%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL947_10 : TPTP v9.3.1. Released v8.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:01:13 PM UTC 2026
% Result : Theorem 0.32s 0.58s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL947_10 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.33 % Computer : n007.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 4 23:59:13 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.32/0.58 % SZS status Theorem
% 0.32/0.58 % SZS output start Proof
% 0.32/0.58 tff(tptp_fun___ki_accessible__type, type, (
% 0.32/0.58 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.32/0.58 tff(tptp_fun_W0_26_type, type, (
% 0.32/0.58 tptp_fun_W0_26: |'$ki_world'|)).
% 0.32/0.58 tff(qmltpeq_type, type, (
% 0.32/0.58 qmltpeq: ( |'$ki_world'| * $i * $i ) > $o)).
% 0.32/0.58 tff(tptp_fun_B_25_type, type, (
% 0.32/0.58 tptp_fun_B_25: $i)).
% 0.32/0.58 tff(union_type, type, (
% 0.32/0.58 union: ( $i * $i ) > $i)).
% 0.32/0.58 tff(subset_type, type, (
% 0.32/0.58 subset: ( |'$ki_world'| * $i * $i ) > $o)).
% 0.32/0.58 tff(tptp_fun_W2_8_type, type, (
% 0.32/0.58 tptp_fun_W2_8: ( |'$ki_world'| * $i * $i ) > |'$ki_world'|)).
% 0.32/0.58 tff(tptp_fun_W2_1_type, type, (
% 0.32/0.58 tptp_fun_W2_1: ( |'$ki_world'| * $i * $i ) > |'$ki_world'|)).
% 0.32/0.58 tff(tptp_fun_W_24_type, type, (
% 0.32/0.58 tptp_fun_W_24: |'$ki_world'|)).
% 0.32/0.58 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.32/0.58 tptp_fun___ki_exists_in_world__i_: ( |'$ki_world'| * $i ) > $o)).
% 0.32/0.58 tff(tptp_fun___ki_local_world__type, type, (
% 0.32/0.58 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.32/0.58 tff(tptp_fun_W2_11_type, type, (
% 0.32/0.58 tptp_fun_W2_11: ( |'$ki_world'| * $i * $i ) > |'$ki_world'|)).
% 0.32/0.58 tff(1,assumption,(~tptp_fun___ki_accessible_(W0!26, W0!26)), introduced(assumption)).
% 0.32/0.58 tff(2,plain,
% 0.32/0.58 (^[W: |'$ki_world'|] : refl(tptp_fun___ki_accessible_(W, W) <=> tptp_fun___ki_accessible_(W, W))),
% 0.32/0.58 inference(bind,[status(th)],[])).
% 0.32/0.58 tff(3,plain,
% 0.32/0.58 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.32/0.58 inference(quant_intro,[status(thm)],[2])).
% 0.32/0.58 tff(4,plain,
% 0.32/0.58 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.32/0.58 inference(rewrite,[status(thm)],[])).
% 0.32/0.58 tff(5,axiom,(![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_reflexive')).
% 0.32/0.58 tff(6,plain,
% 0.32/0.58 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.32/0.58 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.32/0.58 tff(7,plain,(
% 0.32/0.58 ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.32/0.58 inference(skolemize,[status(sab)],[6])).
% 0.32/0.58 tff(8,plain,
% 0.32/0.58 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.32/0.58 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.32/0.58 tff(9,plain,
% 0.32/0.58 ((~![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)) | tptp_fun___ki_accessible_(W0!26, W0!26)),
% 0.32/0.58 inference(quant_inst,[status(thm)],[])).
% 0.32/0.58 tff(10,plain,
% 0.32/0.58 ($false),
% 0.32/0.58 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.32/0.58 tff(11,plain,(tptp_fun___ki_accessible_(W0!26, W0!26)), inference(lemma,lemma(discharge,[]))).
% 0.32/0.58 tff(12,assumption,(~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25))), introduced(assumption)).
% 0.32/0.58 tff(13,plain,
% 0.32/0.58 (((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25)) | (~qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25))),
% 0.32/0.58 inference(tautology,[status(thm)],[])).
% 0.32/0.58 tff(14,plain,
% 0.32/0.58 (~qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25)),
% 0.32/0.58 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.32/0.58 tff(15,plain,
% 0.32/0.58 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24) & (tptp_fun___ki_exists_in_world__i_(W!24, B!25) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24) & tptp_fun___ki_exists_in_world__i_(W!24, B!25) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))))),
% 0.32/0.58 inference(rewrite,[status(thm)],[])).
