @ ( B @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2746,22]) ).
thf(2828,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( B @ ( A @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( C @ ( B @ reachable ) ) ),
inference(simp,[status(thm)],[2827]) ).
thf(2829,plain,
! [A: $i] :
( ( A @ ( initial_world @ reachable ) )
| ~ ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[2828:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world @ sk1 @ sk1 )),bind(C,$thf( C ))]]) ).
thf(2868,plain,
! [A: $i] :
( ( A @ ( initial_world @ reachable ) )
| ~ ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[2829]) ).
thf(8019,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2835,2868]) ).
thf(8020,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[8019]) ).
thf(8021,plain,
initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ),
inference(pattern_uni,[status(thm)],[8020:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 ))]]) ).
thf(8196,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( B @ ( A @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( C @ ( B @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8021,22]) ).
thf(8197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( B @ ( A @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( C @ ( B @ reachable ) ) ),
inference(simp,[status(thm)],[8196]) ).
thf(8198,plain,
! [A: $i] :
( ( A @ ( initial_world @ reachable ) )
| ~ ( A @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[8197:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world @ sk1 @ sk1 @ sk1 )),bind(C,$thf( C ))]]) ).
thf(8246,plain,
! [A: $i] :
( ( A @ ( initial_world @ reachable ) )
| ~ ( A @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[8198]) ).
thf(26014,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2861,8246]) ).
thf(26015,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[26014]) ).
thf(26016,plain,
( ( initial_world @ sk1 @ sk1 @ sk3 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26015:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk3 ))]]) ).
thf(11,plain,
! [A: $i] :
( ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(458,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk5 @ p )
| ( B @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,11]) ).
thf(459,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk5 @ p )
| ( B @ sk2 ) ),
inference(simp,[status(thm)],[458]) ).
thf(460,plain,
( ~ ( initial_world @ sk5 @ p )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[459:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(920,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ~ ( B @ sk3 @ p )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,15]) ).
thf(921,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ~ ( B @ sk3 @ p ) ),
inference(simp,[status(thm)],[920]) ).
thf(922,plain,
( ~ ( initial_world @ sk2 )
| ~ ( initial_world @ sk3 @ p ) ),
inference(pattern_uni,[status(thm)],[921:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(1022,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,922]) ).
thf(1023,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[1022]) ).
thf(1024,plain,
( ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[1023:[]]) ).
thf(14,plain,
! [A: $i] :
( ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(663,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk5 @ ( B @ sk1 @ reachable ) )
| ( B @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,14]) ).
thf(664,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk5 @ ( B @ sk1 @ reachable ) )
| ( B @ sk2 ) ),
inference(simp,[status(thm)],[663]) ).
thf(665,plain,
( ( initial_world @ sk5 @ ( initial_world @ sk1 @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[664:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(2713,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[665,2368]) ).
thf(2714,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2713]) ).
thf(2715,plain,
( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2714:[bind(A,$thf( initial_world @ sk5 ))]]) ).
thf(9,plain,
! [A: $i] :
( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk6 @ ( B @ sk5 @ reachable ) )
| ( B @ sk2 )
| ~ $true
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[9,9]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk6 @ ( B @ sk5 @ reachable ) )
| ( B @ sk2 )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 )
!= B )
| ( ( A @ sk5 )
!= initial_world )
| ~ ( A @ ( initial_world @ reachable ) )
| ( B @ sk6 @ ( B @ sk5 @ reachable ) )
| ( B @ sk2 )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[56]) ).
thf(70,plain,
! [A: $i] :
( ( ( A @ sk5 )
!= initial_world )
| ~ ( A @ ( initial_world @ reachable ) )
| ( A @ sk6 @ sk6 @ ( A @ sk6 @ sk5 @ reachable ) )
| ( A @ sk6 @ sk2 )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[66]) ).
thf(3475,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( ( A @ sk5 )
!= initial_world )
| ~ $true
| ( A @ sk6 @ sk6 @ ( A @ sk6 @ sk5 @ reachable ) )
| ( A @ sk6 @ sk2 )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2715,70]) ).
thf(3476,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( ( A @ sk5 )
!= initial_world )
| ( A @ sk6 @ sk6 @ ( A @ sk6 @ sk5 @ reachable ) )
| ( A @ sk6 @ sk2 )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3475]) ).
thf(3477,plain,
( ( ( initial_world @ sk5 @ sk5 )
!= initial_world )
| ( initial_world @ sk5 @ sk6 @ sk6 @ ( initial_world @ sk5 @ sk6 @ sk5 @ reachable ) )
| ( initial_world @ sk5 @ sk6 @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3476:[bind(A,$thf( initial_world @ sk5 ))]]) ).
thf(455,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,11]) ).
thf(456,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[455]) ).
thf(457,plain,
( ~ ( initial_world @ sk1 @ sk5 @ p )
| ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[456:[bind(A,$thf( initial_world @ sk1 ))]]) ).
thf(1025,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[457,922]) ).
thf(1026,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[1025]) ).
thf(1031,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[1026]) ).
thf(10,plain,
! [A: $i] :
( ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk6 @ q )
| ( B @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,10]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk6 @ q )
| ( B @ sk2 ) ),
inference(simp,[status(thm)],[196]) ).
thf(198,plain,
( ~ ( initial_world @ sk6 @ q )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(247,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,91]) ).
thf(248,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[248:[]]) ).
thf(159,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[88,7]) ).
thf(160,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[159]) ).
thf(166,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 )
!= A )
| ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( initial_world @ sk1 @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(170,plain,
( ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk4 @ sk2 )
| ~ ( initial_world @ sk1 @ sk2 )
| ( initial_world @ sk1 @ sk4 @ sk4 @ ( initial_world @ sk1 @ sk4 @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(2819,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2746,14]) ).
thf(2820,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[2819]) ).
thf(2821,plain,
( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2820:[bind(A,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(26152,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2821,8246]) ).
thf(26153,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[26152]) ).
thf(26154,plain,
( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26153:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk5 ))]]) ).
thf(26744,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( ( A @ sk5 )
!= initial_world )
| ~ $true
| ( A @ sk6 @ sk6 @ ( A @ sk6 @ sk5 @ reachable ) )
| ( A @ sk6 @ sk2 )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[26154,70]) ).
thf(26745,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( ( A @ sk5 )
!= initial_world )
| ( A @ sk6 @ sk6 @ ( A @ sk6 @ sk5 @ reachable ) )
| ( A @ sk6 @ sk2 )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[26744]) ).
thf(26746,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ sk5 )
!= initial_world )
| ( initial_world @ sk1 @ sk1 @ sk5 @ sk6 @ sk6 @ ( initial_world @ sk1 @ sk1 @ sk5 @ sk6 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk5 @ sk6 @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26745:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk5 ))]]) ).
thf(2974,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2715,12]) ).
thf(2975,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2974]) ).
thf(2976,plain,
( ( initial_world @ sk5 @ sk1 @ ( initial_world @ sk5 @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2975:[bind(A,$thf( initial_world @ sk5 ))]]) ).
thf(3070,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2736,11]) ).
thf(3071,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3070]) ).
thf(3072,plain,
( ~ ( initial_world @ sk4 @ sk5 @ p )
| ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3071:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(2951,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2715,9]) ).
thf(2952,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2951]) ).
thf(2953,plain,
( ( initial_world @ sk5 @ sk6 @ ( initial_world @ sk5 @ sk5 @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2952:[bind(A,$thf( initial_world @ sk5 ))]]) ).
thf(288,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[91,8]) ).
thf(289,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[288]) ).
thf(294,plain,
! [A: $i] :
( ( ( initial_world @ sk4 )
!= A )
| ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( initial_world @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[289]) ).
thf(308,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk2 )
| ( initial_world @ sk4 @ sk3 @ ( initial_world @ sk4 @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk6 @ ( B @ sk5 @ reachable ) )
| ( B @ sk2 )
| ~ $true
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[7,9]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk6 @ ( B @ sk5 @ reachable ) )
| ( B @ sk2 )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 )
!= B )
| ( ( A @ sk1 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( B @ sk6 @ ( B @ sk5 @ reachable ) )
| ( B @ sk2 ) ),
inference(simp,[status(thm)],[93]) ).
thf(120,plain,
! [A: $i] :
( ( ( A @ sk1 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( A @ sk4 @ sk6 @ ( A @ sk4 @ sk5 @ reachable ) )
| ( A @ sk4 @ sk2 ) ),
inference(simp,[status(thm)],[109]) ).
thf(193,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,10]) ).
thf(194,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[193]) ).
thf(195,plain,
( ~ ( initial_world @ sk1 @ sk6 @ q )
| ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( initial_world @ sk1 ))]]) ).
thf(13,plain,
! [A: $i] :
( ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(36,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(37,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
( ~ ( initial_world @ sk1 @ sk2 )
| ~ ( initial_world @ sk1 @ sk4 @ q ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( initial_world @ sk1 ))]]) ).
thf(327,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[195,38]) ).
thf(328,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[327]) ).
thf(329,plain,
( ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[328:[]]) ).
thf(378,plain,
( ~ $true
| ( ( initial_world @ sk1 @ sk6 @ q )
!= ( initial_world @ sk1 @ sk4 @ q ) )
| ~ ( initial_world @ sk1 @ sk4 @ q ) ),
inference(eqfactor_ordered,[status(thm)],[329]) ).
thf(379,plain,
( ( ( initial_world @ sk1 @ sk6 @ q )
!= ( initial_world @ sk1 @ sk4 @ q ) )
| ~ ( initial_world @ sk1 @ sk4 @ q ) ),
inference(simp,[status(thm)],[378]) ).
thf(3033,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2736,13]) ).
thf(3034,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3033]) ).
thf(3035,plain,
( ~ ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3034:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(7514,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk2 )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[3072,3035]) ).
thf(7515,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[7514]) ).
thf(7516,plain,
( ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7515:[]]) ).
thf(2856,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2746,11]) ).
thf(2857,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[2856]) ).
thf(2858,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2857:[bind(A,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(27193,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk1 @ sk3 @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2858,26016]) ).
thf(27194,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk1 @ sk3 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[27193]) ).
thf(27195,plain,
( ( initial_world @ sk1 @ sk1 @ sk3 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[27194:[]]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ( B @ sk3 @ ( B @ sk1 @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,8]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ( B @ sk3 @ ( B @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(262,plain,
( ~ ( initial_world @ sk2 )
| ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(2752,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[262,2368]) ).
thf(2753,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2752]) ).
