%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NLP266_23 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:18:38 AM UTC 2025
% Result : Theorem 0.18s 0.47s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NLP266_23 : TPTP v9.0.0. Released v8.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 00:01:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 % SZS output start Proof
% 0.18/0.47 tff(do_type, type, (
% 0.18/0.47 do: ( |'$ki_world'| * $i * $i * $i ) > $o)).
% 0.18/0.47 tff(tptp_fun_A_3_type, type, (
% 0.18/0.47 tptp_fun_A_3: ( $i * $i * $i * |'$ki_world'| ) > $i)).
% 0.18/0.47 tff(tptp_fun_W_4_type, type, (
% 0.18/0.47 tptp_fun_W_4: |'$ki_world'|)).
% 0.18/0.47 tff(tptp_fun_I_1_type, type, (
% 0.18/0.47 tptp_fun_I_1: |'$ki_world'| > $i)).
% 0.18/0.47 tff(tptp_fun_B_2_type, type, (
% 0.18/0.47 tptp_fun_B_2: $i)).
% 0.18/0.47 tff(tptp_fun_W0_6_type, type, (
% 0.18/0.47 tptp_fun_W0_6: ( $i * $i * $i * $i ) > |'$ki_world'|)).
% 0.18/0.47 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.18/0.47 tptp_fun___ki_exists_in_world__i_: ( |'$ki_world'| * $i ) > $o)).
% 0.18/0.47 tff(in_type, type, (
% 0.18/0.47 in: ( |'$ki_world'| * $i * $i * $i ) > $o)).
% 0.18/0.47 tff(tptp_fun___ki_accessible__type, type, (
% 0.18/0.47 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.18/0.47 tff(tptp_fun_S2_7_type, type, (
% 0.18/0.47 tptp_fun_S2_7: ( $i * $i * $i * $i ) > $i)).
% 0.18/0.47 tff(number_type, type, (
% 0.18/0.47 number: ( |'$ki_world'| * $i * $i ) > $o)).
% 0.18/0.47 tff(one_type, type, (
% 0.18/0.47 one: $i)).
% 0.18/0.47 tff(tptp_fun_W0_5_type, type, (
% 0.18/0.47 tptp_fun_W0_5: ( $i * $i ) > |'$ki_world'|)).
% 0.18/0.47 tff(entry_box_type, type, (
% 0.18/0.47 entry_box: ( |'$ki_world'| * $i ) > $o)).
% 0.18/0.47 tff(userid_type, type, (
% 0.18/0.47 userid: ( |'$ki_world'| * $i * $i ) > $o)).
% 0.18/0.47 tff(u_type, type, (
% 0.18/0.47 u: $i)).
% 0.18/0.47 tff(string_type, type, (
% 0.18/0.47 string: ( |'$ki_world'| * $i ) > $o)).
% 0.18/0.47 tff(tptp_fun___ki_local_world__type, type, (
% 0.18/0.47 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.18/0.47 tff(1,assumption,(~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))), introduced(assumption)).
% 0.18/0.47 tff(2,plain,
% 0.18/0.47 (^[W: |'$ki_world'|, V: |'$ki_world'|] : refl(tptp_fun___ki_accessible_(W, V) <=> tptp_fun___ki_accessible_(W, V))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(3,plain,
% 0.18/0.47 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V) <=> ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.18/0.47 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.47 tff(4,plain,
% 0.18/0.47 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V) <=> ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(5,axiom,(![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_universal')).
% 0.18/0.47 tff(6,plain,
% 0.18/0.47 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.47 tff(7,plain,(
% 0.18/0.47 ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.18/0.47 inference(skolemize,[status(sab)],[6])).
% 0.18/0.47 tff(8,plain,
% 0.18/0.47 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.47 tff(9,plain,
% 0.18/0.47 ((~![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(10,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.47 tff(11,plain,(tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(12,plain,
% 0.18/0.47 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(13,plain,
% 0.18/0.47 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.47 tff(14,plain,
% 0.18/0.47 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B!2) & number(W, B!2, one))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(15,plain,
% 0.18/0.47 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B!2) & number(W, B!2, one))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[14])).