% 0.32/0.58 tff(16,plain,
% 0.32/0.58 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B)))))),
% 0.32/0.58 inference(rewrite,[status(thm)],[])).
% 0.32/0.58 tff(17,plain,
% 0.32/0.58 ((~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, union(B, B), B))))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B)))))),
% 0.32/0.58 inference(rewrite,[status(thm)],[])).
% 0.32/0.58 tff(18,axiom,(~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, union(B, B), B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.32/0.58 tff(19,plain,
% 0.32/0.58 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))),
% 0.32/0.58 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.32/0.58 tff(20,plain,
% 0.32/0.58 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))),
% 0.32/0.58 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.32/0.58 tff(21,plain,
% 0.32/0.58 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))),
% 0.32/0.58 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.32/0.58 tff(22,plain,
% 0.32/0.58 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))),
% 0.32/0.58 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.32/0.58 tff(23,plain,
% 0.32/0.58 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24) & tptp_fun___ki_exists_in_world__i_(W!24, B!25) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25)))),
% 0.32/0.58 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.32/0.58 tff(24,plain,
% 0.32/0.58 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)),
% 0.32/0.58 inference(and_elim,[status(thm)],[23])).
% 0.32/0.58 tff(25,plain,
% 0.32/0.58 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))))),
% 0.32/0.58 inference(bind,[status(th)],[])).
% 0.32/0.58 tff(26,plain,
% 0.32/0.58 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))),
% 0.32/0.58 inference(quant_intro,[status(thm)],[25])).
% 0.32/0.58 tff(27,plain,
% 0.32/0.58 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))))),
% 0.32/0.58 inference(bind,[status(th)],[])).
% 0.32/0.58 tff(28,plain,
% 0.32/0.58 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))),
% 0.32/0.58 inference(quant_intro,[status(thm)],[27])).
% 0.32/0.58 tff(29,plain,
% 0.32/0.58 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))),
% 0.32/0.58 inference(transitivity,[status(thm)],[28, 26])).
% 0.32/0.58 tff(30,plain,
% 0.32/0.58 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))),
% 0.32/0.58 inference(rewrite,[status(thm)],[])).
% 0.32/0.58 tff(31,plain,
% 0.32/0.58 (^[W: |'$ki_world'|] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[W0: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, X, X)) <=> ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))), (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, X, X)) <=> ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))), ((tptp_fun___ki_exists_in_world__i_(W, X) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, X, X))) <=> (tptp_fun___ki_exists_in_world__i_(W, X) => ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, X) => ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))), ((tptp_fun___ki_exists_in_world__i_(W, X) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, X, X))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))))), (![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, X, X))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, X, X)))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, X, X)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))))),
% 0.32/0.58 inference(bind,[status(th)],[])).
% 0.32/0.58 tff(32,plain,
% 0.32/0.58 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, X, X)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))),
% 0.32/0.59 inference(quant_intro,[status(thm)],[31])).
% 0.32/0.59 tff(33,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, X, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.32/0.59 tff(34,plain,
% 0.32/0.59 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))),
% 0.32/0.59 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.32/0.59 tff(35,plain,
% 0.32/0.59 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))),
% 0.32/0.59 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.32/0.59 tff(36,plain,(
% 0.32/0.59 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))),
% 0.32/0.59 inference(skolemize,[status(sab)],[35])).
% 0.32/0.59 tff(37,plain,
% 0.32/0.59 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))),
% 0.32/0.59 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.32/0.59 tff(38,plain,
% 0.32/0.59 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, X, X))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, X, X))))),
% 0.32/0.59 inference(rewrite,[status(thm)],[])).
% 0.32/0.59 tff(39,plain,
% 0.32/0.59 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, X, X))))),
% 0.32/0.59 inference(quant_inst,[status(thm)],[])).
% 0.32/0.59 tff(40,plain,
% 0.32/0.59 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, X, X))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, X, X)))),
% 0.32/0.59 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.32/0.59 tff(41,plain,
% 0.32/0.59 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, X, X)))),
% 0.32/0.59 inference(unit_resolution,[status(thm)],[40, 37, 24])).
% 0.32/0.59 tff(42,plain,
% 0.32/0.59 (tptp_fun___ki_exists_in_world__i_(W!24, B!25)),
% 0.32/0.59 inference(and_elim,[status(thm)],[23])).
% 0.32/0.59 tff(43,plain,
% 0.32/0.59 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, X, X)))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, B!25, B!25)))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, X, X)))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, B!25, B!25)))),
% 0.32/0.59 inference(rewrite,[status(thm)],[])).
% 0.32/0.59 tff(44,plain,
% 0.32/0.59 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, X, X)))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, B!25, B!25)))),
% 0.32/0.59 inference(quant_inst,[status(thm)],[])).
