TSTP Solution File: LCL953_8 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL953_8 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 17:26:54 EDT 2024

% Result   : Theorem 0.19s 0.54s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : LCL953_8 : TPTP v8.2.0. Released v8.2.0.
% 0.13/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34  % CPULimit   : 300
% 0.19/0.34  % WCLimit    : 300
% 0.19/0.34  % DateTime   : Mon May 27 20:57:38 EDT 2024
% 0.19/0.35  % CPUTime    : 
% 0.19/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.54  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.54  % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.gwycqHMzHu/cvc5---1.0.5_11520.smt2
% 0.19/0.54  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.gwycqHMzHu/cvc5---1.0.5_11520.smt2
% 0.19/0.54  (assume a0 (forall ((W |tptp.'$ki_world'|)) (|tptp.'$ki_accessible'| W W)))
% 0.19/0.54  (assume a1 (forall ((W |tptp.'$ki_world'|)) (exists ((X $$unsorted)) (|tptp.'$ki_exists_in_world_$i'| W X))))
% 0.19/0.54  (assume a2 (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 A B))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 B A)))))))))))))))
% 0.19/0.54  (assume a3 (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.in W2 A B))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 B A))))))))))))))))))
% 0.19/0.54  (assume a4 (exists ((A $$unsorted)) (and (|tptp.'$ki_exists_in_world_$i'| |tptp.'$ki_local_world'| A) (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (tptp.empty W A))))))
% 0.19/0.54  (assume a5 (exists ((A $$unsorted)) (and (|tptp.'$ki_exists_in_world_$i'| |tptp.'$ki_local_world'| A) (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (not (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (tptp.empty W0 A)))))))))
% 0.19/0.54  (assume a6 (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))))))))
% 0.19/0.54  (assume a7 (not (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))))))))))))
% 0.19/0.54  (assume a8 true)
% 0.19/0.54  (step t1 (cl (not (= (not (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))))))))))) (not (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473)))))) (not (not (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))))))))) (not (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473))))) :rule equiv_pos2)
% 0.19/0.54  (anchor :step t2 :args ((W |tptp.'$ki_world'|) (:= W W)))
% 0.19/0.54  (step t2.t1 (cl (= W W)) :rule refl)
% 0.19/0.54  (step t2.t2 (cl (= (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W))) :rule refl)
% 0.19/0.54  (anchor :step t2.t3 :args ((A $$unsorted) (:= A A)))
% 0.19/0.54  (step t2.t3.t1 (cl (= A A)) :rule refl)
% 0.19/0.54  (step t2.t3.t2 (cl (= (|tptp.'$ki_exists_in_world_$i'| W A) (|tptp.'$ki_exists_in_world_$i'| W A))) :rule refl)
% 0.19/0.54  (anchor :step t2.t3.t3 :args ((W0 |tptp.'$ki_world'|) (:= W0 W0)))
% 0.19/0.54  (step t2.t3.t3.t1 (cl (= W0 W0)) :rule refl)
% 0.19/0.54  (step t2.t3.t3.t2 (cl (= (|tptp.'$ki_accessible'| W W0) (|tptp.'$ki_accessible'| W W0))) :rule refl)
% 0.19/0.54  (anchor :step t2.t3.t3.t3 :args ((B $$unsorted) (:= B B)))
% 0.19/0.54  (step t2.t3.t3.t3.t1 (cl (= B B)) :rule refl)
% 0.19/0.54  (step t2.t3.t3.t3.t2 (cl (= (|tptp.'$ki_exists_in_world_$i'| W0 B) (|tptp.'$ki_exists_in_world_$i'| W0 B))) :rule refl)
% 0.19/0.54  (anchor :step t2.t3.t3.t3.t3 :args ((W1 |tptp.'$ki_world'|) (:= W1 W1)))
% 0.19/0.54  (step t2.t3.t3.t3.t3.t1 (cl (= W1 W1)) :rule refl)
% 0.19/0.54  (step t2.t3.t3.t3.t3.t2 (cl (= (|tptp.'$ki_accessible'| W0 W1) (|tptp.'$ki_accessible'| W0 W1))) :rule refl)
% 0.19/0.54  (anchor :step t2.t3.t3.t3.t3.t3 :args ((W2 |tptp.'$ki_world'|) (:= W2 W2)))
% 0.19/0.54  (step t2.t3.t3.t3.t3.t3.t1 (cl (= W2 W2)) :rule refl)
% 0.19/0.54  (step t2.t3.t3.t3.t3.t3.t2 (cl (= (|tptp.'$ki_accessible'| W1 W2) (|tptp.'$ki_accessible'| W1 W2))) :rule refl)
% 0.19/0.54  (step t2.t3.t3.t3.t3.t3.t3 (cl (= (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B))) (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))) :rule all_simplify)
% 0.19/0.54  (step t2.t3.t3.t3.t3.t3.t4 (cl (= (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) :rule cong :premises (t2.t3.t3.t3.t3.t3.t3))
% 0.19/0.54  (step t2.t3.t3.t3.t3.t3.t5 (cl (= (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B))))) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) :rule cong :premises (t2.t3.t3.t3.t3.t3.t2 t2.t3.t3.t3.t3.t3.t4))
% 0.19/0.54  (step t2.t3.t3.t3.t3.t3 (cl (= (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))))) :rule bind)
% 0.19/0.54  (step t2.t3.t3.t3.t3.t4 (cl (= (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))))) :rule all_simplify)
% 0.19/0.54  (step t2.t3.t3.t3.t3.t5 (cl (= (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))))) :rule trans :premises (t2.t3.t3.t3.t3.t3 t2.t3.t3.t3.t3.t4))
% 0.19/0.54  (step t2.t3.t3.t3.t3.t6 (cl (= (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B))))) :rule all_simplify)