thf(2754,plain,
( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2753:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(3096,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2754,15]) ).
thf(3097,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3096]) ).
thf(3098,plain,
( ~ ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3097:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk6 @ ( B @ sk5 @ reachable ) )
| ( B @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,9]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk6 @ ( B @ sk5 @ reachable ) )
| ( B @ sk2 ) ),
inference(simp,[status(thm)],[52]) ).
thf(54,plain,
( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(697,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[54,14]) ).
thf(698,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[697]) ).
thf(717,plain,
! [A: $i] :
( ( ( initial_world @ sk6 )
!= A )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[698]) ).
thf(741,plain,
( ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk5 @ ( initial_world @ sk6 @ sk1 @ reachable ) )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[717]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ~ ( B @ sk4 @ q )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,13]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ~ ( B @ sk4 @ q ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
( ~ ( initial_world @ sk2 )
| ~ ( initial_world @ sk4 @ q ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(338,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[195,41]) ).
thf(339,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[338]) ).
thf(346,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[339]) ).
thf(876,plain,
( ~ $true
| ( ( initial_world @ sk1 @ sk6 @ q )
!= ( initial_world @ sk4 @ q ) )
| ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk4 @ q ) ),
inference(eqfactor_ordered,[status(thm)],[346]) ).
thf(878,plain,
( ( ( initial_world @ sk1 @ sk6 )
!= ( initial_world @ sk4 ) )
| ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk4 @ q ) ),
inference(simp,[status(thm)],[876]) ).
thf(660,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,14]) ).
thf(661,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[660]) ).
thf(662,plain,
( ( initial_world @ sk1 @ sk5 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[661:[bind(A,$thf( initial_world @ sk1 ))]]) ).
thf(7983,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[662,2868]) ).
thf(7984,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[7983]) ).
thf(7985,plain,
( ( initial_world @ sk1 @ sk5 @ ( initial_world @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7984:[bind(A,$thf( initial_world @ sk1 @ sk5 ))]]) ).
thf(8389,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[7985,9]) ).
thf(8390,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[8389]) ).
thf(8391,plain,
( ( initial_world @ sk1 @ sk5 @ sk6 @ ( initial_world @ sk1 @ sk5 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8390:[bind(A,$thf( initial_world @ sk1 @ sk5 ))]]) ).
thf(11455,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk6 @ ( initial_world @ sk1 @ sk5 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[8391,14]) ).
thf(11456,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk6 @ ( initial_world @ sk1 @ sk5 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[11455]) ).
thf(11513,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk6 )
!= A )
| ( ( initial_world @ sk1 @ sk5 @ sk5 )
!= initial_world )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[11456]) ).
thf(11556,plain,
( ( ( initial_world @ sk1 @ sk5 @ sk5 )
!= initial_world )
| ( initial_world @ sk1 @ sk5 @ sk6 @ sk5 @ ( initial_world @ sk1 @ sk5 @ sk6 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk5 @ sk6 @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[11513]) ).
thf(257,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,8]) ).
thf(258,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(259,plain,
( ~ ( initial_world @ sk1 @ sk2 )
| ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( initial_world @ sk1 ))]]) ).
thf(810,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ $true
| ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[457,259]) ).
thf(811,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[810]) ).
thf(812,plain,
( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[811:[]]) ).
thf(18354,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[812,2412]) ).
thf(18355,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[18354]) ).
thf(18356,plain,
( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[18355:[bind(A,$thf( initial_world @ sk1 @ sk3 ))]]) ).
thf(8208,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8021,12]) ).
thf(8209,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[8208]) ).
thf(8210,plain,
initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ),
inference(pattern_uni,[status(thm)],[8209:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 ))]]) ).
thf(8606,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8210,2368]) ).
thf(8607,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[8606]) ).
thf(8648,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 )
!= A )
| ( ( initial_world @ sk1 @ sk1 @ sk1 )
!= ( initial_world @ sk1 ) )
| ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[8607]) ).
thf(8668,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[8648]) ).
thf(15504,plain,
( ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[8668]) ).
thf(18219,plain,
! [A: $i] :
( ( ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ $true
| ( ( initial_world @ sk1 @ sk1 )
!= initial_world ) ),
inference(paramod_ordered,[status(thm)],[15504,2412]) ).
thf(18220,plain,
! [A: $i] :
( ( ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ( ( initial_world @ sk1 @ sk1 )
!= initial_world ) ),
inference(simp,[status(thm)],[18219]) ).
thf(18507,plain,
! [A: $i] :
( ( A
!= ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 ) )
| ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ( A @ ( initial_world @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[18220]) ).
thf(18592,plain,
( ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[18507]) ).
thf(531,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,91]) ).
thf(532,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[531]) ).
thf(533,plain,
( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[532:[]]) ).
thf(548,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ $true
| ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[457,88]) ).
thf(549,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[548]) ).
thf(550,plain,
( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[549:[]]) ).
thf(4106,plain,
( ~ $true
| ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[3098]) ).
thf(4110,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4106]) ).
thf(324,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ $true
| ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[195,88]) ).
thf(325,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[324]) ).
thf(326,plain,
( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[325:[]]) ).
thf(8055,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[326,2868]) ).
thf(8056,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[8055]) ).
thf(8057,plain,
( ( initial_world @ sk1 @ sk4 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[8056:[bind(A,$thf( initial_world @ sk1 @ sk4 ))]]) ).
thf(2694,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[249,2368]) ).
thf(2695,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[2694]) ).
thf(2696,plain,
( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[2695:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(3336,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2696,15]) ).
thf(3337,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[3336]) ).
thf(3338,plain,
( ~ ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[3337:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(49,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,9]) ).
thf(50,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[49]) ).
thf(51,plain,
( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( initial_world @ sk1 ))]]) ).
thf(141,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[51,9]) ).
thf(142,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[141]) ).
thf(149,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 )
!= A )
| ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[142]) ).
thf(153,plain,
( ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ( initial_world @ sk1 @ sk6 @ sk6 @ ( initial_world @ sk1 @ sk6 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk6 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[149]) ).
thf(537,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,262]) ).
thf(538,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[537]) ).
thf(539,plain,
( ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[538:[]]) ).
thf(2689,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[539,2368]) ).
thf(2690,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[2689]) ).
thf(2691,plain,
( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[2690:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(3274,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2691,10]) ).
thf(3275,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[3274]) ).
thf(3276,plain,
( ~ ( initial_world @ sk3 @ sk6 @ q )
| ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[3275:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(3314,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2691,11]) ).
thf(3315,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[3314]) ).
thf(3316,plain,
( ~ ( initial_world @ sk3 @ sk5 @ p )
| ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[3315:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(3271,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2691,15]) ).
thf(3272,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[3271]) ).
thf(3273,plain,
( ~ ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[3272:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(13828,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[3316,3273]) ).
thf(13829,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[13828]) ).
thf(13830,plain,
( ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[13829:[]]) ).
thf(2960,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2715,14]) ).
thf(2961,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2960]) ).
thf(2962,plain,
( ( initial_world @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2961:[bind(A,$thf( initial_world @ sk5 ))]]) ).
thf(4154,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2962,2368]) ).
thf(4155,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4154]) ).
thf(4199,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 )
!= A )
| ( ( initial_world @ sk5 @ sk1 )
!= ( initial_world @ sk1 ) )
| ( A @ ( initial_world @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4155]) ).
thf(4212,plain,
( ( ( initial_world @ sk5 @ sk1 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk5 @ ( initial_world @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4199]) ).
thf(20660,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( ( initial_world @ sk5 @ sk1 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[4212,9]) ).
thf(20661,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( ( initial_world @ sk5 @ sk1 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[20660]) ).
thf(20662,plain,
( ( initial_world @ sk5 @ sk5 @ sk6 @ ( initial_world @ sk5 @ sk5 @ sk5 @ reachable ) )
| ( initial_world @ sk5 @ sk5 @ sk2 )
| ( ( initial_world @ sk5 @ sk1 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[20661:[bind(A,$thf( initial_world @ sk5 @ sk5 ))]]) ).
thf(2830,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( C @ ( B @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ $true
| ~ ( B @ ( A @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[2746,22]) ).
thf(2831,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( C @ ( B @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( B @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[2830]) ).
thf(2832,plain,
! [A: $i] :
( ( initial_world @ sk1 @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ ( A @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[2831:[bind(A,$thf( A )),bind(B,$thf( initial_world )),bind(C,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(8646,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ sk1 @ ( A @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8210,2832]) ).
thf(8647,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ sk1 @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[8646]) ).
thf(8651,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 )
!= initial_world )
| ( ( initial_world @ sk1 @ sk1 @ sk1 )
!= A )
| ( initial_world @ sk1 @ sk1 @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[8647]) ).
thf(8671,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 )
!= initial_world )
| ( initial_world @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[8651]) ).
thf(2836,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2746,7]) ).
thf(2837,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[2836]) ).
thf(2838,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[2837:[bind(A,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(26165,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2838,8246]) ).
thf(26166,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[26165]) ).
thf(26167,plain,
( ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26166:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk4 ))]]) ).
thf(27401,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2858,26167]) ).
thf(27402,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[27401]) ).
thf(27403,plain,
( ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[27402:[]]) ).
thf(25989,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8210,8246]) ).
thf(25990,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[25989]) ).
thf(25991,plain,
initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ),
inference(pattern_uni,[status(thm)],[25990:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 @ sk1 ))]]) ).
thf(26545,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25991,11]) ).
thf(26546,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[26545]) ).
thf(26547,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk5 @ p )
| ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26546:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 @ sk1 ))]]) ).
thf(2816,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2746,10]) ).
thf(2817,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[2816]) ).
thf(2818,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2817:[bind(A,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(27264,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk1 @ sk3 @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2818,26016]) ).
thf(27265,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk1 @ sk3 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[27264]) ).
thf(27266,plain,
( ( initial_world @ sk1 @ sk1 @ sk3 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[27265:[]]) ).
thf(26551,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25991,15]) ).
thf(26552,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p ) ),
inference(simp,[status(thm)],[26551]) ).
thf(26553,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk2 )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk3 @ p ) ),
inference(pattern_uni,[status(thm)],[26552:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 @ sk1 ))]]) ).
thf(917,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,15]) ).
thf(918,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p ) ),
inference(simp,[status(thm)],[917]) ).
thf(919,plain,
( ~ ( initial_world @ sk1 @ sk2 )
| ~ ( initial_world @ sk1 @ sk3 @ p ) ),
inference(pattern_uni,[status(thm)],[918:[bind(A,$thf( initial_world @ sk1 ))]]) ).