% 0.32/0.59 tff(45,plain,
% 0.32/0.59 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, X, X)))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, B!25, B!25))),
% 0.32/0.59 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.32/0.59 tff(46,plain,
% 0.32/0.59 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, B!25, B!25))),
% 0.32/0.59 inference(unit_resolution,[status(thm)],[45, 42, 41])).
% 0.32/0.59 tff(47,plain,
% 0.32/0.59 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, B!25, B!25))) | ((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, B!25, B!25))) | (~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25))),
% 0.32/0.59 inference(rewrite,[status(thm)],[])).
% 0.32/0.59 tff(48,plain,
% 0.32/0.59 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, B!25, B!25))) | ((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25))),
% 0.32/0.59 inference(quant_inst,[status(thm)],[])).
% 0.32/0.59 tff(49,plain,
% 0.32/0.59 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | qmltpeq(W0, B!25, B!25))) | (~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25)),
% 0.32/0.59 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.32/0.59 tff(50,plain,
% 0.32/0.59 (~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25))),
% 0.32/0.59 inference(unit_resolution,[status(thm)],[49, 46, 14])).
% 0.32/0.59 tff(51,plain,
% 0.32/0.59 (((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25)) | tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))),
% 0.32/0.59 inference(tautology,[status(thm)],[])).
% 0.32/0.59 tff(52,plain,
% 0.32/0.59 (tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))),
% 0.32/0.59 inference(unit_resolution,[status(thm)],[51, 12])).
% 0.32/0.59 tff(53,plain,
% 0.32/0.59 (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))),
% 0.32/0.59 inference(and_elim,[status(thm)],[23])).
% 0.32/0.59 tff(54,plain,
% 0.32/0.59 (tptp_fun___ki_accessible_(W!24, W0!26)),
% 0.32/0.59 inference(or_elim,[status(thm)],[53])).
% 0.32/0.59 tff(55,plain,
% 0.32/0.59 (![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V))) <=> ![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))),
% 0.32/0.59 inference(rewrite,[status(thm)],[])).
% 0.32/0.59 tff(56,plain,
% 0.32/0.59 (^[W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U)) <=> (~((~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V))))), ((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) <=> (~(~((~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V))))))), rewrite((~(~((~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V))))) <=> ((~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))), ((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) <=> ((~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V))))), (((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) | tptp_fun___ki_accessible_(W, U)) <=> (((~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_accessible_(W, U)))), rewrite((((~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_accessible_(W, U)) <=> (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))), (((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) | tptp_fun___ki_accessible_(W, U)) <=> (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))))),
% 0.32/0.59 inference(bind,[status(th)],[])).
% 0.32/0.59 tff(57,plain,
% 0.32/0.59 (![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : ((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) | tptp_fun___ki_accessible_(W, U)) <=> ![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))),
% 0.32/0.59 inference(quant_intro,[status(thm)],[56])).
% 0.32/0.59 tff(58,plain,
% 0.32/0.59 (![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : ((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) | tptp_fun___ki_accessible_(W, U)) <=> ![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : ((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) | tptp_fun___ki_accessible_(W, U))),
% 0.32/0.59 inference(rewrite,[status(thm)],[])).
% 0.32/0.59 tff(59,plain,
% 0.32/0.59 (^[W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : rewrite(((tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U)) => tptp_fun___ki_accessible_(W, U)) <=> ((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) | tptp_fun___ki_accessible_(W, U)))),
% 0.32/0.59 inference(bind,[status(th)],[])).
% 0.32/0.59 tff(60,plain,
% 0.32/0.59 (![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : ((tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U)) => tptp_fun___ki_accessible_(W, U)) <=> ![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : ((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) | tptp_fun___ki_accessible_(W, U))),
% 0.32/0.59 inference(quant_intro,[status(thm)],[59])).
% 0.32/0.59 tff(61,axiom,(![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : ((tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U)) => tptp_fun___ki_accessible_(W, U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_transitive')).
% 0.32/0.59 tff(62,plain,
% 0.32/0.59 (![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : ((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) | tptp_fun___ki_accessible_(W, U))),
% 0.32/0.59 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.32/0.59 tff(63,plain,
% 0.32/0.59 (![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : ((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) | tptp_fun___ki_accessible_(W, U))),
% 0.32/0.59 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.32/0.59 tff(64,plain,(
% 0.32/0.59 ![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : ((~(tptp_fun___ki_accessible_(W, V) & tptp_fun___ki_accessible_(V, U))) | tptp_fun___ki_accessible_(W, U))),
% 0.32/0.59 inference(skolemize,[status(sab)],[63])).