% 0.18/0.47 tff(16,plain,
% 0.18/0.47 ((tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B!2) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B!2) & number(W, B!2, one)))) <=> (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B!2) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B!2) & number(W, B!2, one))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(17,plain,
% 0.18/0.47 (?[B: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B) & number(W, B, one)))) <=> ?[B: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B) & number(W, B, one))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(18,plain,
% 0.18/0.47 (^[B: $i] : rewrite((tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B) & ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (entry_box(W, B) & number(W, B, one)))) <=> (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B) & number(W, B, one)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(19,plain,
% 0.18/0.47 (?[B: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B) & ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (entry_box(W, B) & number(W, B, one)))) <=> ?[B: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B) & number(W, B, one))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[18])).
% 0.18/0.47 tff(20,axiom,(?[B: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B) & ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (entry_box(W, B) & number(W, B, one))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax2')).
% 0.18/0.47 tff(21,plain,
% 0.18/0.47 (?[B: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B) & number(W, B, one))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.47 tff(22,plain,
% 0.18/0.47 (?[B: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B) & number(W, B, one))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.18/0.47 tff(23,plain,
% 0.18/0.47 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, B!2) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B!2) & number(W, B!2, one)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.18/0.47 tff(24,plain,
% 0.18/0.47 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (entry_box(W, B!2) & number(W, B!2, one)))),
% 0.18/0.47 inference(and_elim,[status(thm)],[23])).
% 0.18/0.47 tff(25,plain,
% 0.18/0.47 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[24, 15])).
% 0.18/0.47 tff(26,plain,
% 0.18/0.47 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[25, 13])).
% 0.18/0.47 tff(27,plain,
% 0.18/0.47 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(28,plain,
% 0.18/0.47 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(29,plain,
% 0.18/0.47 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.47 tff(30,plain,
% 0.18/0.47 (~((~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[29, 26, 11])).
% 0.18/0.47 tff(31,plain,
% 0.18/0.47 (((~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one))) | number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(32,plain,
% 0.18/0.47 (number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.18/0.47 tff(33,plain,
% 0.18/0.47 (((~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one))) | entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(34,plain,
% 0.18/0.47 (entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[33, 30])).
% 0.18/0.47 tff(35,assumption,(~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))), introduced(assumption)).
% 0.18/0.47 tff(36,plain,
% 0.18/0.47 (((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one))))) | ((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(37,plain,
% 0.18/0.47 ((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.18/0.47 tff(38,plain,
% 0.18/0.47 ((~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))) | (~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(39,plain,
% 0.18/0.47 (~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[38, 37, 34, 32])).
% 0.18/0.47 tff(40,plain,
% 0.18/0.47 (((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~string(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4)))) | userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(41,plain,
% 0.18/0.47 ((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~string(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.18/0.47 tff(42,plain,
% 0.18/0.47 (((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one))))) | tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(43,plain,
% 0.18/0.47 (tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[42, 35])).