thf(1043,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,919]) ).
thf(1044,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[1043]) ).
thf(1046,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[1044]) ).
thf(3339,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2696,10]) ).
thf(3340,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[3339]) ).
thf(3341,plain,
( ~ ( initial_world @ sk4 @ sk6 @ q )
| ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[3340:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(3345,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2696,13]) ).
thf(3346,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[3345]) ).
thf(3347,plain,
( ~ ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[3346:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(14667,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[3341,3347]) ).
thf(14668,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[14667]) ).
thf(14669,plain,
( ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[14668:[]]) ).
thf(14550,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[3341,3338]) ).
thf(14551,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[14550]) ).
thf(14552,plain,
( ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[14551:[]]) ).
thf(3044,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2736,12]) ).
thf(3045,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3044]) ).
thf(3046,plain,
( ( initial_world @ sk4 @ sk1 @ ( initial_world @ sk4 @ reachable ) )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3045:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(2699,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[533,2368]) ).
thf(2700,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[2699]) ).
thf(2701,plain,
( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[2700:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(3651,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2701,13]) ).
thf(3652,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[3651]) ).
thf(3653,plain,
( ~ ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[3652:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(3099,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2754,10]) ).
thf(3100,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3099]) ).
thf(3101,plain,
( ~ ( initial_world @ sk3 @ sk6 @ q )
| ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3100:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(3110,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2754,13]) ).
thf(3111,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3110]) ).
thf(3112,plain,
( ~ ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3111:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(9097,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk2 )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[3101,3112]) ).
thf(9098,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[9097]) ).
thf(9099,plain,
( ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9098:[]]) ).
thf(3642,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2701,10]) ).
thf(3643,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[3642]) ).
thf(3644,plain,
( ~ ( initial_world @ sk4 @ sk6 @ q )
| ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[3643:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(516,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,38]) ).
thf(517,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[516]) ).
thf(542,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[517]) ).
thf(26780,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[26154,12]) ).
thf(26781,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[26780]) ).
thf(26782,plain,
( ( initial_world @ sk1 @ sk1 @ sk5 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26781:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk5 ))]]) ).
thf(8171,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8021,10]) ).
thf(8172,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[8171]) ).
thf(8173,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk6 @ q )
| ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8172:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 ))]]) ).
thf(8188,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8021,13]) ).
thf(8189,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q ) ),
inference(simp,[status(thm)],[8188]) ).
thf(8190,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk4 @ q ) ),
inference(pattern_uni,[status(thm)],[8189:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 ))]]) ).
thf(11979,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[8173,8190]) ).
thf(11980,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[11979]) ).
thf(11981,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[11980:[]]) ).
thf(74,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[54,9]) ).
thf(75,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[74]) ).
thf(80,plain,
! [A: $i] :
( ( ( initial_world @ sk6 )
!= A )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[75]) ).
thf(83,plain,
( ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk5 @ reachable ) )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[80]) ).
thf(179,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[83,13]) ).
thf(180,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[179]) ).
thf(185,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 )
!= A )
| ( ( initial_world @ sk6 @ sk5 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[180]) ).
thf(189,plain,
( ( ( initial_world @ sk6 @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk6 @ sk6 @ sk2 )
| ~ ( initial_world @ sk6 @ sk6 @ sk4 @ q )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[185]) ).
thf(2957,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2715,10]) ).
thf(2958,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2957]) ).
thf(2959,plain,
( ~ ( initial_world @ sk5 @ sk6 @ q )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2958:[bind(A,$thf( initial_world @ sk5 ))]]) ).
thf(2963,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2715,13]) ).
thf(2964,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2963]) ).
thf(2965,plain,
( ~ ( initial_world @ sk5 @ sk2 )
| ~ ( initial_world @ sk5 @ sk4 @ q )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2964:[bind(A,$thf( initial_world @ sk5 ))]]) ).
thf(5800,plain,
( ( ( initial_world @ sk5 @ sk2 )
!= ( initial_world @ sk5 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk5 @ sk4 @ q )
| ( initial_world @ sk2 )
| ~ ( initial_world @ sk5 @ sk6 @ q )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2959,2965]) ).
thf(5801,plain,
( ( ( initial_world @ sk5 @ sk2 )
!= ( initial_world @ sk5 @ sk2 ) )
| ~ ( initial_world @ sk5 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ sk6 @ q )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[5800]) ).
thf(5802,plain,
( ~ ( initial_world @ sk5 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ sk6 @ q )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5801:[]]) ).
thf(8168,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8021,15]) ).
thf(8169,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p ) ),
inference(simp,[status(thm)],[8168]) ).
thf(8170,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk3 @ p ) ),
inference(pattern_uni,[status(thm)],[8169:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 ))]]) ).
thf(11825,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[8173,8170]) ).
thf(11826,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[11825]) ).
thf(11827,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[11826:[]]) ).
thf(360,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,262]) ).
thf(361,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[360]) ).
thf(362,plain,
( ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[361:[]]) ).
thf(2728,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[362,2368]) ).
thf(2729,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[2728]) ).
thf(2730,plain,
( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[2729:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(207,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[51,10]) ).
thf(208,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[207]) ).
thf(220,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 )
!= A )
| ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[208]) ).
thf(228,plain,
( ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk6 @ sk6 @ q )
| ( initial_world @ sk1 @ sk6 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[220]) ).
thf(4754,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,3798]) ).
thf(4755,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[4754]) ).
thf(4756,plain,
( ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[4755:[]]) ).
thf(2997,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2715,11]) ).
thf(2998,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2997]) ).
thf(2999,plain,
( ~ ( initial_world @ sk5 @ sk5 @ p )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2998:[bind(A,$thf( initial_world @ sk5 ))]]) ).
thf(5972,plain,
( ( ( initial_world @ sk5 @ sk2 )
!= ( initial_world @ sk5 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk5 @ sk4 @ q )
| ( initial_world @ sk2 )
| ~ ( initial_world @ sk5 @ sk5 @ p )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2999,2965]) ).
thf(5973,plain,
( ( ( initial_world @ sk5 @ sk2 )
!= ( initial_world @ sk5 @ sk2 ) )
| ~ ( initial_world @ sk5 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ sk5 @ p )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[5972]) ).
thf(5974,plain,
( ~ ( initial_world @ sk5 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ sk5 @ p )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5973:[]]) ).
thf(5764,plain,
( ~ $true
| ( ( initial_world @ sk5 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk5 @ sk6 @ q )
| ( initial_world @ sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[2959]) ).
thf(5792,plain,
( ( ( initial_world @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk5 @ sk6 @ q )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[5764]) ).
thf(8414,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[7985,12]) ).
thf(8415,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[8414]) ).
thf(8416,plain,
( ( initial_world @ sk1 @ sk5 @ sk1 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8415:[bind(A,$thf( initial_world @ sk1 @ sk5 ))]]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ( B @ sk4 @ ( B @ sk1 @ reachable ) )
| ~ $true
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ( B @ sk4 @ ( B @ sk1 @ reachable ) )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 )
!= B )
| ( ( A @ sk1 )
!= initial_world )
| ~ ( B @ sk2 )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( B @ sk4 @ ( B @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(121,plain,
! [A: $i] :
( ( ( A @ sk1 )
!= initial_world )
| ~ ( A @ sk4 @ sk2 )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( A @ sk4 @ sk4 @ ( A @ sk4 @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(3685,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2701,11]) ).
thf(3686,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[3685]) ).
thf(3687,plain,
( ~ ( initial_world @ sk4 @ sk5 @ p )
| ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[3686:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(16170,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[3687,3653]) ).
thf(16171,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[16170]) ).
thf(16172,plain,
( ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[16171:[]]) ).
thf(76,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[54,13]) ).
thf(77,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[76]) ).
thf(81,plain,
! [A: $i] :
( ( ( initial_world @ sk6 )
!= A )
| ( ( initial_world @ sk5 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[77]) ).
thf(84,plain,
( ( ( initial_world @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk6 @ sk2 )
| ~ ( initial_world @ sk6 @ sk4 @ q )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[81]) ).
thf(4111,plain,
( ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4106]) ).
thf(5399,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,4111]) ).
thf(5400,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[5399]) ).
thf(5401,plain,
( ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[5400:[]]) ).
thf(3710,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2730,10]) ).
thf(3711,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[3710]) ).
thf(3712,plain,
( ~ ( initial_world @ sk3 @ sk6 @ q )
| ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[3711:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(2954,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2715,15]) ).
thf(2955,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2954]) ).
thf(2956,plain,
( ~ ( initial_world @ sk5 @ sk2 )
| ~ ( initial_world @ sk5 @ sk3 @ p )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2955:[bind(A,$thf( initial_world @ sk5 ))]]) ).
thf(6019,plain,
( ( ( initial_world @ sk5 @ sk2 )
!= ( initial_world @ sk5 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk5 @ sk3 @ p )
| ( initial_world @ sk2 )
| ~ ( initial_world @ sk5 @ sk5 @ p )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2999,2956]) ).
thf(6020,plain,
( ( ( initial_world @ sk5 @ sk2 )
!= ( initial_world @ sk5 @ sk2 ) )
| ~ ( initial_world @ sk5 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ sk5 @ p )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[6019]) ).
thf(6021,plain,
( ~ ( initial_world @ sk5 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ sk5 @ p )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6020:[]]) ).
thf(2813,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2746,15]) ).
thf(2814,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p ) ),
inference(simp,[status(thm)],[2813]) ).
thf(2815,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk2 )
| ~ ( initial_world @ sk1 @ sk1 @ sk3 @ p ) ),
inference(pattern_uni,[status(thm)],[2814:[bind(A,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(4632,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2858,2815]) ).
thf(4633,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[4632]) ).
thf(4634,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[4633:[]]) ).
thf(5817,plain,
( ~ $true
| ( ( initial_world @ sk1 @ sk1 @ sk5 @ p )
!= ( initial_world @ sk1 @ sk1 @ sk3 @ p ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk3 @ p ) ),
inference(eqfactor_ordered,[status(thm)],[4634]) ).
thf(5819,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk5 )
!= ( initial_world @ sk1 @ sk1 @ sk3 ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk3 @ p ) ),
inference(simp,[status(thm)],[5817]) ).
thf(525,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,41]) ).
thf(526,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[525]) ).
thf(527,plain,
( ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[526:[]]) ).
thf(3833,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 @ ( initial_world @ sk5 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2953,14]) ).
thf(3834,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 @ ( initial_world @ sk5 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3833]) ).