% 0.32/0.59 tff(65,plain,
% 0.32/0.59 (![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))),
% 0.32/0.59 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.32/0.59 tff(66,plain,
% 0.32/0.59 (![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))),
% 0.32/0.59 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.32/0.59 tff(67,plain,
% 0.32/0.59 (((~![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))) | ((~tptp_fun___ki_accessible_(W!24, W0!26)) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25)))) <=> ((~![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))) | (~tptp_fun___ki_accessible_(W!24, W0!26)) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25)))),
% 0.32/0.59 inference(rewrite,[status(thm)],[])).
% 0.32/0.59 tff(68,plain,
% 0.32/0.59 ((tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25)) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | (~tptp_fun___ki_accessible_(W!24, W0!26))) <=> ((~tptp_fun___ki_accessible_(W!24, W0!26)) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25)))),
% 0.32/0.59 inference(rewrite,[status(thm)],[])).
% 0.32/0.59 tff(69,plain,
% 0.32/0.59 (((~![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))) | (tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25)) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | (~tptp_fun___ki_accessible_(W!24, W0!26)))) <=> ((~![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))) | ((~tptp_fun___ki_accessible_(W!24, W0!26)) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25))))),
% 0.32/0.59 inference(monotonicity,[status(thm)],[68])).
% 0.32/0.59 tff(70,plain,
% 0.32/0.59 (((~![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))) | (tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25)) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | (~tptp_fun___ki_accessible_(W!24, W0!26)))) <=> ((~![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))) | (~tptp_fun___ki_accessible_(W!24, W0!26)) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25)))),
% 0.32/0.59 inference(transitivity,[status(thm)],[69, 67])).
% 0.32/0.59 tff(71,plain,
% 0.32/0.59 ((~![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))) | (tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25)) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | (~tptp_fun___ki_accessible_(W!24, W0!26)))),
% 0.32/0.59 inference(quant_inst,[status(thm)],[])).
% 0.32/0.59 tff(72,plain,
% 0.32/0.59 ((~![W: |'$ki_world'|, V: |'$ki_world'|, U: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, U) | (~tptp_fun___ki_accessible_(V, U)) | (~tptp_fun___ki_accessible_(W, V)))) | (~tptp_fun___ki_accessible_(W!24, W0!26)) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | tptp_fun___ki_accessible_(W!24, tptp_fun_W2_1(W0!26, B!25, B!25))),
% 0.32/0.59 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.32/0.59 tff(73,plain,
% 0.32/0.59 ($false),
% 0.32/0.59 inference(unit_resolution,[status(thm)],[72, 66, 54, 52, 50])).
% 0.32/0.59 tff(74,plain,((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25)), inference(lemma,lemma(discharge,[]))).
% 0.32/0.59 tff(75,assumption,(~tptp_fun___ki_accessible_(W!24, W!24)), introduced(assumption)).
% 0.32/0.59 tff(76,plain,
% 0.32/0.59 ((~![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)) | tptp_fun___ki_accessible_(W!24, W!24)),
% 0.32/0.59 inference(quant_inst,[status(thm)],[])).
% 0.32/0.59 tff(77,plain,
% 0.32/0.59 ($false),
% 0.32/0.59 inference(unit_resolution,[status(thm)],[76, 8, 75])).
% 0.32/0.59 tff(78,plain,(tptp_fun___ki_accessible_(W!24, W!24)), inference(lemma,lemma(discharge,[]))).
% 0.32/0.59 tff(79,plain,
% 0.32/0.59 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)))))))))))),
% 0.32/0.59 inference(bind,[status(th)],[])).
% 0.32/0.59 tff(80,plain,
% 0.32/0.59 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))))))))))),
% 0.32/0.59 inference(quant_intro,[status(thm)],[79])).
% 0.32/0.59 tff(81,plain,
% 0.32/0.59 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))))),
% 0.32/0.59 inference(bind,[status(th)],[])).
% 0.32/0.59 tff(82,plain,
% 0.32/0.59 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B)))))))))))),
% 0.32/0.59 inference(quant_intro,[status(thm)],[81])).
% 0.32/0.59 tff(83,plain,
% 0.32/0.59 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))))),
% 0.32/0.59 inference(bind,[status(th)],[])).
% 0.32/0.59 tff(84,plain,
% 0.32/0.59 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B)))))))))))),
% 0.32/0.60 inference(quant_intro,[status(thm)],[83])).
% 0.32/0.60 tff(85,plain,
% 0.32/0.60 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B)))))))))))),
% 0.32/0.60 inference(transitivity,[status(thm)],[84, 82])).