% 0.18/0.47 tff(44,plain,
% 0.18/0.47 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4) & ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (userid(tptp_fun_W0_5(B, I), u, I) & entry_box(tptp_fun_W0_5(B, I), B) & number(tptp_fun_W0_5(B, I), B, one)))) | (tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I)) & (~(in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I))))))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4) & ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (userid(tptp_fun_W0_5(B, I), u, I) & entry_box(tptp_fun_W0_5(B, I), B) & number(tptp_fun_W0_5(B, I), B, one)))) | (tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I)) & (~(in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(45,plain,
% 0.18/0.47 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ?[B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) & ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ?[S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & entry_box(W0, B) & number(W0, B, one))) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~tptp_fun___ki_exists_in_world__i_(W0, S2)) | (~do(W0, S, A, S2)))))))))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ?[B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) & ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ?[S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & entry_box(W0, B) & number(W0, B, one))) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~tptp_fun___ki_exists_in_world__i_(W0, S2)) | (~do(W0, S, A, S2))))))))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(46,plain,
% 0.18/0.47 ((~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ?[B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) & ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ?[S: $i] : ((tptp_fun___ki_exists_in_world__i_(W, S) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ((userid(W0, u, I) & entry_box(W0, B)) & number(W0, B, one)))) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2)))))))))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ?[B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) & ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ?[S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & entry_box(W0, B) & number(W0, B, one))) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~tptp_fun___ki_exists_in_world__i_(W0, S2)) | (~do(W0, S, A, S2))))))))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(47,axiom,(~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ?[B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) & ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ?[S: $i] : ((tptp_fun___ki_exists_in_world__i_(W, S) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ((userid(W0, u, I) & entry_box(W0, B)) & number(W0, B, one)))) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.18/0.47 tff(48,plain,
% 0.18/0.47 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ?[B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) & ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ?[S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & entry_box(W0, B) & number(W0, B, one))) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~tptp_fun___ki_exists_in_world__i_(W0, S2)) | (~do(W0, S, A, S2)))))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.47 tff(49,plain,
% 0.18/0.47 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ?[B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) & ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ?[S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & entry_box(W0, B) & number(W0, B, one))) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~tptp_fun___ki_exists_in_world__i_(W0, S2)) | (~do(W0, S, A, S2)))))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.18/0.47 tff(50,plain,
% 0.18/0.47 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ?[B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) & ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ?[S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & entry_box(W0, B) & number(W0, B, one))) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~tptp_fun___ki_exists_in_world__i_(W0, S2)) | (~do(W0, S, A, S2)))))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.18/0.47 tff(51,plain,
% 0.18/0.47 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ?[B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) & ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ?[S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & entry_box(W0, B) & number(W0, B, one))) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~tptp_fun___ki_exists_in_world__i_(W0, S2)) | (~do(W0, S, A, S2)))))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[50, 45])).
% 0.18/0.47 tff(52,plain,
% 0.18/0.47 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4) & ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (userid(tptp_fun_W0_5(B, I), u, I) & entry_box(tptp_fun_W0_5(B, I), B) & number(tptp_fun_W0_5(B, I), B, one)))) | (tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I)) & (~(in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I))))))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.18/0.47 tff(53,plain,
% 0.18/0.47 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)),
% 0.18/0.47 inference(and_elim,[status(thm)],[52])).
% 0.18/0.47 tff(54,plain,
% 0.18/0.47 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W)))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W)))))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(55,plain,
% 0.18/0.47 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W)))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W))))))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[54])).
% 0.18/0.47 tff(56,plain,
% 0.18/0.47 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W)))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W)))))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(57,plain,
% 0.18/0.47 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W)))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W))))))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[56])).
% 0.18/0.47 tff(58,plain,
% 0.18/0.47 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W)))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W))))))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[57, 55])).
% 0.18/0.47 tff(59,plain,
% 0.18/0.47 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W)) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, tptp_fun_I_1(W)) & string(W0, tptp_fun_I_1(W)))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W)))))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(60,plain,
% 0.18/0.47 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W)) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, tptp_fun_I_1(W)) & string(W0, tptp_fun_I_1(W)))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W))))))))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.48 tff(61,plain,
% 0.18/0.48 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & string(W0, I))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & string(W0, I)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(62,plain,
% 0.18/0.48 (^[W: |'$ki_world'|] : trans(monotonicity(quant_intro(proof_bind(^[I: $i] : rewrite((tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => (userid(W0, u, I) & string(W0, I)))) <=> (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & string(W0, I)))))), (?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => (userid(W0, u, I) & string(W0, I)))) <=> ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & string(W0, I)))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => (userid(W0, u, I) & string(W0, I))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & string(W0, I))))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & string(W0, I))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & string(W0, I)))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => (userid(W0, u, I) & string(W0, I))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & string(W0, I)))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(63,plain,
% 0.18/0.48 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => (userid(W0, u, I) & string(W0, I))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & string(W0, I)))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.48 tff(64,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => (userid(W0, u, I) & string(W0, I)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax1')).