thf(3883,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 )
!= A )
| ( ( initial_world @ sk5 @ sk5 )
!= initial_world )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3834]) ).
thf(3899,plain,
( ( ( initial_world @ sk5 @ sk5 )
!= initial_world )
| ( initial_world @ sk5 @ sk6 @ sk5 @ ( initial_world @ sk5 @ sk6 @ sk1 @ reachable ) )
| ( initial_world @ sk5 @ sk6 @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3883]) ).
thf(8231,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8021,11]) ).
thf(8232,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[8231]) ).
thf(8233,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk5 @ p )
| ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8232:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 ))]]) ).
thf(78,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[54,12]) ).
thf(79,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[78]) ).
thf(82,plain,
! [A: $i] :
( ( ( initial_world @ sk6 )
!= A )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( A @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[79]) ).
thf(85,plain,
( ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk1 @ ( initial_world @ sk6 @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[82]) ).
thf(8380,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[7985,14]) ).
thf(8381,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[8380]) ).
thf(8382,plain,
( ( initial_world @ sk1 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk5 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8381:[bind(A,$thf( initial_world @ sk1 @ sk5 ))]]) ).
thf(27472,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2818,26167]) ).
thf(27473,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[27472]) ).
thf(27474,plain,
( ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[27473:[]]) ).
thf(275,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[51,8]) ).
thf(276,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[275]) ).
thf(293,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 )
!= A )
| ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ~ ( A @ sk2 )
| ( A @ sk3 @ ( A @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[276]) ).
thf(307,plain,
( ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk6 @ sk2 )
| ( initial_world @ sk1 @ sk6 @ sk3 @ ( initial_world @ sk1 @ sk6 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[293]) ).
thf(380,plain,
( ( ( initial_world @ sk1 @ sk6 )
!= ( initial_world @ sk1 @ sk4 ) )
| ~ ( initial_world @ sk1 @ sk4 @ q ) ),
inference(simp,[status(thm)],[378]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ~ ( B @ sk4 @ q )
| ~ $true
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[7,13]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ~ ( B @ sk4 @ q )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 )
!= B )
| ( ( A @ sk1 )
!= initial_world )
| ~ ( B @ sk2 )
| ~ ( B @ sk4 @ q )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(117,plain,
! [A: $i] :
( ( ( A @ sk1 )
!= initial_world )
| ~ ( A @ sk4 @ sk2 )
| ~ ( A @ sk4 @ sk4 @ q )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(8199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( C @ ( B @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ $true
| ~ ( B @ ( A @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[8021,22]) ).
thf(8200,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( C @ ( B @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( B @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[8199]) ).
thf(8201,plain,
! [A: $i] :
( ( initial_world @ sk1 @ sk1 @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ ( A @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[8200:[bind(A,$thf( A )),bind(B,$thf( initial_world )),bind(C,$thf( initial_world @ sk1 @ sk1 @ sk1 ))]]) ).
thf(5749,plain,
( ( ( initial_world @ sk5 @ sk2 )
!= ( initial_world @ sk5 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk5 @ sk3 @ p )
| ( initial_world @ sk2 )
| ~ ( initial_world @ sk5 @ sk6 @ q )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2959,2956]) ).
thf(5750,plain,
( ( ( initial_world @ sk5 @ sk2 )
!= ( initial_world @ sk5 @ sk2 ) )
| ~ ( initial_world @ sk5 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ sk6 @ q )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[5749]) ).
thf(5751,plain,
( ~ ( initial_world @ sk5 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ sk6 @ q )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5750:[]]) ).
thf(1040,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[457,919]) ).
thf(1041,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[1040]) ).
thf(1042,plain,
( ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[1041:[]]) ).
thf(3662,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2701,12]) ).
thf(3663,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[3662]) ).
thf(3664,plain,
( ( initial_world @ sk4 @ sk1 @ ( initial_world @ sk4 @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[3663:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(3280,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2691,13]) ).
thf(3281,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[3280]) ).
thf(3282,plain,
( ~ ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[3281:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(13581,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[3276,3282]) ).
thf(13582,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[13581]) ).
thf(13583,plain,
( ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[13582:[]]) ).
thf(3839,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 @ ( initial_world @ sk5 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2953,2368]) ).
thf(3840,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 @ ( initial_world @ sk5 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3839]) ).
thf(3874,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 )
!= A )
| ( ( initial_world @ sk5 @ sk5 )
!= ( initial_world @ sk1 ) )
| ( A @ ( initial_world @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3840]) ).
thf(3889,plain,
( ( ( initial_world @ sk5 @ sk5 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk6 @ ( initial_world @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3874]) ).
thf(234,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,38]) ).
thf(235,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[234]) ).
thf(252,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[235]) ).
thf(8024,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[812,2868]) ).
thf(8025,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[8024]) ).
thf(8026,plain,
( ( initial_world @ sk1 @ sk3 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[8025:[bind(A,$thf( initial_world @ sk1 @ sk3 ))]]) ).
thf(20637,plain,
( ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk5 @ sk5 @ ( initial_world @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4212]) ).
thf(801,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ $true
| ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[195,259]) ).
thf(802,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[801]) ).
thf(803,plain,
( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[802:[]]) ).
thf(8062,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[803,2868]) ).
thf(8063,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[8062]) ).
thf(8064,plain,
( ( initial_world @ sk1 @ sk3 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[8063:[bind(A,$thf( initial_world @ sk1 @ sk3 ))]]) ).
thf(10578,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[8064,12]) ).
thf(10579,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[10578]) ).
thf(10580,plain,
( ( initial_world @ sk1 @ sk3 @ sk1 @ ( initial_world @ sk1 @ sk3 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[10579:[bind(A,$thf( initial_world @ sk1 @ sk3 ))]]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk6 @ q )
| ( B @ sk2 )
| ~ $true
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[7,10]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk6 @ q )
| ( B @ sk2 )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 )
!= B )
| ( ( A @ sk1 )
!= initial_world )
| ~ ( B @ sk6 @ q )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( B @ sk2 ) ),
inference(simp,[status(thm)],[202]) ).
thf(224,plain,
! [A: $i] :
( ( ( A @ sk1 )
!= initial_world )
| ~ ( A @ sk4 @ sk6 @ q )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( A @ sk4 @ sk2 ) ),
inference(simp,[status(thm)],[216]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk6 @ q )
| ( B @ sk2 )
| ~ $true
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[9,10]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk6 @ q )
| ( B @ sk2 )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 )
!= B )
| ( ( A @ sk5 )
!= initial_world )
| ~ ( B @ sk6 @ q )
| ~ ( A @ ( initial_world @ reachable ) )
| ( B @ sk2 )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[200]) ).
thf(229,plain,
! [A: $i] :
( ( ( A @ sk5 )
!= initial_world )
| ~ ( A @ sk6 @ sk6 @ q )
| ~ ( A @ ( initial_world @ reachable ) )
| ( A @ sk6 @ sk2 )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[221]) ).
thf(554,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[457,41]) ).
thf(555,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[554]) ).
thf(566,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[555]) ).
thf(2298,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ sk1 @ reachable ) )
!= ( C @ ( B @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ $true
| ~ ( B @ ( A @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(2299,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ sk1 @ reachable ) )
!= ( C @ ( B @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( B @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[2298]) ).
thf(2300,plain,
! [A: $i] :
( ( initial_world @ sk1 @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk1 @ ( A @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[2299:[bind(A,$thf( A )),bind(B,$thf( initial_world @ sk1 )),bind(C,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(18291,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[662,2412]) ).
thf(18292,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[18291]) ).
thf(18293,plain,
( ( initial_world @ sk1 @ sk5 @ ( initial_world @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[18292:[bind(A,$thf( initial_world @ sk1 @ sk5 ))]]) ).
thf(147,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[51,12]) ).
thf(148,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[147]) ).
thf(152,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 )
!= A )
| ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ( A @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[148]) ).
thf(156,plain,
( ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ( initial_world @ sk1 @ sk6 @ sk1 @ ( initial_world @ sk1 @ sk6 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[152]) ).
thf(2971,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( C @ ( B @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ $true
| ~ ( B @ ( A @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2715,22]) ).
thf(2972,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk5 @ ( initial_world @ reachable ) )
!= ( C @ ( B @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( B @ ( A @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2971]) ).
thf(2973,plain,
! [A: $i] :
( ( initial_world @ sk5 @ ( A @ reachable ) )
| ~ ( initial_world @ ( A @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2972:[bind(A,$thf( A )),bind(B,$thf( initial_world )),bind(C,$thf( initial_world @ sk5 ))]]) ).
thf(3379,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2696,11]) ).
thf(3380,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[3379]) ).
thf(3381,plain,
( ~ ( initial_world @ sk4 @ sk5 @ p )
| ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[3380:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(177,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ~ $true
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[83,7]) ).
thf(178,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[177]) ).
thf(184,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 )
!= A )
| ( ( initial_world @ sk6 @ sk5 )
!= initial_world )
| ~ ( A @ sk2 )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[178]) ).
thf(188,plain,
( ( ( initial_world @ sk6 @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk6 @ sk6 @ sk2 )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk6 @ sk4 @ ( initial_world @ sk6 @ sk6 @ sk1 @ reachable ) )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[184]) ).
thf(26497,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25991,9]) ).
thf(26498,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[26497]) ).
thf(26499,plain,
( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26498:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 @ sk1 ))]]) ).
thf(157,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[88,9]) ).
thf(158,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[157]) ).
thf(165,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 )
!= A )
| ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk2 )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[158]) ).
thf(169,plain,
( ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk2 )
| ( initial_world @ sk1 @ sk4 @ sk6 @ ( initial_world @ sk1 @ sk4 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk4 @ sk2 ) ),
inference(simp,[status(thm)],[165]) ).
thf(11189,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[8382,9]) ).
thf(11190,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[11189]) ).
thf(11252,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk5 )
!= A )
| ( ( initial_world @ sk1 @ sk5 @ sk1 )
!= initial_world )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[11190]) ).
thf(11278,plain,
( ( ( initial_world @ sk1 @ sk5 @ sk1 )
!= initial_world )
| ( initial_world @ sk1 @ sk5 @ sk5 @ sk6 @ ( initial_world @ sk1 @ sk5 @ sk5 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk5 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[11252]) ).
thf(8174,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8021,14]) ).
thf(8175,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[8174]) ).
thf(8176,plain,
( ( initial_world @ sk1 @ sk1 @ sk1 @ sk5 @ ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8175:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 ))]]) ).