% 0.19/0.54  (step t2.t3.t3.t3.t3.t7 (cl (= (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))) (=> (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B)))))) :rule cong :premises (t2.t3.t3.t3.t3.t5 t2.t3.t3.t3.t3.t6))
% 0.19/0.54  (step t2.t3.t3.t3.t3.t8 (cl (= (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B))))))) :rule cong :premises (t2.t3.t3.t3.t3.t2 t2.t3.t3.t3.t3.t7))
% 0.19/0.54  (step t2.t3.t3.t3.t3 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B)))))))) :rule bind)
% 0.19/0.54  (step t2.t3.t3.t3.t4 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B)))))) (forall ((W1 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B))))))) :rule all_simplify)
% 0.19/0.54  (step t2.t3.t3.t3.t5 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B))))) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (or (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B)))))) :rule all_simplify)
% 0.19/0.54  (anchor :step t2.t3.t3.t3.t6 :args ((W1 |tptp.'$ki_world'|) (:= W1 W1) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1360 BOUND_VARIABLE_1360)))
% 0.19/0.54  (step t2.t3.t3.t3.t6.t1 (cl (= W1 W1)) :rule refl)
% 0.19/0.54  (step t2.t3.t3.t3.t6.t2 (cl (= BOUND_VARIABLE_1360 BOUND_VARIABLE_1360)) :rule refl)
% 0.19/0.54  (step t2.t3.t3.t3.t6.t3 (cl (= (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (or (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B))) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B)))) :rule all_simplify)
% 0.19/0.54  (step t2.t3.t3.t3.t6 (cl (= (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (or (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B)))) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B))))) :rule bind)
% 0.19/0.54  (step t2.t3.t3.t3.t7 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B))))) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B))))) :rule trans :premises (t2.t3.t3.t3.t5 t2.t3.t3.t3.t6))
% 0.19/0.54  (step t2.t3.t3.t3.t8 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B)))))) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B))))) :rule trans :premises (t2.t3.t3.t3.t4 t2.t3.t3.t3.t7))
% 0.19/0.54  (step t2.t3.t3.t3.t9 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B))))) :rule trans :premises (t2.t3.t3.t3.t3 t2.t3.t3.t3.t8))
% 0.19/0.54  (step t2.t3.t3.t3.t10 (cl (= (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B)))))) :rule cong :premises (t2.t3.t3.t3.t2 t2.t3.t3.t3.t9))
% 0.19/0.54  (step t2.t3.t3.t3 (cl (= (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B))))))) :rule bind)
% 0.19/0.54  (step t2.t3.t3.t4 (cl (= (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B))))) (forall ((B $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B))))))) :rule all_simplify)
% 0.19/0.54  (step t2.t3.t3.t5 (cl (= (forall ((B $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B))))) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (or (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B)))))) :rule all_simplify)
% 0.19/0.54  (anchor :step t2.t3.t3.t6 :args ((B $$unsorted) (:= B B) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1378 BOUND_VARIABLE_1378) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1376 BOUND_VARIABLE_1376)))
% 0.19/0.54  (step t2.t3.t3.t6.t1 (cl (= B B)) :rule refl)
% 0.19/0.54  (step t2.t3.t3.t6.t2 (cl (= BOUND_VARIABLE_1378 BOUND_VARIABLE_1378)) :rule refl)
% 0.19/0.54  (step t2.t3.t3.t6.t3 (cl (= BOUND_VARIABLE_1376 BOUND_VARIABLE_1376)) :rule refl)
% 0.19/0.54  (step t2.t3.t3.t6.t4 (cl (= (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (or (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B))) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B)))) :rule all_simplify)
% 0.19/0.54  (step t2.t3.t3.t6 (cl (= (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (or (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B)))) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B))))) :rule bind)
% 0.19/0.54  (step t2.t3.t3.t7 (cl (= (forall ((B $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B))))) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B))))) :rule trans :premises (t2.t3.t3.t5 t2.t3.t3.t6))
% 0.19/0.54  (step t2.t3.t3.t8 (cl (= (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1360 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1360)) (tptp.disjoint BOUND_VARIABLE_1360 (tptp.singleton A) B))))) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B))))) :rule trans :premises (t2.t3.t3.t4 t2.t3.t3.t7))
% 0.19/0.54  (step t2.t3.t3.t9 (cl (= (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B))))) :rule trans :premises (t2.t3.t3.t3 t2.t3.t3.t8))
% 0.19/0.54  (step t2.t3.t3.t10 (cl (= (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))))) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B)))))) :rule cong :premises (t2.t3.t3.t2 t2.t3.t3.t9))
% 0.19/0.54  (step t2.t3.t3 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B))))))) :rule bind)