% 0.32/0.60 tff(86,plain,
% 0.32/0.60 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))))),
% 0.32/0.60 inference(bind,[status(th)],[])).
% 0.32/0.60 tff(87,plain,
% 0.32/0.60 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B)))))))))))),
% 0.32/0.60 inference(quant_intro,[status(thm)],[86])).
% 0.32/0.60 tff(88,plain,
% 0.32/0.60 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | ((~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B)))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))),
% 0.32/0.60 inference(bind,[status(th)],[])).
% 0.32/0.60 tff(89,plain,
% 0.32/0.60 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | ((~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B)))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B)))))))))),
% 0.32/0.60 inference(quant_intro,[status(thm)],[88])).
% 0.32/0.60 tff(90,plain,
% 0.32/0.60 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))))),
% 0.32/0.60 inference(rewrite,[status(thm)],[])).
% 0.32/0.60 tff(91,plain,
% 0.32/0.60 (^[W: |'$ki_world'|] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[W0: |'$ki_world'|] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C))))) <=> (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))), ((tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)))))) <=> (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))))))), ((tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))))))))), (![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)))))) <=> ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))), ((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C))))))) <=> (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))))))))), rewrite((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))), ((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C))))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))))), (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C))))))) <=> ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))))))))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)))))))) <=> (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))))))))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))))))))))), (![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)))))))) <=> ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C))))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))))))))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))))))),
% 0.32/0.61 inference(bind,[status(th)],[])).
% 0.32/0.61 tff(92,plain,
% 0.32/0.61 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))))),
% 0.32/0.61 inference(quant_intro,[status(thm)],[91])).
% 0.32/0.61 tff(93,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))))) & ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) & ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, C, B))) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, B, C)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_defn')).
% 0.32/0.61 tff(94,plain,
% 0.32/0.61 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))))),
% 0.32/0.61 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.32/0.61 tff(95,plain,
% 0.32/0.61 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))))))),
% 0.32/0.61 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.32/0.61 tff(96,plain,(
% 0.32/0.61 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | ((~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))))))))))),
% 0.32/0.61 inference(skolemize,[status(sab)],[95])).
% 0.32/0.61 tff(97,plain,
% 0.32/0.61 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) & ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B)))) & ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B)))))))))),
% 0.32/0.61 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.32/0.61 tff(98,plain,
% 0.32/0.61 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B)))))))))))),
% 0.32/0.61 inference(modus_ponens,[status(thm)],[97, 87])).
% 0.32/0.61 tff(99,plain,
% 0.32/0.61 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B)))))))))))),
% 0.32/0.61 inference(modus_ponens,[status(thm)],[98, 85])).
% 0.32/0.61 tff(100,plain,
% 0.32/0.61 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))))))))))),
% 0.32/0.61 inference(modus_ponens,[status(thm)],[99, 80])).
% 0.32/0.61 tff(101,plain,
% 0.32/0.61 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))))))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))))))))))),
% 0.32/0.61 inference(rewrite,[status(thm)],[])).
% 0.32/0.61 tff(102,plain,
% 0.32/0.61 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))))))))))),
% 0.32/0.61 inference(quant_inst,[status(thm)],[])).
% 0.32/0.61 tff(103,plain,
% 0.32/0.61 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C))))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)))))))))),
% 0.32/0.61 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.32/0.61 tff(104,plain,
% 0.32/0.61 (![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)))))))))),
% 0.32/0.61 inference(unit_resolution,[status(thm)],[103, 100, 24])).
% 0.32/0.61 tff(105,plain,
% 0.32/0.61 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))))))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))))))))),
% 0.32/0.61 inference(rewrite,[status(thm)],[])).
% 0.32/0.61 tff(106,plain,
% 0.32/0.61 (((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))))))))),
% 0.32/0.61 inference(rewrite,[status(thm)],[])).
% 0.32/0.61 tff(107,plain,
% 0.32/0.61 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)))))))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))))),
% 0.32/0.62 inference(monotonicity,[status(thm)],[106])).
% 0.32/0.62 tff(108,plain,
% 0.32/0.62 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)))))))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))))))))),
% 0.32/0.62 inference(transitivity,[status(thm)],[107, 105])).
% 0.32/0.62 tff(109,plain,
% 0.32/0.62 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)))))))))),
% 0.32/0.62 inference(quant_inst,[status(thm)],[])).