thf(3022,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2736,10]) ).
thf(3023,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3022]) ).
thf(3024,plain,
( ~ ( initial_world @ sk4 @ sk6 @ q )
| ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3023:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(6591,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk2 )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[3024,3035]) ).
thf(6592,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[6591]) ).
thf(6593,plain,
( ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6592:[]]) ).
thf(2190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( C @ ( B @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ $true
| ~ ( B @ ( A @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[25,22]) ).
thf(2191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( initial_world @ sk1 @ ( initial_world @ reachable ) )
!= ( C @ ( B @ reachable ) ) )
| ( C @ ( A @ reachable ) )
| ~ ( B @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[2190]) ).
thf(2192,plain,
! [A: $i] :
( ( initial_world @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ ( A @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[2191:[bind(A,$thf( A )),bind(B,$thf( initial_world )),bind(C,$thf( initial_world @ sk1 ))]]) ).
thf(8624,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ ( A @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8210,2192]) ).
thf(8625,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[8624]) ).
thf(8667,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 )
!= initial_world )
| ( ( initial_world @ sk1 @ sk1 @ sk1 )
!= A )
| ( initial_world @ sk1 @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[8625]) ).
thf(8687,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 )
!= initial_world )
| ( initial_world @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[8667]) ).
thf(2822,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2746,13]) ).
thf(2823,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q ) ),
inference(simp,[status(thm)],[2822]) ).
thf(2824,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk2 )
| ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q ) ),
inference(pattern_uni,[status(thm)],[2823:[bind(A,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(4528,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2818,2824]) ).
thf(4529,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[4528]) ).
thf(4530,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[4529:[]]) ).
thf(6036,plain,
( ~ $true
| ( ( initial_world @ sk5 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk5 @ sk5 @ p )
| ( initial_world @ sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[2999]) ).
thf(6065,plain,
( ( ( initial_world @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk5 @ sk5 @ p )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[6036]) ).
thf(18223,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[550,2412]) ).
thf(18224,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[18223]) ).
thf(18225,plain,
( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[18224:[bind(A,$thf( initial_world @ sk1 @ sk4 ))]]) ).
thf(26522,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25991,12]) ).
thf(26523,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[26522]) ).
thf(26524,plain,
initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ reachable ),
inference(pattern_uni,[status(thm)],[26523:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 @ sk1 ))]]) ).
thf(18345,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2835,2412]) ).
thf(18346,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[18345]) ).
thf(18347,plain,
initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ reachable ),
inference(pattern_uni,[status(thm)],[18346:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 ))]]) ).
thf(17557,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,9099]) ).
thf(17558,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[17557]) ).
thf(17559,plain,
( ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[17558:[]]) ).
thf(3147,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2754,11]) ).
thf(3148,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3147]) ).
thf(3149,plain,
( ~ ( initial_world @ sk3 @ sk5 @ p )
| ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3148:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(9898,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk2 )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[3149,3098]) ).
thf(9899,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[9898]) ).
thf(9900,plain,
( ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9899:[]]) ).
thf(3753,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2730,11]) ).
thf(3754,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk5 @ p )
| ( A @ sk2 )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[3753]) ).
thf(3755,plain,
( ~ ( initial_world @ sk3 @ sk5 @ p )
| ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[3754:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(9019,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk2 )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[3101,3098]) ).
thf(9020,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[9019]) ).
thf(9021,plain,
( ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9020:[]]) ).
thf(17497,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,9021]) ).
thf(17498,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[17497]) ).
thf(17499,plain,
( ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[17498:[]]) ).
thf(20646,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( ( initial_world @ sk5 @ sk1 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[4212,14]) ).
thf(20647,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( ( initial_world @ sk5 @ sk1 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[20646]) ).
thf(20648,plain,
( ( initial_world @ sk5 @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk5 @ sk1 @ reachable ) )
| ( initial_world @ sk5 @ sk5 @ sk2 )
| ( ( initial_world @ sk5 @ sk1 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[20647:[bind(A,$thf( initial_world @ sk5 @ sk5 ))]]) ).
thf(21759,plain,
( ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk5 @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk5 @ sk1 @ reachable ) )
| ( initial_world @ sk5 @ sk5 @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[20648]) ).
thf(4133,plain,
( ~ $true
| ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[3112]) ).
thf(4139,plain,
( ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4133]) ).
thf(5417,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,4139]) ).
thf(5418,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[5417]) ).
thf(5419,plain,
( ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[5418:[]]) ).
thf(2726,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[54,2368]) ).
thf(2727,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2726]) ).
thf(2773,plain,
! [A: $i] :
( ( ( initial_world @ sk6 )
!= A )
| ( ( initial_world @ sk5 )
!= ( initial_world @ sk1 ) )
| ( A @ ( initial_world @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2727]) ).
thf(2793,plain,
( ( ( initial_world @ sk5 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk6 @ ( initial_world @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2773]) ).
thf(3818,plain,
( ~ $true
| ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[3035]) ).
thf(3824,plain,
( ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3818]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk1 @ ( B @ reachable ) )
| ~ $true
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[9,12]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk1 @ ( B @ reachable ) )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 )
!= B )
| ( ( A @ sk5 )
!= initial_world )
| ~ ( A @ ( initial_world @ reachable ) )
| ( B @ sk1 @ ( B @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[58]) ).
thf(73,plain,
! [A: $i] :
( ( ( A @ sk5 )
!= initial_world )
| ~ ( A @ ( initial_world @ reachable ) )
| ( A @ sk6 @ sk1 @ ( A @ sk6 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[69]) ).
thf(3356,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2696,12]) ).
thf(3357,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[3356]) ).
thf(3358,plain,
( ( initial_world @ sk4 @ sk1 @ ( initial_world @ sk4 @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[3357:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(9633,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[8026,12]) ).
thf(9634,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[9633]) ).
thf(9635,plain,
( ( initial_world @ sk1 @ sk3 @ sk1 @ ( initial_world @ sk1 @ sk3 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[9634:[bind(A,$thf( initial_world @ sk1 @ sk3 ))]]) ).
thf(12285,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[8233,8170]) ).
thf(12286,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[12285]) ).
thf(12287,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[12286:[]]) ).
thf(18416,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[803,2412]) ).
thf(18417,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[18416]) ).
thf(18418,plain,
( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[18417:[bind(A,$thf( initial_world @ sk1 @ sk3 ))]]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk1 @ ( B @ reachable ) )
| ~ $true
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[7,12]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk1 @ ( B @ reachable ) )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 )
!= B )
| ( ( A @ sk1 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( B @ sk1 @ ( B @ reachable ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(118,plain,
! [A: $i] :
( ( ( A @ sk1 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( A @ sk4 @ sk1 @ ( A @ sk4 @ reachable ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(543,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[457,38]) ).
thf(544,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[543]) ).
thf(545,plain,
( ~ ( initial_world @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[544:[]]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ~ ( B @ sk4 @ q )
| ~ $true
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[9,13]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ~ ( B @ sk4 @ q )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 )
!= B )
| ( ( A @ sk5 )
!= initial_world )
| ~ ( B @ sk2 )
| ~ ( B @ sk4 @ q )
| ~ ( A @ ( initial_world @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[65]) ).
thf(71,plain,
! [A: $i] :
( ( ( A @ sk5 )
!= initial_world )
| ~ ( A @ sk6 @ sk2 )
| ~ ( A @ sk6 @ sk4 @ q )
| ~ ( A @ ( initial_world @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[67]) ).
thf(15282,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,6593]) ).
thf(15283,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[15282]) ).
thf(15284,plain,
( ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[15283:[]]) ).
thf(2907,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ ( A @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2835,2192]) ).
thf(2908,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[2907]) ).
thf(2921,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 )
!= initial_world )
| ( ( initial_world @ sk1 @ sk1 )
!= A )
| ( initial_world @ sk1 @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[2908]) ).
thf(2935,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 )
!= initial_world )
| ( initial_world @ sk1 @ ( initial_world @ sk1 @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[2921]) ).
thf(7993,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[259,2868]) ).
thf(7994,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[7993]) ).
thf(7995,plain,
( ( initial_world @ sk1 @ sk3 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7994:[bind(A,$thf( initial_world @ sk1 @ sk3 ))]]) ).
thf(8743,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[7995,12]) ).
thf(8744,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[8743]) ).
thf(8745,plain,
( ( initial_world @ sk1 @ sk3 @ sk1 @ ( initial_world @ sk1 @ sk3 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8744:[bind(A,$thf( initial_world @ sk1 @ sk3 ))]]) ).
thf(3121,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2754,12]) ).
thf(3122,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3121]) ).
thf(3123,plain,
( ( initial_world @ sk3 @ sk1 @ ( initial_world @ sk3 @ reachable ) )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3122:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(15840,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( ( initial_world @ sk5 @ sk5 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[3889,14]) ).
thf(15841,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( ( initial_world @ sk5 @ sk5 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[15840]) ).
thf(15842,plain,
( ( initial_world @ sk5 @ sk6 @ sk5 @ ( initial_world @ sk5 @ sk6 @ sk1 @ reachable ) )
| ( initial_world @ sk5 @ sk6 @ sk2 )
| ( ( initial_world @ sk5 @ sk5 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[15841:[bind(A,$thf( initial_world @ sk5 @ sk6 ))]]) ).
thf(18307,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[259,2412]) ).
thf(18308,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[18307]) ).
thf(18309,plain,
( ( initial_world @ sk1 @ sk3 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[18308:[bind(A,$thf( initial_world @ sk1 @ sk3 ))]]) ).
thf(3719,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2730,13]) ).
thf(3720,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[3719]) ).
thf(3721,plain,
( ~ ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[3720:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(18122,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[3755,3721]) ).
thf(18123,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[18122]) ).
thf(18124,plain,
( ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[18123:[]]) ).
thf(3639,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2701,15]) ).
thf(3640,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[3639]) ).
thf(3641,plain,
( ~ ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[3640:[bind(A,$thf( initial_world @ sk4 ))]]) ).
thf(7931,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[88,2868]) ).
thf(7932,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[7931]) ).
thf(7933,plain,
( ( initial_world @ sk1 @ sk4 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7932:[bind(A,$thf( initial_world @ sk1 @ sk4 ))]]) ).
thf(3730,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2730,12]) ).
thf(3731,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[3730]) ).
thf(3732,plain,
( ( initial_world @ sk3 @ sk1 @ ( initial_world @ sk3 @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[3731:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(214,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[54,10]) ).
thf(215,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[214]) ).