% 0.19/0.54  (step t2.t3.t4 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B))))) (forall ((W0 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W W0)) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B))))))) :rule all_simplify)
% 0.19/0.54  (step t2.t3.t5 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W W0)) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B))))) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401)))))) :rule all_simplify)
% 0.19/0.54  (anchor :step t2.t3.t6 :args ((W0 |tptp.'$ki_world'|) (:= W0 W0) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1405 BOUND_VARIABLE_1405) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1403 BOUND_VARIABLE_1403) (BOUND_VARIABLE_1401 $$unsorted) (:= BOUND_VARIABLE_1401 BOUND_VARIABLE_1401)))
% 0.19/0.54  (step t2.t3.t6.t1 (cl (= W0 W0)) :rule refl)
% 0.19/0.54  (step t2.t3.t6.t2 (cl (= BOUND_VARIABLE_1405 BOUND_VARIABLE_1405)) :rule refl)
% 0.19/0.54  (step t2.t3.t6.t3 (cl (= BOUND_VARIABLE_1403 BOUND_VARIABLE_1403)) :rule refl)
% 0.19/0.54  (step t2.t3.t6.t4 (cl (= BOUND_VARIABLE_1401 BOUND_VARIABLE_1401)) :rule refl)
% 0.19/0.54  (step t2.t3.t6.t5 (cl (= (or (not (|tptp.'$ki_accessible'| W W0)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401))) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401)))) :rule all_simplify)
% 0.19/0.54  (step t2.t3.t6 (cl (= (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401)))) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401))))) :rule bind)
% 0.19/0.54  (step t2.t3.t7 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W W0)) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B))))) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401))))) :rule trans :premises (t2.t3.t5 t2.t3.t6))
% 0.19/0.54  (step t2.t3.t8 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted) (BOUND_VARIABLE_1378 |tptp.'$ki_world'|) (BOUND_VARIABLE_1376 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1376)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1376 BOUND_VARIABLE_1378)) (tptp.disjoint BOUND_VARIABLE_1378 (tptp.singleton A) B))))) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401))))) :rule trans :premises (t2.t3.t4 t2.t3.t7))
% 0.19/0.54  (step t2.t3.t9 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401))))) :rule trans :premises (t2.t3.t3 t2.t3.t8))
% 0.19/0.54  (step t2.t3.t10 (cl (= (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))))))) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401)))))) :rule cong :premises (t2.t3.t2 t2.t3.t9))
% 0.19/0.54  (step t2.t3 (cl (= (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))))) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401))))))) :rule bind)
% 0.19/0.54  (step t2.t4 (cl (= (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401))))) (forall ((A $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401))))))) :rule all_simplify)
% 0.19/0.54  (step t2.t5 (cl (= (forall ((A $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401))))) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (or (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440)))))) :rule all_simplify)
% 0.19/0.54  (anchor :step t2.t6 :args ((A $$unsorted) (:= A A) (BOUND_VARIABLE_1440 $$unsorted) (:= BOUND_VARIABLE_1440 BOUND_VARIABLE_1440) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1438 BOUND_VARIABLE_1438) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1436 BOUND_VARIABLE_1436) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1434 BOUND_VARIABLE_1434)))
% 0.19/0.54  (step t2.t6.t1 (cl (= A A)) :rule refl)
% 0.19/0.54  (step t2.t6.t2 (cl (= BOUND_VARIABLE_1440 BOUND_VARIABLE_1440)) :rule refl)
% 0.19/0.54  (step t2.t6.t3 (cl (= BOUND_VARIABLE_1438 BOUND_VARIABLE_1438)) :rule refl)
% 0.19/0.54  (step t2.t6.t4 (cl (= BOUND_VARIABLE_1436 BOUND_VARIABLE_1436)) :rule refl)
% 0.19/0.54  (step t2.t6.t5 (cl (= BOUND_VARIABLE_1434 BOUND_VARIABLE_1434)) :rule refl)
% 0.19/0.54  (step t2.t6.t6 (cl (= (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (or (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440))) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440)))) :rule all_simplify)
% 0.19/0.54  (step t2.t6 (cl (= (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (or (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440)))) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440))))) :rule bind)
% 0.19/0.54  (step t2.t7 (cl (= (forall ((A $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401))))) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440))))) :rule trans :premises (t2.t5 t2.t6))
% 0.19/0.54  (step t2.t8 (cl (= (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1405 |tptp.'$ki_world'|) (BOUND_VARIABLE_1403 |tptp.'$ki_world'|) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1401)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1405)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1401))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1405 BOUND_VARIABLE_1403)) (tptp.disjoint BOUND_VARIABLE_1403 (tptp.singleton A) BOUND_VARIABLE_1401))))) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440))))) :rule trans :premises (t2.t4 t2.t7))