% 0.18/0.48 tff(65,plain,
% 0.18/0.48 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & string(W0, I)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.18/0.48 tff(66,plain,
% 0.18/0.48 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, I) & string(W0, I)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.18/0.48 tff(67,plain,(
% 0.18/0.48 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W)) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (userid(W0, u, tptp_fun_I_1(W)) & string(W0, tptp_fun_I_1(W))))))),
% 0.18/0.48 inference(skolemize,[status(sab)],[66])).
% 0.18/0.48 tff(68,plain,
% 0.18/0.48 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W))))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.18/0.48 tff(69,plain,
% 0.18/0.48 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W))))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.18/0.48 tff(70,plain,
% 0.18/0.48 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W))))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W))))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(71,plain,
% 0.18/0.48 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W))))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(72,plain,
% 0.18/0.48 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_I_1(W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W))) | (~string(W0, tptp_fun_I_1(W))))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4)))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.18/0.48 tff(73,plain,
% 0.18/0.48 (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[72, 69, 53])).
% 0.18/0.48 tff(74,plain,
% 0.18/0.48 (((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4)))))))) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(75,plain,
% 0.18/0.48 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.18/0.48 tff(76,plain,
% 0.18/0.48 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | ((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~string(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~string(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(77,plain,
% 0.18/0.48 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | ((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~string(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(78,plain,
% 0.18/0.48 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~string(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.48 tff(79,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[78, 75, 43, 41])).
% 0.18/0.48 tff(80,plain,((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(81,assumption,(~tptp_fun___ki_exists_in_world__i_(W!4, B!2)), introduced(assumption)).
% 0.18/0.48 tff(82,plain,
% 0.18/0.48 (^[W: |'$ki_world'|, X: $i] : refl(tptp_fun___ki_exists_in_world__i_(W, X) <=> tptp_fun___ki_exists_in_world__i_(W, X))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(83,plain,
% 0.18/0.48 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X) <=> ![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.18/0.48 inference(quant_intro,[status(thm)],[82])).
% 0.18/0.48 tff(84,plain,
% 0.18/0.48 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X) <=> ![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(85,axiom,(![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''$ki_exists_in_world_$i_const'')).
% 0.18/0.48 tff(86,plain,
% 0.18/0.48 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.48 tff(87,plain,(
% 0.18/0.48 ![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.18/0.48 inference(skolemize,[status(sab)],[86])).
% 0.18/0.48 tff(88,plain,
% 0.18/0.48 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.18/0.48 tff(89,plain,
% 0.18/0.48 ((~![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)) | tptp_fun___ki_exists_in_world__i_(W!4, B!2)),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(90,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[89, 88, 81])).
% 0.18/0.48 tff(91,plain,(tptp_fun___ki_exists_in_world__i_(W!4, B!2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(92,plain,
% 0.18/0.48 (((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4)))))))) | tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(93,plain,
% 0.18/0.48 (tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[92, 73])).
% 0.18/0.48 tff(94,plain,
% 0.18/0.48 (^[I: $i] : refl(((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I))))))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(95,plain,
% 0.18/0.48 (![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I))))))))) <=> ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[94])).
% 0.18/0.48 tff(96,plain,
% 0.18/0.48 (^[I: $i] : rewrite(((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I))))))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(97,plain,
% 0.18/0.48 (![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I))))))))) <=> ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[96])).
% 0.18/0.48 tff(98,plain,
% 0.18/0.48 (![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I))))))))) <=> ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[97, 95])).