thf(222,plain,
! [A: $i] :
( ( ( initial_world @ sk6 )
!= A )
| ( ( initial_world @ sk5 )
!= initial_world )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[215]) ).
thf(230,plain,
( ( ( initial_world @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk6 @ sk6 @ q )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[222]) ).
thf(175,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[83,9]) ).
thf(176,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[175]) ).
thf(183,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 )
!= A )
| ( ( initial_world @ sk6 @ sk5 )
!= initial_world )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[176]) ).
thf(187,plain,
( ( ( initial_world @ sk6 @ sk5 )
!= initial_world )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk6 @ sk5 @ reachable ) )
| ( initial_world @ sk6 @ sk6 @ sk2 )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[183]) ).
thf(2810,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2746,9]) ).
thf(2811,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[2810]) ).
thf(2812,plain,
( ( initial_world @ sk1 @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk1 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2811:[bind(A,$thf( initial_world @ sk1 @ sk1 ))]]) ).
thf(244,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,41]) ).
thf(245,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[244]) ).
thf(246,plain,
( ~ ( initial_world @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[245:[]]) ).
thf(321,plain,
( ~ $true
| ( ( initial_world @ sk6 @ q )
!= ( initial_world @ sk4 @ q ) )
| ~ ( initial_world @ sk4 @ q ) ),
inference(eqfactor_ordered,[status(thm)],[246]) ).
thf(323,plain,
( ( ( initial_world @ sk6 )
!= ( initial_world @ sk4 ) )
| ~ ( initial_world @ sk4 @ q ) ),
inference(simp,[status(thm)],[321]) ).
thf(45,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,13]) ).
thf(46,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q ) ),
inference(simp,[status(thm)],[45]) ).
thf(47,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 )
!= A )
| ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q ) ),
inference(simp,[status(thm)],[46]) ).
thf(48,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk1 @ sk2 )
| ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q ) ),
inference(simp,[status(thm)],[47]) ).
thf(239,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk1 )
!= initial_world )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,48]) ).
thf(240,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[239]) ).
thf(251,plain,
( ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[240]) ).
thf(1027,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,922]) ).
thf(1028,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[1027]) ).
thf(1029,plain,
( ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[1028:[]]) ).
thf(145,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[51,13]) ).
thf(146,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[145]) ).
thf(151,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 )
!= A )
| ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[146]) ).
thf(155,plain,
( ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk6 @ sk2 )
| ~ ( initial_world @ sk1 @ sk6 @ sk4 @ q )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[151]) ).
thf(7948,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[550,2868]) ).
thf(7949,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[7948]) ).
thf(7950,plain,
( ( initial_world @ sk1 @ sk4 @ ( initial_world @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[7949:[bind(A,$thf( initial_world @ sk1 @ sk4 ))]]) ).
thf(8851,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[7950,12]) ).
thf(8852,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[8851]) ).
thf(8853,plain,
( ( initial_world @ sk1 @ sk4 @ sk1 @ ( initial_world @ sk1 @ sk4 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[8852:[bind(A,$thf( initial_world @ sk1 @ sk4 ))]]) ).
thf(14874,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[3381,3347]) ).
thf(14875,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[14874]) ).
thf(14876,plain,
( ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[14875:[]]) ).
thf(191,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[88,10]) ).
thf(192,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[191]) ).
thf(218,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 )
!= A )
| ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ~ ( A @ sk6 @ q )
| ~ ( initial_world @ sk1 @ sk2 )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[192]) ).
thf(226,plain,
( ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk1 @ sk2 )
| ( initial_world @ sk1 @ sk4 @ sk2 ) ),
inference(simp,[status(thm)],[218]) ).
thf(123,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[91,9]) ).
thf(124,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[123]) ).
thf(131,plain,
! [A: $i] :
( ( ( initial_world @ sk4 )
!= A )
| ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk2 )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[124]) ).
thf(135,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk2 )
| ( initial_world @ sk4 @ sk6 @ ( initial_world @ sk4 @ sk5 @ reachable ) )
| ( initial_world @ sk4 @ sk2 ) ),
inference(simp,[status(thm)],[131]) ).
thf(14285,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ~ $true
| ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2858,2838]) ).
thf(14286,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[14285]) ).
thf(14287,plain,
( ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[14286:[]]) ).
thf(26502,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25991,13]) ).
thf(26503,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q ) ),
inference(simp,[status(thm)],[26502]) ).
thf(26504,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk2 )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk4 @ q ) ),
inference(pattern_uni,[status(thm)],[26503:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 @ sk1 ))]]) ).
thf(1032,plain,
( ~ $true
| ( ( initial_world @ sk5 @ p )
!= ( initial_world @ sk3 @ p ) )
| ~ ( initial_world @ sk3 @ p ) ),
inference(eqfactor_ordered,[status(thm)],[1024]) ).
thf(1034,plain,
( ( ( initial_world @ sk5 )
!= ( initial_world @ sk3 ) )
| ~ ( initial_world @ sk3 @ p ) ),
inference(simp,[status(thm)],[1032]) ).
thf(9725,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[8057,12]) ).
thf(9726,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[9725]) ).
thf(9727,plain,
( ( initial_world @ sk1 @ sk4 @ sk1 @ ( initial_world @ sk1 @ sk4 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[9726:[bind(A,$thf( initial_world @ sk1 @ sk4 ))]]) ).
thf(3291,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2691,12]) ).
thf(3292,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[3291]) ).
thf(3293,plain,
( ( initial_world @ sk3 @ sk1 @ ( initial_world @ sk3 @ reachable ) )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[3292:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(13779,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[3316,3282]) ).
thf(13780,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[13779]) ).
thf(13781,plain,
( ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[13780:[]]) ).
thf(26731,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[26154,14]) ).
thf(26732,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[26731]) ).
thf(26733,plain,
( ( initial_world @ sk1 @ sk1 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk1 @ sk5 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26732:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk5 ))]]) ).
thf(2475,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ ( A @ reachable ) )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[54,2192]) ).
thf(2476,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2475]) ).
thf(2536,plain,
! [A: $i] :
( ( ( initial_world @ sk6 )
!= initial_world )
| ( ( initial_world @ sk5 )
!= A )
| ( initial_world @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2476]) ).
thf(2582,plain,
( ( ( initial_world @ sk6 )
!= initial_world )
| ( initial_world @ sk1 @ ( initial_world @ sk5 @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[2536]) ).
thf(4747,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,3798]) ).
thf(4748,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[4747]) ).
thf(4749,plain,
( ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[4748:[]]) ).
thf(3857,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 @ ( initial_world @ sk5 @ sk5 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ ( A @ reachable ) )
| ~ $true
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2953,2192]) ).
thf(3858,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 @ ( initial_world @ sk5 @ sk5 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3857]) ).
thf(3871,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 )
!= initial_world )
| ( ( initial_world @ sk5 @ sk5 )
!= A )
| ( initial_world @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3858]) ).
thf(3904,plain,
( ( ( initial_world @ sk5 @ sk6 )
!= initial_world )
| ( initial_world @ sk1 @ ( initial_world @ sk5 @ sk5 @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3871]) ).
thf(7035,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ sk1 @ ( A @ reachable ) )
| ~ $true
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2962,2832]) ).
thf(7036,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[7035]) ).
thf(7127,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 )
!= initial_world )
| ( ( initial_world @ sk5 @ sk1 )
!= A )
| ( initial_world @ sk1 @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[7036]) ).
thf(7196,plain,
( ( ( initial_world @ sk5 @ sk5 )
!= initial_world )
| ( initial_world @ sk1 @ sk1 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[7127]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( ( A @ sk3 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk6 @ q )
| ( B @ sk2 )
| ~ $true
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[8,10]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( ( A @ sk3 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk6 @ q )
| ( B @ sk2 )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( ( A @ sk3 )
!= B )
| ( ( A @ sk1 )
!= initial_world )
| ~ ( B @ sk6 @ q )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( B @ sk2 ) ),
inference(simp,[status(thm)],[256]) ).
thf(310,plain,
! [A: $i] :
( ( ( A @ sk1 )
!= initial_world )
| ~ ( A @ sk3 @ sk6 @ q )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( A @ sk3 @ sk2 ) ),
inference(simp,[status(thm)],[296]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ q )
| ~ ( C @ ( A @ sk1 @ reachable ) )
| ( B @ p )
| ~ ( B @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ q )
| ~ ( C @ ( A @ sk1 @ reachable ) )
| ( B @ p )
| ~ ( B @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(9978,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk2 )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[3149,3112]) ).
thf(9979,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[9978]) ).
thf(9980,plain,
( ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9979:[]]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk2 )
| ( C @ q )
| ~ ( C @ ( B @ reachable ) )
| ( B @ p )
| ~ ( B @ ( A @ sk1 @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(4547,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2818,2815]) ).
thf(4548,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[4547]) ).
thf(4549,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[4548:[]]) ).
thf(18200,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[88,2412]) ).
thf(18201,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[18200]) ).
thf(18202,plain,
( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[18201:[bind(A,$thf( initial_world @ sk1 @ sk4 ))]]) ).
thf(3823,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3818]) ).
thf(5558,plain,
( ~ $true
| ( ( initial_world @ sk1 @ sk1 @ sk6 @ q )
!= ( initial_world @ sk1 @ sk1 @ sk4 @ q ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q ) ),
inference(eqfactor_ordered,[status(thm)],[4530]) ).
thf(5560,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk6 )
!= ( initial_world @ sk1 @ sk1 @ sk4 ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q ) ),
inference(simp,[status(thm)],[5558]) ).
thf(1083,plain,
( ~ $true
| ( ( initial_world @ sk1 @ sk5 @ p )
!= ( initial_world @ sk1 @ sk3 @ p ) )
| ~ ( initial_world @ sk1 @ sk3 @ p ) ),
inference(eqfactor_ordered,[status(thm)],[1042]) ).
thf(1085,plain,
( ( ( initial_world @ sk1 @ sk5 )
!= ( initial_world @ sk1 @ sk3 ) )
| ~ ( initial_world @ sk1 @ sk3 @ p ) ),
inference(simp,[status(thm)],[1083]) ).
thf(2054,plain,
( ~ $true
| ( ( initial_world @ sk1 @ sk5 @ p )
!= ( initial_world @ sk3 @ p ) )
| ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk3 @ p ) ),
inference(eqfactor_ordered,[status(thm)],[1031]) ).
thf(2056,plain,
( ( ( initial_world @ sk1 @ sk5 )
!= ( initial_world @ sk3 ) )
| ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk3 @ p ) ),
inference(simp,[status(thm)],[2054]) ).