% 0.19/0.54  (step t2.t9 (cl (= (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))))) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440))))) :rule trans :premises (t2.t3 t2.t8))
% 0.19/0.54  (step t2.t10 (cl (= (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))))))))) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440)))))) :rule cong :premises (t2.t2 t2.t9))
% 0.19/0.54  (step t2 (cl (= (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))))))) (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440))))))) :rule bind)
% 0.19/0.54  (step t3 (cl (= (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440))))) (forall ((W |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440))))))) :rule all_simplify)
% 0.19/0.54  (step t4 (cl (= (forall ((W |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440))))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (or (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473)))))) :rule all_simplify)
% 0.19/0.54  (anchor :step t5 :args ((W |tptp.'$ki_world'|) (:= W W) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1479 BOUND_VARIABLE_1479) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1477 BOUND_VARIABLE_1477) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1475 BOUND_VARIABLE_1475) (BOUND_VARIABLE_1473 $$unsorted) (:= BOUND_VARIABLE_1473 BOUND_VARIABLE_1473) (BOUND_VARIABLE_1471 $$unsorted) (:= BOUND_VARIABLE_1471 BOUND_VARIABLE_1471)))
% 0.19/0.54  (step t5.t1 (cl (= W W)) :rule refl)
% 0.19/0.54  (step t5.t2 (cl (= BOUND_VARIABLE_1479 BOUND_VARIABLE_1479)) :rule refl)
% 0.19/0.54  (step t5.t3 (cl (= BOUND_VARIABLE_1477 BOUND_VARIABLE_1477)) :rule refl)
% 0.19/0.54  (step t5.t4 (cl (= BOUND_VARIABLE_1475 BOUND_VARIABLE_1475)) :rule refl)
% 0.19/0.54  (step t5.t5 (cl (= BOUND_VARIABLE_1473 BOUND_VARIABLE_1473)) :rule refl)
% 0.19/0.54  (step t5.t6 (cl (= BOUND_VARIABLE_1471 BOUND_VARIABLE_1471)) :rule refl)
% 0.19/0.54  (step t5.t7 (cl (= (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (or (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473))) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473)))) :rule all_simplify)
% 0.19/0.54  (step t5 (cl (= (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (or (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473)))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473))))) :rule bind)
% 0.19/0.54  (step t6 (cl (= (forall ((W |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440))))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473))))) :rule trans :premises (t4 t5))
% 0.19/0.54  (step t7 (cl (= (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted) (BOUND_VARIABLE_1438 |tptp.'$ki_world'|) (BOUND_VARIABLE_1436 |tptp.'$ki_world'|) (BOUND_VARIABLE_1434 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1434)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1440)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1434 BOUND_VARIABLE_1436)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1440))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1436 BOUND_VARIABLE_1438)) (tptp.disjoint BOUND_VARIABLE_1438 (tptp.singleton A) BOUND_VARIABLE_1440))))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473))))) :rule trans :premises (t3 t6))
% 0.19/0.54  (step t8 (cl (= (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))))))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473))))) :rule trans :premises (t2 t7))
% 0.19/0.54  (step t9 (cl (= (not (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))))))))))) (not (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473)))))) :rule cong :premises (t8))
% 0.19/0.54  (step t10 (cl (not (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473))))) :rule resolution :premises (t1 t9 a7))
% 0.19/0.54  (step t11 (cl (= (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473))))) :rule hole :args ((forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304))) (= BOUND_VARIABLE_1306 BOUND_VARIABLE_1475) (= BOUND_VARIABLE_1302 BOUND_VARIABLE_1471) (= BOUND_VARIABLE_1304 BOUND_VARIABLE_1473) (= W W) (= BOUND_VARIABLE_1310 BOUND_VARIABLE_1479) (= BOUND_VARIABLE_1308 BOUND_VARIABLE_1477) (= W2 W2) (= W3 W3)))
% 0.19/0.54  (step t12 (cl (not (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304)))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473)))) :rule equiv1 :premises (t11))
% 0.19/0.54  (step t13 (cl (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473))) (not (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304))))) :rule reordering :premises (t12))