% 0.32/0.62 tff(110,plain,
% 0.32/0.62 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B))) | qmltpeq(tptp_fun_W2_1(W1, C, B), B, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B))) | subset(tptp_fun_W2_11(W1, C, B), C, B))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B, C)))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))),
% 0.32/0.62 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.32/0.62 tff(111,plain,
% 0.32/0.62 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))),
% 0.32/0.62 inference(unit_resolution,[status(thm)],[110, 42, 104])).
% 0.32/0.62 tff(112,plain,
% 0.32/0.62 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))) | ((~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25)))))))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))) | (~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25)))))))))))),
% 0.32/0.62 inference(rewrite,[status(thm)],[])).
% 0.32/0.62 tff(113,plain,
% 0.32/0.62 (((~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))))))) <=> ((~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25)))))))))))),
% 0.32/0.62 inference(rewrite,[status(thm)],[])).
% 0.32/0.62 tff(114,plain,
% 0.32/0.62 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))) | ((~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))) | ((~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))))))))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[113])).
% 0.39/0.62 tff(115,plain,
% 0.39/0.62 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))) | ((~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))) | (~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25)))))))))))),
% 0.39/0.63 inference(transitivity,[status(thm)],[114, 112])).
% 0.39/0.63 tff(116,plain,
% 0.39/0.63 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))) | ((~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))),
% 0.39/0.63 inference(quant_inst,[status(thm)],[])).
% 0.39/0.63 tff(117,plain,
% 0.39/0.63 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25)))))))))) | (~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))))))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.39/0.63 tff(118,plain,
% 0.39/0.63 (![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))))))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[117, 111, 78])).
% 0.39/0.63 tff(119,plain,
% 0.39/0.63 (((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))))))) <=> ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(120,plain,
% 0.39/0.63 (((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(121,plain,
% 0.39/0.63 (((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25))))))))))) <=> ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25))))))))),
% 0.39/0.63 inference(monotonicity,[status(thm)],[120])).
% 0.39/0.63 tff(122,plain,
% 0.39/0.63 (((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25))))))))))) <=> ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))))))),
% 0.39/0.63 inference(transitivity,[status(thm)],[121, 119])).
% 0.39/0.63 tff(123,plain,
% 0.39/0.63 ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25))))))))))),
% 0.39/0.64 inference(quant_inst,[status(thm)],[])).
% 0.39/0.64 tff(124,plain,
% 0.39/0.64 ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, C, B!25))) | subset(tptp_fun_W2_11(W1, C, B!25), C, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, C, B!25))) | qmltpeq(tptp_fun_W2_1(W1, C, B!25), B!25, C))) | (~((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, C))) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, C, B!25))))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25))))))),
% 0.39/0.64 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.39/0.64 tff(125,plain,
% 0.39/0.64 (~((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))))),
% 0.39/0.64 inference(unit_resolution,[status(thm)],[124, 42, 118])).
% 0.39/0.64 tff(126,plain,
% 0.39/0.64 (((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, B!25, B!25)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_11(W1, B!25, B!25))) | subset(tptp_fun_W2_11(W1, B!25, B!25), B!25, B!25))))) | (~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25))))) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))),
% 0.39/0.64 inference(tautology,[status(thm)],[])).
% 0.39/0.64 tff(127,plain,
% 0.39/0.64 (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))),
% 0.39/0.64 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.39/0.64 tff(128,plain,
% 0.39/0.64 (((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))) | ((~tptp_fun___ki_accessible_(W!24, W0!26)) | (~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25)))) <=> ((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))) | (~tptp_fun___ki_accessible_(W!24, W0!26)) | (~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25)))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(129,plain,
% 0.39/0.64 ((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))) | ((~tptp_fun___ki_accessible_(W!24, W0!26)) | (~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25)))),
% 0.39/0.64 inference(quant_inst,[status(thm)],[])).
% 0.39/0.64 tff(130,plain,
% 0.39/0.64 ((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_1(W1, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B!25, B!25)))) | (~tptp_fun___ki_accessible_(W!24, W0!26)) | (~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25))),
% 0.39/0.64 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.39/0.64 tff(131,plain,
% 0.39/0.64 ((~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_1(W0!26, B!25, B!25))) | qmltpeq(tptp_fun_W2_1(W0!26, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25))),
% 0.39/0.64 inference(unit_resolution,[status(thm)],[130, 54, 127])).
% 0.39/0.64 tff(132,plain,
% 0.39/0.64 (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25))),
% 0.39/0.64 inference(unit_resolution,[status(thm)],[131, 74])).
% 0.39/0.64 tff(133,assumption,(![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25))), introduced(assumption)).
% 0.39/0.64 tff(134,assumption,(~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25))), introduced(assumption)).
% 0.39/0.64 tff(135,plain,
% 0.39/0.64 (((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25)) | (~subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25))),
% 0.39/0.64 inference(tautology,[status(thm)],[])).