thf(713,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[51,14]) ).
thf(714,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[713]) ).
thf(720,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 )
!= A )
| ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[714]) ).
thf(744,plain,
( ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ( initial_world @ sk1 @ sk6 @ sk5 @ ( initial_world @ sk1 @ sk6 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk6 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[720]) ).
thf(143,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ~ $true
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[51,7]) ).
thf(144,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[143]) ).
thf(150,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk6 )
!= A )
| ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[144]) ).
thf(154,plain,
( ( ( initial_world @ sk1 @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk6 @ sk2 )
| ( initial_world @ sk1 @ sk6 @ sk4 @ ( initial_world @ sk1 @ sk6 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[150]) ).
thf(8183,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8021,9]) ).
thf(8184,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[8183]) ).
thf(8185,plain,
( ( initial_world @ sk1 @ sk1 @ sk1 @ sk6 @ ( initial_world @ sk1 @ sk1 @ sk1 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8184:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 ))]]) ).
thf(26470,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25991,10]) ).
thf(26471,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[26470]) ).
thf(26472,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk6 @ q )
| ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26471:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 @ sk1 ))]]) ).
thf(26755,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[26154,9]) ).
thf(26756,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[26755]) ).
thf(26757,plain,
( ( initial_world @ sk1 @ sk1 @ sk5 @ sk6 @ ( initial_world @ sk1 @ sk1 @ sk5 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26756:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk5 ))]]) ).
thf(30925,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk5 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk5 @ ( A @ reachable ) )
| ~ $true
| ( initial_world @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[8382,2973]) ).
thf(30926,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk5 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk5 @ ( A @ reachable ) )
| ( initial_world @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[30925]) ).
thf(31345,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk5 )
!= initial_world )
| ( ( initial_world @ sk1 @ sk5 @ sk1 )
!= A )
| ( initial_world @ sk5 @ ( A @ reachable ) )
| ( initial_world @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[30926]) ).
thf(31486,plain,
( ( ( initial_world @ sk1 @ sk5 @ sk5 )
!= initial_world )
| ( initial_world @ sk5 @ ( initial_world @ sk1 @ sk5 @ sk1 @ reachable ) )
| ( initial_world @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[31345]) ).
thf(3707,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2730,15]) ).
thf(3708,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[3707]) ).
thf(3709,plain,
( ~ ( initial_world @ sk3 @ sk2 )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[3708:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(18083,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[3755,3709]) ).
thf(18084,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[18083]) ).
thf(18085,plain,
( ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[18084:[]]) ).
thf(14342,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ~ $true
| ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[2818,2838]) ).
thf(14343,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[14342]) ).
thf(14344,plain,
( ( initial_world @ sk1 @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[14343:[]]) ).
thf(13630,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[3276,3273]) ).
thf(13631,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk3 @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[13630]) ).
thf(13632,plain,
( ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk3 @ sk6 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[13631:[]]) ).
thf(3797,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[3791]) ).
thf(232,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,88]) ).
thf(233,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[232]) ).
thf(250,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk6 @ q )
| ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(209,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ~ $true
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[83,10]) ).
thf(210,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk6 @ q )
| ( A @ sk2 )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[209]) ).
thf(223,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 )
!= A )
| ( ( initial_world @ sk6 @ sk5 )
!= initial_world )
| ~ ( A @ sk6 @ q )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( A @ sk2 )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[210]) ).
thf(231,plain,
( ( ( initial_world @ sk6 @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk6 @ sk6 @ sk6 @ q )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk6 @ sk2 )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[223]) ).
thf(4138,plain,
( ( ( initial_world @ sk3 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4133]) ).
thf(1084,plain,
( ( ( initial_world @ sk1 @ sk5 @ p )
!= ( initial_world @ sk1 @ sk3 @ p ) )
| ~ ( initial_world @ sk1 @ sk3 @ p ) ),
inference(simp,[status(thm)],[1083]) ).
thf(4613,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[2858,2824]) ).
thf(4614,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[4613]) ).
thf(4615,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[4614:[]]) ).
thf(5424,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,4139]) ).
thf(5425,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[5424]) ).
thf(5426,plain,
( ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[5425:[]]) ).
thf(161,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ $true
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[88,13]) ).
thf(162,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[161]) ).
thf(167,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 )
!= A )
| ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( A @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[162]) ).
thf(171,plain,
( ( ( initial_world @ sk1 @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk4 @ sk2 )
| ~ ( initial_world @ sk1 @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[167]) ).
thf(11181,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[8382,14]) ).
thf(11182,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[11181]) ).
thf(11261,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ sk5 )
!= A )
| ( ( initial_world @ sk1 @ sk5 @ sk1 )
!= initial_world )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[11182]) ).
thf(11287,plain,
( ( ( initial_world @ sk1 @ sk5 @ sk1 )
!= initial_world )
| ( initial_world @ sk1 @ sk5 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk5 @ sk5 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk5 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[11261]) ).
thf(4772,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,3824]) ).
thf(4773,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[4772]) ).
thf(4774,plain,
( ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[4773:[]]) ).
thf(7397,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk2 )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[3072,3021]) ).
thf(7398,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[7397]) ).
thf(7399,plain,
( ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7398:[]]) ).
thf(1020,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[195,922]) ).
thf(1021,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[1020]) ).
thf(1030,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[1021]) ).
thf(107,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ~ $true
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[54,7]) ).
thf(108,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ ( initial_world @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[107]) ).
thf(115,plain,
! [A: $i] :
( ( ( initial_world @ sk6 )
!= A )
| ( ( initial_world @ sk5 )
!= initial_world )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[108]) ).
thf(119,plain,
( ( ( initial_world @ sk5 )
!= initial_world )
| ~ ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk6 @ sk4 @ ( initial_world @ sk6 @ sk1 @ reachable ) )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[115]) ).
thf(5406,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ $true
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[198,4111]) ).
thf(5407,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[5406]) ).
thf(5408,plain,
( ( ( initial_world @ sk3 )
!= initial_world )
| ~ ( initial_world @ sk3 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[5407:[]]) ).
thf(12271,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[8233,8190]) ).
thf(12272,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk1 @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk5 @ p ) ),
inference(simp,[status(thm)],[12271]) ).
thf(12273,plain,
( ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk4 @ q )
| ~ ( initial_world @ sk1 @ sk1 @ sk1 @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[12272:[]]) ).
thf(8386,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( ( A @ sk5 )
!= initial_world )
| ~ $true
| ( A @ sk6 @ sk6 @ ( A @ sk6 @ sk5 @ reachable ) )
| ( A @ sk6 @ sk2 )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[7985,70]) ).
thf(8387,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( ( A @ sk5 )
!= initial_world )
| ( A @ sk6 @ sk6 @ ( A @ sk6 @ sk5 @ reachable ) )
| ( A @ sk6 @ sk2 )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[8386]) ).
thf(8388,plain,
( ( ( initial_world @ sk1 @ sk5 @ sk5 )
!= initial_world )
| ( initial_world @ sk1 @ sk5 @ sk6 @ sk6 @ ( initial_world @ sk1 @ sk5 @ sk6 @ sk5 @ reachable ) )
| ( initial_world @ sk1 @ sk5 @ sk6 @ sk2 )
| ( initial_world @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8387:[bind(A,$thf( initial_world @ sk1 @ sk5 ))]]) ).
thf(4148,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2962,14]) ).
thf(4149,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4148]) ).
thf(4201,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 )
!= A )
| ( ( initial_world @ sk5 @ sk1 )
!= initial_world )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4149]) ).
thf(4214,plain,
( ( ( initial_world @ sk5 @ sk1 )
!= initial_world )
| ( initial_world @ sk5 @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk5 @ sk1 @ reachable ) )
| ( initial_world @ sk5 @ sk5 @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4201]) ).
thf(18407,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[326,2412]) ).
thf(18408,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ sk1 @ sk1 @ reachable ) ) )
| ( A @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[18407]) ).
thf(18409,plain,
( ( initial_world @ sk1 @ sk4 @ ( initial_world @ sk1 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[18408:[bind(A,$thf( initial_world @ sk1 @ sk4 ))]]) ).
thf(16223,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[3687,3641]) ).
thf(16224,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[16223]) ).
thf(16225,plain,
( ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[16224:[]]) ).
thf(15852,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( ( initial_world @ sk5 @ sk5 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[3889,9]) ).
thf(15853,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk6 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( ( initial_world @ sk5 @ sk5 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[15852]) ).
thf(15854,plain,
( ( initial_world @ sk5 @ sk6 @ sk6 @ ( initial_world @ sk5 @ sk6 @ sk5 @ reachable ) )
| ( initial_world @ sk5 @ sk6 @ sk2 )
| ( ( initial_world @ sk5 @ sk5 )
!= ( initial_world @ sk1 ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[15853:[bind(A,$thf( initial_world @ sk5 @ sk6 ))]]) ).
thf(1038,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,919]) ).
thf(1039,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[1038]) ).
thf(1045,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[1039]) ).
thf(6488,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk2 )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[3024,3021]) ).
thf(6489,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[6488]) ).
thf(6490,plain,
( ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6489:[]]) ).
thf(181,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[83,12]) ).
thf(182,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 @ ( initial_world @ sk6 @ sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[181]) ).
thf(186,plain,
! [A: $i] :
( ( ( initial_world @ sk6 @ sk6 )
!= A )
| ( ( initial_world @ sk6 @ sk5 )
!= initial_world )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( A @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[182]) ).
thf(190,plain,
( ( ( initial_world @ sk6 @ sk5 )
!= initial_world )
| ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk6 @ sk6 @ sk1 @ ( initial_world @ sk6 @ sk6 @ reachable ) )
| ( initial_world @ sk6 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[186]) ).
thf(8307,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[7933,12]) ).
thf(8308,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk4 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk1 @ ( A @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[8307]) ).
thf(8309,plain,
( ( initial_world @ sk1 @ sk4 @ sk1 @ ( initial_world @ sk1 @ sk4 @ reachable ) )
| ~ ( initial_world @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8308:[bind(A,$thf( initial_world @ sk1 @ sk4 ))]]) ).
thf(15228,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,6490]) ).
thf(15229,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[15228]) ).
thf(15230,plain,
( ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk6 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[15229:[]]) ).
thf(4142,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2962,9]) ).
thf(4143,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4142]) ).
thf(4197,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 )
!= A )
| ( ( initial_world @ sk5 @ sk1 )
!= initial_world )
| ( A @ sk6 @ ( A @ sk5 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4143]) ).