% 0.19/0.54  (step t14 (cl (not (= (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))))))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304))))) (not (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))))))))))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304)))) :rule equiv_pos2)
% 0.19/0.54  (anchor :step t15 :args ((W |tptp.'$ki_world'|) (:= W W)))
% 0.19/0.54  (step t15.t1 (cl (= W W)) :rule refl)
% 0.19/0.54  (step t15.t2 (cl (= (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W))) :rule refl)
% 0.19/0.54  (anchor :step t15.t3 :args ((A $$unsorted) (:= A A)))
% 0.19/0.54  (step t15.t3.t1 (cl (= A A)) :rule refl)
% 0.19/0.54  (step t15.t3.t2 (cl (= (|tptp.'$ki_exists_in_world_$i'| W A) (|tptp.'$ki_exists_in_world_$i'| W A))) :rule refl)
% 0.19/0.54  (anchor :step t15.t3.t3 :args ((W0 |tptp.'$ki_world'|) (:= W0 W0)))
% 0.19/0.54  (step t15.t3.t3.t1 (cl (= W0 W0)) :rule refl)
% 0.19/0.54  (step t15.t3.t3.t2 (cl (= (|tptp.'$ki_accessible'| W W0) (|tptp.'$ki_accessible'| W W0))) :rule refl)
% 0.19/0.54  (anchor :step t15.t3.t3.t3 :args ((B $$unsorted) (:= B B)))
% 0.19/0.54  (step t15.t3.t3.t3.t1 (cl (= B B)) :rule refl)
% 0.19/0.54  (step t15.t3.t3.t3.t2 (cl (= (|tptp.'$ki_exists_in_world_$i'| W0 B) (|tptp.'$ki_exists_in_world_$i'| W0 B))) :rule refl)
% 0.19/0.54  (anchor :step t15.t3.t3.t3.t3 :args ((W1 |tptp.'$ki_world'|) (:= W1 W1)))
% 0.19/0.54  (step t15.t3.t3.t3.t3.t1 (cl (= W1 W1)) :rule refl)
% 0.19/0.54  (step t15.t3.t3.t3.t3.t2 (cl (= (|tptp.'$ki_accessible'| W0 W1) (|tptp.'$ki_accessible'| W0 W1))) :rule refl)
% 0.19/0.54  (anchor :step t15.t3.t3.t3.t3.t3 :args ((W2 |tptp.'$ki_world'|) (:= W2 W2)))
% 0.19/0.54  (step t15.t3.t3.t3.t3.t3.t1 (cl (= W2 W2)) :rule refl)
% 0.19/0.54  (step t15.t3.t3.t3.t3.t3.t2 (cl (= (|tptp.'$ki_accessible'| W1 W2) (|tptp.'$ki_accessible'| W1 W2))) :rule refl)
% 0.19/0.54  (step t15.t3.t3.t3.t3.t3.t3 (cl (= (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B))) (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))) :rule all_simplify)
% 0.19/0.54  (step t15.t3.t3.t3.t3.t3.t4 (cl (= (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) :rule cong :premises (t15.t3.t3.t3.t3.t3.t3))
% 0.19/0.54  (step t15.t3.t3.t3.t3.t3.t5 (cl (= (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B))))) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) :rule cong :premises (t15.t3.t3.t3.t3.t3.t2 t15.t3.t3.t3.t3.t3.t4))
% 0.19/0.54  (step t15.t3.t3.t3.t3.t3 (cl (= (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))))) :rule bind)
% 0.19/0.54  (step t15.t3.t3.t3.t3.t4 (cl (= (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))))) :rule all_simplify)
% 0.19/0.54  (step t15.t3.t3.t3.t3.t5 (cl (= (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))))) :rule trans :premises (t15.t3.t3.t3.t3.t3 t15.t3.t3.t3.t3.t4))
% 0.19/0.54  (step t15.t3.t3.t3.t3.t6 (cl (= (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B))))) :rule all_simplify)
% 0.19/0.54  (step t15.t3.t3.t3.t3.t7 (cl (= (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))) (=> (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B)))))) :rule cong :premises (t15.t3.t3.t3.t3.t5 t15.t3.t3.t3.t3.t6))
% 0.19/0.54  (step t15.t3.t3.t3.t3.t8 (cl (= (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B))))))) :rule cong :premises (t15.t3.t3.t3.t3.t2 t15.t3.t3.t3.t3.t7))
% 0.19/0.54  (step t15.t3.t3.t3.t3 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B)))))))) :rule bind)
% 0.19/0.54  (step t15.t3.t3.t3.t4 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B)))))) (forall ((W1 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B))))))) :rule all_simplify)
% 0.19/0.54  (step t15.t3.t3.t3.t5 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B))))) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (or (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B)))))) :rule all_simplify)
% 0.19/0.54  (anchor :step t15.t3.t3.t3.t6 :args ((W1 |tptp.'$ki_world'|) (:= W1 W1) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1191 BOUND_VARIABLE_1191)))
% 0.19/0.54  (step t15.t3.t3.t3.t6.t1 (cl (= W1 W1)) :rule refl)
% 0.19/0.54  (step t15.t3.t3.t3.t6.t2 (cl (= BOUND_VARIABLE_1191 BOUND_VARIABLE_1191)) :rule refl)
% 0.19/0.54  (step t15.t3.t3.t3.t6.t3 (cl (= (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (or (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B))) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B)))) :rule all_simplify)
% 0.19/0.54  (step t15.t3.t3.t3.t6 (cl (= (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (or (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B)))) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B))))) :rule bind)
% 0.19/0.54  (step t15.t3.t3.t3.t7 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B))))) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B))))) :rule trans :premises (t15.t3.t3.t3.t5 t15.t3.t3.t3.t6))
% 0.19/0.54  (step t15.t3.t3.t3.t8 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (tptp.disjoint W2 (tptp.singleton A) B)))))) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B))))) :rule trans :premises (t15.t3.t3.t3.t4 t15.t3.t3.t3.t7))