% 0.18/0.48 tff(99,plain,
% 0.18/0.48 (^[I: $i] : rewrite(((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (userid(tptp_fun_W0_5(B, I), u, I) & entry_box(tptp_fun_W0_5(B, I), B) & number(tptp_fun_W0_5(B, I), B, one)))) | (tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I)) & (~(in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I))))))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(100,plain,
% 0.18/0.48 (![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (userid(tptp_fun_W0_5(B, I), u, I) & entry_box(tptp_fun_W0_5(B, I), B) & number(tptp_fun_W0_5(B, I), B, one)))) | (tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I)) & (~(in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))) <=> ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.48 tff(101,plain,
% 0.18/0.48 (![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (userid(tptp_fun_W0_5(B, I), u, I) & entry_box(tptp_fun_W0_5(B, I), B) & number(tptp_fun_W0_5(B, I), B, one)))) | (tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I)) & (~(in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I))))))))))),
% 0.18/0.48 inference(and_elim,[status(thm)],[52])).
% 0.18/0.48 tff(102,plain,
% 0.18/0.48 (![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.18/0.48 tff(103,plain,
% 0.18/0.48 (![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.18/0.48 tff(104,plain,
% 0.18/0.48 (((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~(in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))))))))))) <=> ((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~(in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))))))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(105,plain,
% 0.18/0.48 (((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~(in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))))))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(106,plain,
% 0.18/0.48 (((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))))))))))) <=> ((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~(in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))))))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[105])).
% 0.18/0.48 tff(107,plain,
% 0.18/0.48 (((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))))))))))) <=> ((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~(in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))))))))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[106, 104])).
% 0.18/0.49 tff(108,plain,
% 0.18/0.49 ((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))))))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(109,plain,
% 0.18/0.49 ((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, I))) | (~((~userid(tptp_fun_W0_5(B, I), u, I)) | (~entry_box(tptp_fun_W0_5(B, I), B)) | (~number(tptp_fun_W0_5(B, I), B, one)))))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, I))) | in(tptp_fun_W0_6(S, A, B, I), I, B, tptp_fun_S2_7(S, A, B, I)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, I), tptp_fun_S2_7(S, A, B, I))) | (~do(tptp_fun_W0_6(S, A, B, I), S, A, tptp_fun_S2_7(S, A, B, I)))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~(in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))))))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.18/0.49 tff(110,plain,
% 0.18/0.49 (![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~(in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))))))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[109, 103, 93])).
% 0.18/0.49 tff(111,plain,
% 0.18/0.49 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~(in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))))))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~(in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(112,plain,
% 0.18/0.49 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~(in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(113,plain,
% 0.18/0.49 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B)) | (~number(tptp_fun_W0_5(B, tptp_fun_I_1(W!4)), B, one)))))) | (~(in(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B, tptp_fun_I_1(W!4)))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))))))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.18/0.49 tff(114,plain,
% 0.18/0.49 ((~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))))))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[113, 110])).
% 0.18/0.49 tff(115,plain,
% 0.18/0.49 (![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))))))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[114, 91])).
% 0.18/0.49 tff(116,assumption,(~tptp_fun___ki_accessible_(W!4, W!4)), introduced(assumption)).
% 0.18/0.49 tff(117,plain,
% 0.18/0.49 ((~![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(W!4, W!4)),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(118,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[117, 8, 116])).
% 0.18/0.49 tff(119,plain,(tptp_fun___ki_accessible_(W!4, W!4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(120,plain,
% 0.18/0.49 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | ((~tptp_fun___ki_accessible_(W!4, W!4)) | (~((~string(W!4, tptp_fun_I_1(W!4))) | (~userid(W!4, u, tptp_fun_I_1(W!4))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | (~tptp_fun___ki_accessible_(W!4, W!4)) | (~((~string(W!4, tptp_fun_I_1(W!4))) | (~userid(W!4, u, tptp_fun_I_1(W!4))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(121,plain,
% 0.18/0.49 (((~tptp_fun___ki_accessible_(W!4, W!4)) | (~((~userid(W!4, u, tptp_fun_I_1(W!4))) | (~string(W!4, tptp_fun_I_1(W!4)))))) <=> ((~tptp_fun___ki_accessible_(W!4, W!4)) | (~((~string(W!4, tptp_fun_I_1(W!4))) | (~userid(W!4, u, tptp_fun_I_1(W!4))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(122,plain,
% 0.18/0.49 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | ((~tptp_fun___ki_accessible_(W!4, W!4)) | (~((~userid(W!4, u, tptp_fun_I_1(W!4))) | (~string(W!4, tptp_fun_I_1(W!4))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | ((~tptp_fun___ki_accessible_(W!4, W!4)) | (~((~string(W!4, tptp_fun_I_1(W!4))) | (~userid(W!4, u, tptp_fun_I_1(W!4)))))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[121])).