thf(4210,plain,
( ( ( initial_world @ sk5 @ sk1 )
!= initial_world )
| ( initial_world @ sk5 @ sk5 @ sk6 @ ( initial_world @ sk5 @ sk5 @ sk5 @ reachable ) )
| ( initial_world @ sk5 @ sk5 @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4197]) ).
thf(1033,plain,
( ( ( initial_world @ sk5 @ p )
!= ( initial_world @ sk3 @ p ) )
| ~ ( initial_world @ sk3 @ p ) ),
inference(simp,[status(thm)],[1032]) ).
thf(125,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ~ $true
| ~ ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[91,7]) ).
thf(126,plain,
! [A: $i] :
( ( ( initial_world @ sk4 @ ( initial_world @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) )
| ~ ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[125]) ).
thf(132,plain,
! [A: $i] :
( ( ( initial_world @ sk4 )
!= A )
| ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( A @ sk2 )
| ~ ( initial_world @ sk2 )
| ( A @ sk4 @ ( A @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(136,plain,
( ( ( initial_world @ sk1 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk2 )
| ~ ( initial_world @ sk2 )
| ( initial_world @ sk4 @ sk4 @ ( initial_world @ sk4 @ sk1 @ reachable ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(28914,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk1 @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true
| ( initial_world @ sk1 @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[26733,14]) ).
thf(28915,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk1 @ sk5 @ sk1 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[28914]) ).
thf(28994,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ sk5 )
!= A )
| ( ( initial_world @ sk1 @ sk1 @ sk5 @ sk1 )
!= initial_world )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[28915]) ).
thf(29015,plain,
( ( ( initial_world @ sk1 @ sk1 @ sk5 @ sk1 )
!= initial_world )
| ( initial_world @ sk1 @ sk1 @ sk5 @ sk5 @ sk5 @ ( initial_world @ sk1 @ sk1 @ sk5 @ sk5 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk5 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk5 @ sk2 )
| ( initial_world @ sk1 @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[28994]) ).
thf(23322,plain,
( ( ( initial_world @ sk5 )
!= initial_world )
| ( initial_world @ sk5 @ sk5 @ sk6 @ ( initial_world @ sk5 @ sk5 @ sk5 @ reachable ) )
| ( initial_world @ sk5 @ sk5 @ sk2 )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[20662]) ).
thf(26473,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25991,14]) ).
thf(26474,plain,
! [A: $i] :
( ( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk5 @ ( A @ sk1 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[26473]) ).
thf(26475,plain,
( ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk5 @ ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk1 @ reachable ) )
| ( initial_world @ sk1 @ sk1 @ sk1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26474:[bind(A,$thf( initial_world @ sk1 @ sk1 @ sk1 @ sk1 ))]]) ).
thf(14757,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk6 @ q )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[3381,3338]) ).
thf(14758,plain,
( ( ( initial_world @ sk4 @ sk2 )
!= ( initial_world @ sk4 @ sk2 ) )
| ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(simp,[status(thm)],[14757]) ).
thf(14759,plain,
( ~ ( initial_world @ sk4 @ sk3 @ p )
| ~ ( initial_world @ sk4 @ sk5 @ p )
| ~ ( initial_world @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[14758:[]]) ).
thf(4168,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ ( A @ reachable ) )
| ~ $true
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2962,2192]) ).
thf(4169,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
!= ( initial_world @ ( A @ reachable ) ) )
| ( initial_world @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4168]) ).
thf(4190,plain,
! [A: $i] :
( ( ( initial_world @ sk5 @ sk5 )
!= initial_world )
| ( ( initial_world @ sk5 @ sk1 )
!= A )
| ( initial_world @ sk1 @ ( A @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4169]) ).
thf(4221,plain,
( ( ( initial_world @ sk5 @ sk5 )
!= initial_world )
| ( initial_world @ sk1 @ ( initial_world @ sk5 @ sk1 @ reachable ) )
| ( initial_world @ sk5 @ sk2 )
| ( initial_world @ sk2 ) ),
inference(simp,[status(thm)],[4190]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ( B @ sk4 @ ( B @ sk1 @ reachable ) )
| ~ $true
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[9,7]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk5 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ( B @ sk4 @ ( B @ sk1 @ reachable ) )
| ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 )
!= B )
| ( ( A @ sk5 )
!= initial_world )
| ~ ( B @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( B @ sk4 @ ( B @ sk1 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[95]) ).
thf(122,plain,
! [A: $i] :
( ( ( A @ sk5 )
!= initial_world )
| ~ ( A @ sk6 @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) )
| ( A @ sk6 @ sk4 @ ( A @ sk6 @ sk1 @ reachable ) )
| ( A @ sk2 ) ),
inference(simp,[status(thm)],[111]) ).
thf(4765,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ $true
| ~ ( initial_world @ sk5 @ p ) ),
inference(paramod_ordered,[status(thm)],[460,3824]) ).
thf(4766,plain,
( ( ( initial_world @ sk2 )
!= ( initial_world @ sk2 ) )
| ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(simp,[status(thm)],[4765]) ).
thf(4767,plain,
( ( ( initial_world @ sk4 )
!= initial_world )
| ~ ( initial_world @ sk4 @ sk4 @ q )
| ~ ( initial_world @ sk5 @ p ) ),
inference(pattern_uni,[status(thm)],[4766:[]]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( ( A @ sk3 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ~ ( B @ sk4 @ q )
| ~ $true
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(paramod_ordered,[status(thm)],[8,13]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( ( A @ sk3 @ ( A @ sk1 @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk2 )
| ~ ( B @ sk4 @ q )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[279]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ( ( A @ sk3 )
!= B )
| ( ( A @ sk1 )
!= initial_world )
| ~ ( B @ sk2 )
| ~ ( B @ sk4 @ q )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(309,plain,
! [A: $i] :
( ( ( A @ sk1 )
!= initial_world )
| ~ ( A @ sk3 @ sk2 )
| ~ ( A @ sk3 @ sk4 @ q )
| ~ ( A @ sk2 )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[295]) ).
thf(1035,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ $true
| ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(paramod_ordered,[status(thm)],[195,919]) ).
thf(1036,plain,
( ( ( initial_world @ sk1 @ sk2 )
!= ( initial_world @ sk1 @ sk2 ) )
| ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(simp,[status(thm)],[1035]) ).
thf(1037,plain,
( ~ ( initial_world @ sk1 @ sk3 @ p )
| ~ ( initial_world @ sk1 @ sk6 @ q ) ),
inference(pattern_uni,[status(thm)],[1036:[]]) ).
thf(322,plain,
( ( ( initial_world @ sk6 @ q )
!= ( initial_world @ sk4 @ q ) )
| ~ ( initial_world @ sk4 @ q ) ),
inference(simp,[status(thm)],[321]) ).
thf(43011,plain,
$false,
inference(e,[status(thm)],[3021,3798,2412,88,26016,1024,3477,1031,249,170,26746,2976,3072,2953,308,5,120,379,7516,27195,3098,741,878,11556,10,18356,18592,533,550,4110,8057,3338,8210,153,3276,13830,20662,8671,27403,25,26547,27266,26553,1046,14669,14,14552,3046,3653,9099,3644,542,460,2691,26782,11981,189,20,5802,11827,2730,228,4756,5974,5792,8190,8416,121,16172,8246,84,5401,2861,3712,6021,8173,2965,5819,527,3899,8170,8233,85,8382,27474,307,380,117,8201,5751,1042,38,70,21,3664,13583,3889,3282,252,8026,329,20637,10580,224,229,566,665,8021,2300,18293,156,2973,3381,9,188,26499,2858,169,11278,8176,6593,2868,8687,4530,6065,18225,26524,457,18347,13,17559,9900,41,3755,17499,4212,21759,2368,5419,2793,662,3824,73,7985,3358,9021,9635,12287,22,18418,118,545,259,2959,8064,71,12,54,15284,2935,8745,3123,15842,18309,18124,919,3641,7995,7933,3732,230,362,3101,187,7,4139,2824,2812,323,91,251,1029,155,198,8853,2962,2835,14876,3687,226,2999,922,135,14287,26504,1034,9727,3293,13781,812,26733,2582,4749,2715,2192,3904,7196,2821,310,18,3112,9980,3273,16,4549,2701,18202,31,3823,5560,1085,8391,2056,744,2838,154,11,8185,4634,3024,4111,26472,26757,31486,18085,2818,539,2696,14344,13632,3797,250,231,4138,1084,7950,3709,4615,5426,171,11287,8,4774,7399,1030,2956,119,25991,5408,246,12273,8388,4214,18409,3149,346,16225,15854,1045,26167,262,51,19,6490,2815,2736,190,8309,15230,326,3347,4210,195,1033,20648,136,2746,29015,23322,26475,15,14759,26154,4221,3341,803,122,83,4767,309,2832,1037,3316,3721,3035,2754,322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN548+1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % 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
% 0.14/5.42 % Computer : n006.cluster.edu
% 0.14/5.42 % Model : x86_64 x86_64
% 0.14/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.42 % Memory : 8046.5625MB
% 0.14/5.42 % OS : Linux 6.8.0-71-generic
% 0.14/5.42 % CPULimit : 300
% 0.14/5.42 % WCLimit : 300
% 0.14/5.42 % DateTime : Sat Sep 26 18:13:03 UTC 2026
% 0.14/5.42 % CPUTime :
% 0.14/5.42 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
% 0.18/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.39/6.20 % [INFO] Parsing done (188ms).
% 1.39/6.22 % [INFO] Running in sequential loop mode.
% 2.05/6.61 % [INFO] eprover registered as external prover.
% 2.05/6.62 % [INFO] Scanning for conjecture ...
% 2.25/6.72 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.25/6.76 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.25/6.77 % [INFO] Problem is first-order (TPTP FOF).
% 2.25/6.78 % [INFO] Type checking passed.
% 2.25/6.78 % [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 ...
% 80.40/23.08 % External prover 'e' found a proof!
% 80.40/23.08 % [INFO] Killing All external provers ...
% 80.40/23.09 % Time passed: 17522ms (effective reasoning time: 16860ms)
% 80.40/23.09 % 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)>
% 80.40/23.09 % Axioms used in derivation (2): reflexivity_of_reachable, transitivity_of_reachable
% 80.40/23.09 % No. of inferences in proof: 929
% 80.40/23.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17522 ms resp. 16860 ms w/o parsing
% 67.20/23.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 67.20/23.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------