% 0.19/0.54  (step t15.t3.t3.t3.t9 (cl (= (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B))))) :rule trans :premises (t15.t3.t3.t3.t3 t15.t3.t3.t3.t8))
% 0.19/0.54  (step t15.t3.t3.t3.t10 (cl (= (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B)))))) :rule cong :premises (t15.t3.t3.t3.t2 t15.t3.t3.t3.t9))
% 0.19/0.54  (step t15.t3.t3.t3 (cl (= (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B))))))) :rule bind)
% 0.19/0.54  (step t15.t3.t3.t4 (cl (= (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B))))) (forall ((B $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B))))))) :rule all_simplify)
% 0.19/0.54  (step t15.t3.t3.t5 (cl (= (forall ((B $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B))))) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (or (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B)))))) :rule all_simplify)
% 0.19/0.54  (anchor :step t15.t3.t3.t6 :args ((B $$unsorted) (:= B B) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1209 BOUND_VARIABLE_1209) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1207 BOUND_VARIABLE_1207)))
% 0.19/0.54  (step t15.t3.t3.t6.t1 (cl (= B B)) :rule refl)
% 0.19/0.54  (step t15.t3.t3.t6.t2 (cl (= BOUND_VARIABLE_1209 BOUND_VARIABLE_1209)) :rule refl)
% 0.19/0.54  (step t15.t3.t3.t6.t3 (cl (= BOUND_VARIABLE_1207 BOUND_VARIABLE_1207)) :rule refl)
% 0.19/0.54  (step t15.t3.t3.t6.t4 (cl (= (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (or (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B))) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B)))) :rule all_simplify)
% 0.19/0.54  (step t15.t3.t3.t6 (cl (= (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (or (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B)))) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B))))) :rule bind)
% 0.19/0.54  (step t15.t3.t3.t7 (cl (= (forall ((B $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B))))) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B))))) :rule trans :premises (t15.t3.t3.t5 t15.t3.t3.t6))
% 0.19/0.54  (step t15.t3.t3.t8 (cl (= (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|) (BOUND_VARIABLE_1191 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W0 W1)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W1 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| W1 BOUND_VARIABLE_1191)) (tptp.disjoint BOUND_VARIABLE_1191 (tptp.singleton A) B))))) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B))))) :rule trans :premises (t15.t3.t3.t4 t15.t3.t3.t7))
% 0.19/0.54  (step t15.t3.t3.t9 (cl (= (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B))))) :rule trans :premises (t15.t3.t3.t3 t15.t3.t3.t8))
% 0.19/0.54  (step t15.t3.t3.t10 (cl (= (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))))) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B)))))) :rule cong :premises (t15.t3.t3.t2 t15.t3.t3.t9))
% 0.19/0.54  (step t15.t3.t3 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B))))))) :rule bind)
% 0.19/0.54  (step t15.t3.t4 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B))))) (forall ((W0 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W W0)) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B))))))) :rule all_simplify)
% 0.19/0.54  (step t15.t3.t5 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W W0)) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B))))) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232)))))) :rule all_simplify)
% 0.19/0.54  (anchor :step t15.t3.t6 :args ((W0 |tptp.'$ki_world'|) (:= W0 W0) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1236 BOUND_VARIABLE_1236) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1234 BOUND_VARIABLE_1234) (BOUND_VARIABLE_1232 $$unsorted) (:= BOUND_VARIABLE_1232 BOUND_VARIABLE_1232)))
% 0.19/0.54  (step t15.t3.t6.t1 (cl (= W0 W0)) :rule refl)
% 0.19/0.54  (step t15.t3.t6.t2 (cl (= BOUND_VARIABLE_1236 BOUND_VARIABLE_1236)) :rule refl)
% 0.19/0.54  (step t15.t3.t6.t3 (cl (= BOUND_VARIABLE_1234 BOUND_VARIABLE_1234)) :rule refl)
% 0.19/0.54  (step t15.t3.t6.t4 (cl (= BOUND_VARIABLE_1232 BOUND_VARIABLE_1232)) :rule refl)
% 0.19/0.54  (step t15.t3.t6.t5 (cl (= (or (not (|tptp.'$ki_accessible'| W W0)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232))) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232)))) :rule all_simplify)
% 0.19/0.54  (step t15.t3.t6 (cl (= (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232)))) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232))))) :rule bind)
% 0.19/0.54  (step t15.t3.t7 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W W0)) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B))))) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232))))) :rule trans :premises (t15.t3.t5 t15.t3.t6))