% 0.39/0.64 tff(136,plain,
% 0.39/0.64 (~subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25)),
% 0.39/0.64 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.39/0.64 tff(137,plain,
% 0.39/0.64 (((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25)) | tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))),
% 0.39/0.64 inference(tautology,[status(thm)],[])).
% 0.39/0.64 tff(138,plain,
% 0.39/0.64 (tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))),
% 0.39/0.64 inference(unit_resolution,[status(thm)],[137, 134])).
% 0.39/0.64 tff(139,plain,
% 0.39/0.64 (((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25))) | ((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25))) <=> ((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25))) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(140,plain,
% 0.39/0.64 ((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25))) | ((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25))),
% 0.39/0.64 inference(quant_inst,[status(thm)],[])).
% 0.39/0.64 tff(141,plain,
% 0.39/0.64 ((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25))) | (~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25)),
% 0.39/0.64 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.39/0.64 tff(142,plain,
% 0.39/0.64 ($false),
% 0.39/0.64 inference(unit_resolution,[status(thm)],[141, 138, 136, 133])).
% 0.39/0.64 tff(143,plain,(((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | subset(W2, B!25, B!25)))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.64 tff(144,plain,
% 0.39/0.64 ((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25)),
% 0.39/0.64 inference(unit_resolution,[status(thm)],[143, 132])).
% 0.39/0.64 tff(145,plain,
% 0.39/0.64 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))))),
% 0.39/0.64 inference(bind,[status(th)],[])).
% 0.39/0.64 tff(146,plain,
% 0.39/0.64 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))),
% 0.39/0.64 inference(quant_intro,[status(thm)],[145])).
% 0.39/0.64 tff(147,plain,
% 0.39/0.64 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))))),
% 0.39/0.64 inference(bind,[status(th)],[])).
% 0.39/0.64 tff(148,plain,
% 0.39/0.64 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))))))))),
% 0.39/0.64 inference(quant_intro,[status(thm)],[147])).
% 0.39/0.64 tff(149,plain,
% 0.39/0.64 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))))),
% 0.39/0.64 inference(bind,[status(th)],[])).
% 0.39/0.64 tff(150,plain,
% 0.39/0.64 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))))))))),
% 0.39/0.64 inference(quant_intro,[status(thm)],[149])).
% 0.39/0.64 tff(151,plain,
% 0.39/0.64 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))))))))),
% 0.39/0.64 inference(transitivity,[status(thm)],[150, 148])).
% 0.39/0.64 tff(152,plain,
% 0.39/0.64 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(153,plain,
% 0.39/0.64 (^[W: |'$ki_world'|] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[W0: |'$ki_world'|] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: |'$ki_world'|] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W2: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) <=> ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))), (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) <=> ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))), quant_intro(proof_bind(^[W2: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)) <=> ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))), (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)) <=> ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))), ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))) <=> (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) => ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))), rewrite((![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) => ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))) <=> ((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))), ((![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))) <=> ((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))), ((tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))) <=> (tptp_fun___ki_accessible_(W0, W1) => ((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))), rewrite((tptp_fun___ki_accessible_(W0, W1) => ((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))) <=> ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))), ((tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))) <=> ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))), (![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))) <=> ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))), ((tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))) <=> (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))), ((tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))), (![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))) <=> ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))), ((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))) <=> (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))), rewrite((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))), ((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))), (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))) <=> ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))))) <=> (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))))), (![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))))) <=> ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))))),
% 0.39/0.65 inference(bind,[status(th)],[])).
% 0.39/0.65 tff(154,plain,
% 0.39/0.65 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))),
% 0.39/0.65 inference(quant_intro,[status(thm)],[153])).
% 0.39/0.65 tff(155,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: |'$ki_world'|] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_union')).
% 0.39/0.65 tff(156,plain,
% 0.39/0.65 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))),
% 0.39/0.65 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.39/0.65 tff(157,plain,
% 0.39/0.65 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))),
% 0.39/0.65 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.39/0.65 tff(158,plain,(
% 0.39/0.65 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))))))))),
% 0.39/0.65 inference(skolemize,[status(sab)],[157])).
% 0.39/0.65 tff(159,plain,
% 0.39/0.65 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))))))))),
% 0.39/0.65 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.39/0.65 tff(160,plain,
% 0.39/0.65 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))),
% 0.39/0.65 inference(modus_ponens,[status(thm)],[159, 146])).
% 0.39/0.65 tff(161,plain,
% 0.39/0.65 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(162,plain,
% 0.39/0.65 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))),
% 0.39/0.65 inference(quant_inst,[status(thm)],[])).