% 0.19/0.54  (step t15.t3.t8 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted) (BOUND_VARIABLE_1209 |tptp.'$ki_world'|) (BOUND_VARIABLE_1207 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W0 B)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1207)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A B))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1207 BOUND_VARIABLE_1209)) (tptp.disjoint BOUND_VARIABLE_1209 (tptp.singleton A) B))))) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232))))) :rule trans :premises (t15.t3.t4 t15.t3.t7))
% 0.19/0.54  (step t15.t3.t9 (cl (= (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232))))) :rule trans :premises (t15.t3.t3 t15.t3.t8))
% 0.19/0.54  (step t15.t3.t10 (cl (= (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))))))) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232)))))) :rule cong :premises (t15.t3.t2 t15.t3.t9))
% 0.19/0.54  (step t15.t3 (cl (= (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))))) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232))))))) :rule bind)
% 0.19/0.54  (step t15.t4 (cl (= (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232))))) (forall ((A $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232))))))) :rule all_simplify)
% 0.19/0.54  (step t15.t5 (cl (= (forall ((A $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232))))) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (or (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271)))))) :rule all_simplify)
% 0.19/0.54  (anchor :step t15.t6 :args ((A $$unsorted) (:= A A) (BOUND_VARIABLE_1271 $$unsorted) (:= BOUND_VARIABLE_1271 BOUND_VARIABLE_1271) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1269 BOUND_VARIABLE_1269) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1267 BOUND_VARIABLE_1267) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1265 BOUND_VARIABLE_1265)))
% 0.19/0.54  (step t15.t6.t1 (cl (= A A)) :rule refl)
% 0.19/0.54  (step t15.t6.t2 (cl (= BOUND_VARIABLE_1271 BOUND_VARIABLE_1271)) :rule refl)
% 0.19/0.54  (step t15.t6.t3 (cl (= BOUND_VARIABLE_1269 BOUND_VARIABLE_1269)) :rule refl)
% 0.19/0.54  (step t15.t6.t4 (cl (= BOUND_VARIABLE_1267 BOUND_VARIABLE_1267)) :rule refl)
% 0.19/0.54  (step t15.t6.t5 (cl (= BOUND_VARIABLE_1265 BOUND_VARIABLE_1265)) :rule refl)
% 0.19/0.54  (step t15.t6.t6 (cl (= (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (or (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271))) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271)))) :rule all_simplify)
% 0.19/0.54  (step t15.t6 (cl (= (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (or (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271)))) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271))))) :rule bind)
% 0.19/0.54  (step t15.t7 (cl (= (forall ((A $$unsorted)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232))))) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271))))) :rule trans :premises (t15.t5 t15.t6))
% 0.19/0.54  (step t15.t8 (cl (= (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|) (BOUND_VARIABLE_1236 |tptp.'$ki_world'|) (BOUND_VARIABLE_1234 |tptp.'$ki_world'|) (BOUND_VARIABLE_1232 $$unsorted)) (or (not (|tptp.'$ki_accessible'| W W0)) (not (|tptp.'$ki_exists_in_world_$i'| W0 BOUND_VARIABLE_1232)) (not (|tptp.'$ki_accessible'| W0 BOUND_VARIABLE_1236)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1232))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1236 BOUND_VARIABLE_1234)) (tptp.disjoint BOUND_VARIABLE_1234 (tptp.singleton A) BOUND_VARIABLE_1232))))) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271))))) :rule trans :premises (t15.t4 t15.t7))
% 0.19/0.54  (step t15.t9 (cl (= (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))))) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271))))) :rule trans :premises (t15.t3 t15.t8))
% 0.19/0.54  (step t15.t10 (cl (= (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B))))))))))))) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271)))))) :rule cong :premises (t15.t2 t15.t9))
% 0.19/0.54  (step t15 (cl (= (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))))))) (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271))))))) :rule bind)
% 0.19/0.54  (step t16 (cl (= (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271))))) (forall ((W |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271))))))) :rule all_simplify)
% 0.19/0.54  (step t17 (cl (= (forall ((W |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271))))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (or (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304)))))) :rule all_simplify)
% 0.19/0.54  (anchor :step t18 :args ((W |tptp.'$ki_world'|) (:= W W) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1310 BOUND_VARIABLE_1310) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1308 BOUND_VARIABLE_1308) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (:= BOUND_VARIABLE_1306 BOUND_VARIABLE_1306) (BOUND_VARIABLE_1304 $$unsorted) (:= BOUND_VARIABLE_1304 BOUND_VARIABLE_1304) (BOUND_VARIABLE_1302 $$unsorted) (:= BOUND_VARIABLE_1302 BOUND_VARIABLE_1302)))
% 0.19/0.54  (step t18.t1 (cl (= W W)) :rule refl)
% 0.19/0.54  (step t18.t2 (cl (= BOUND_VARIABLE_1310 BOUND_VARIABLE_1310)) :rule refl)
% 0.19/0.54  (step t18.t3 (cl (= BOUND_VARIABLE_1308 BOUND_VARIABLE_1308)) :rule refl)
% 0.19/0.54  (step t18.t4 (cl (= BOUND_VARIABLE_1306 BOUND_VARIABLE_1306)) :rule refl)
% 0.19/0.54  (step t18.t5 (cl (= BOUND_VARIABLE_1304 BOUND_VARIABLE_1304)) :rule refl)
% 0.19/0.54  (step t18.t6 (cl (= BOUND_VARIABLE_1302 BOUND_VARIABLE_1302)) :rule refl)
% 0.19/0.54  (step t18.t7 (cl (= (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (or (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304))) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304)))) :rule all_simplify)
% 0.19/0.54  (step t18 (cl (= (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (or (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304)))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304))))) :rule bind)
% 0.19/0.54  (step t19 (cl (= (forall ((W |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271))))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304))))) :rule trans :premises (t17 t18))
% 0.19/0.54  (step t20 (cl (= (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted) (BOUND_VARIABLE_1271 $$unsorted) (BOUND_VARIABLE_1269 |tptp.'$ki_world'|) (BOUND_VARIABLE_1267 |tptp.'$ki_world'|) (BOUND_VARIABLE_1265 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_exists_in_world_$i'| W A)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1265)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1271)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1265 BOUND_VARIABLE_1267)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 A BOUND_VARIABLE_1271))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1267 BOUND_VARIABLE_1269)) (tptp.disjoint BOUND_VARIABLE_1269 (tptp.singleton A) BOUND_VARIABLE_1271))))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304))))) :rule trans :premises (t16 t19))
% 0.19/0.54  (step t21 (cl (= (forall ((W |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W) (forall ((A $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W A) (forall ((W0 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W W0) (forall ((B $$unsorted)) (=> (|tptp.'$ki_exists_in_world_$i'| W0 B) (forall ((W1 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W0 W1) (=> (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (not (forall ((W3 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W2 W3) (tptp.in W3 A B)))))) (forall ((W2 |tptp.'$ki_world'|)) (=> (|tptp.'$ki_accessible'| W1 W2) (tptp.disjoint W2 (tptp.singleton A) B)))))))))))))) (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304))))) :rule trans :premises (t15 t20))
% 0.19/0.54  (step t22 (cl (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1310 |tptp.'$ki_world'|) (BOUND_VARIABLE_1308 |tptp.'$ki_world'|) (BOUND_VARIABLE_1306 |tptp.'$ki_world'|) (BOUND_VARIABLE_1304 $$unsorted) (BOUND_VARIABLE_1302 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1302)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1310)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1304)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1310 BOUND_VARIABLE_1308)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1302 BOUND_VARIABLE_1304))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1308 BOUND_VARIABLE_1306)) (tptp.disjoint BOUND_VARIABLE_1306 (tptp.singleton BOUND_VARIABLE_1302) BOUND_VARIABLE_1304)))) :rule resolution :premises (t14 t21 a6))
% 0.19/0.54  (step t23 (cl (forall ((W |tptp.'$ki_world'|) (BOUND_VARIABLE_1479 |tptp.'$ki_world'|) (BOUND_VARIABLE_1477 |tptp.'$ki_world'|) (BOUND_VARIABLE_1475 |tptp.'$ki_world'|) (BOUND_VARIABLE_1473 $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| W)) (not (|tptp.'$ki_exists_in_world_$i'| W BOUND_VARIABLE_1471)) (not (|tptp.'$ki_accessible'| W BOUND_VARIABLE_1479)) (not (|tptp.'$ki_exists_in_world_$i'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1473)) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1479 BOUND_VARIABLE_1477)) (not (forall ((W2 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 W2)) (not (forall ((W3 |tptp.'$ki_world'|)) (or (not (|tptp.'$ki_accessible'| W2 W3)) (tptp.in W3 BOUND_VARIABLE_1471 BOUND_VARIABLE_1473))))))) (not (|tptp.'$ki_accessible'| BOUND_VARIABLE_1477 BOUND_VARIABLE_1475)) (tptp.disjoint BOUND_VARIABLE_1475 (tptp.singleton BOUND_VARIABLE_1471) BOUND_VARIABLE_1473)))) :rule resolution :premises (t13 t22))
% 0.19/0.54  (step t24 (cl) :rule resolution :premises (t10 t23))
% 0.19/0.54  
% 0.19/0.54  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.gwycqHMzHu/cvc5---1.0.5_11520.smt2
% 0.19/0.55  % cvc5---1.0.5 exiting
% 0.19/0.55  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------