% 0.39/0.65 tff(163,plain,
% 0.39/0.65 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))),
% 0.39/0.65 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.39/0.65 tff(164,plain,
% 0.39/0.65 (![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))),
% 0.39/0.65 inference(unit_resolution,[status(thm)],[163, 160, 24])).
% 0.39/0.65 tff(165,plain,
% 0.39/0.65 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))))),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(166,plain,
% 0.39/0.65 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))))),
% 0.39/0.65 inference(quant_inst,[status(thm)],[])).
% 0.39/0.65 tff(167,plain,
% 0.39/0.65 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))),
% 0.39/0.65 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.39/0.65 tff(168,plain,
% 0.39/0.65 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))),
% 0.39/0.65 inference(unit_resolution,[status(thm)],[167, 42, 164])).
% 0.39/0.65 tff(169,plain,
% 0.39/0.65 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))) | ((~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))) | (~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))),
% 0.39/0.66 inference(rewrite,[status(thm)],[])).
% 0.39/0.66 tff(170,plain,
% 0.39/0.66 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))) | ((~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))),
% 0.39/0.66 inference(quant_inst,[status(thm)],[])).
% 0.39/0.66 tff(171,plain,
% 0.39/0.66 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))) | (~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))),
% 0.39/0.66 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.39/0.66 tff(172,plain,
% 0.39/0.66 (![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))),
% 0.39/0.66 inference(unit_resolution,[status(thm)],[171, 168, 78])).
% 0.39/0.66 tff(173,plain,
% 0.39/0.66 (((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))))) <=> ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))))),
% 0.39/0.66 inference(rewrite,[status(thm)],[])).
% 0.39/0.66 tff(174,plain,
% 0.39/0.66 ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))))),
% 0.39/0.66 inference(quant_inst,[status(thm)],[])).
% 0.39/0.66 tff(175,plain,
% 0.39/0.66 ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))),
% 0.39/0.66 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.39/0.66 tff(176,plain,
% 0.39/0.66 (![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))),
% 0.39/0.66 inference(unit_resolution,[status(thm)],[175, 42, 172])).
% 0.39/0.66 tff(177,plain,
% 0.39/0.66 (((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))) | ((~tptp_fun___ki_accessible_(W!24, W0!26)) | (~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))) <=> ((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))) | (~tptp_fun___ki_accessible_(W!24, W0!26)) | (~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))),
% 0.39/0.66 inference(rewrite,[status(thm)],[])).
% 0.39/0.66 tff(178,plain,
% 0.39/0.66 ((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))) | ((~tptp_fun___ki_accessible_(W!24, W0!26)) | (~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))),
% 0.39/0.67 inference(quant_inst,[status(thm)],[])).
% 0.39/0.67 tff(179,plain,
% 0.39/0.67 ((~![W1: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))) | (~tptp_fun___ki_accessible_(W!24, W0!26)) | (~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))),
% 0.39/0.67 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.39/0.67 tff(180,plain,
% 0.39/0.67 ((~((~tptp_fun___ki_accessible_(W0!26, tptp_fun_W2_8(W0!26, B!25, B!25))) | subset(tptp_fun_W2_8(W0!26, B!25, B!25), B!25, B!25))) | ![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[179, 54, 176])).
% 0.39/0.67 tff(181,plain,
% 0.39/0.67 (![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[180, 144])).
% 0.39/0.67 tff(182,plain,
% 0.39/0.67 (~qmltpeq(W0!26, union(B!25, B!25), B!25)),
% 0.39/0.67 inference(or_elim,[status(thm)],[53])).
% 0.39/0.67 tff(183,plain,
% 0.39/0.67 (((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))) | ((~tptp_fun___ki_accessible_(W0!26, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))) <=> ((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))) | (~tptp_fun___ki_accessible_(W0!26, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))),
% 0.39/0.67 inference(rewrite,[status(thm)],[])).
% 0.39/0.67 tff(184,plain,
% 0.39/0.67 ((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))) | ((~tptp_fun___ki_accessible_(W0!26, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))),
% 0.39/0.67 inference(quant_inst,[status(thm)],[])).
% 0.39/0.67 tff(185,plain,
% 0.39/0.67 ((~![W2: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W0!26, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))) | (~tptp_fun___ki_accessible_(W0!26, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25)),
% 0.39/0.67 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.39/0.67 tff(186,plain,
% 0.39/0.67 ($false),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[185, 182, 181, 11])).
% 0.39/0.67 % SZS output end Proof
% 0.39/0.67 % E exiting
%------------------------------------------------------------------------------