% 0.18/0.49 tff(123,plain,
% 0.18/0.49 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | ((~tptp_fun___ki_accessible_(W!4, W!4)) | (~((~userid(W!4, u, tptp_fun_I_1(W!4))) | (~string(W!4, tptp_fun_I_1(W!4))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | (~tptp_fun___ki_accessible_(W!4, W!4)) | (~((~string(W!4, tptp_fun_I_1(W!4))) | (~userid(W!4, u, tptp_fun_I_1(W!4))))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[122, 120])).
% 0.18/0.49 tff(124,plain,
% 0.18/0.49 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | ((~tptp_fun___ki_accessible_(W!4, W!4)) | (~((~userid(W!4, u, tptp_fun_I_1(W!4))) | (~string(W!4, tptp_fun_I_1(W!4))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(125,plain,
% 0.18/0.49 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | (~((~userid(W0, u, tptp_fun_I_1(W!4))) | (~string(W0, tptp_fun_I_1(W!4))))))) | (~tptp_fun___ki_accessible_(W!4, W!4)) | (~((~string(W!4, tptp_fun_I_1(W!4))) | (~userid(W!4, u, tptp_fun_I_1(W!4)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.49 tff(126,plain,
% 0.18/0.49 ((~tptp_fun___ki_accessible_(W!4, W!4)) | (~((~string(W!4, tptp_fun_I_1(W!4))) | (~userid(W!4, u, tptp_fun_I_1(W!4)))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[125, 75])).
% 0.18/0.49 tff(127,plain,
% 0.18/0.49 (~((~string(W!4, tptp_fun_I_1(W!4))) | (~userid(W!4, u, tptp_fun_I_1(W!4))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[126, 119])).
% 0.18/0.49 tff(128,plain,
% 0.18/0.49 (((~string(W!4, tptp_fun_I_1(W!4))) | (~userid(W!4, u, tptp_fun_I_1(W!4)))) | string(W!4, tptp_fun_I_1(W!4))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(129,plain,
% 0.18/0.49 (string(W!4, tptp_fun_I_1(W!4))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.18/0.49 tff(130,plain,
% 0.18/0.49 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2))))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2))))))))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(131,plain,
% 0.18/0.49 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2))))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[130])).
% 0.18/0.49 tff(132,plain,
% 0.18/0.49 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2))))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2))))))))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(133,plain,
% 0.18/0.49 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2))))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[132])).
% 0.18/0.49 tff(134,plain,
% 0.18/0.49 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2))))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[133, 131])).
% 0.18/0.49 tff(135,plain,
% 0.18/0.49 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W)) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2))))))))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(136,plain,
% 0.18/0.49 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W)) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[135])).
% 0.18/0.49 tff(137,plain,
% 0.18/0.49 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W)) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W)) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2))))))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(138,plain,
% 0.18/0.49 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W)) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W)) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[137])).
% 0.18/0.49 tff(139,plain,
% 0.18/0.49 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(140,plain,
% 0.18/0.49 (^[W: |'$ki_world'|] : trans(monotonicity(quant_intro(proof_bind(^[S: $i] : trans(monotonicity(quant_intro(proof_bind(^[I: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[A: $i] : rewrite((tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2))))) <=> (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))))), (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2))))) <=> ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))))), (((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2)))))) <=> ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2)))))))), rewrite(((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2)))))) <=> ((~(string(W, I) & entry_box(W, B))) | ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))))), (((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2)))))) <=> ((~(string(W, I) & entry_box(W, B))) | ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2)))))))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2))))))) <=> (tptp_fun___ki_exists_in_world__i_(W, B) => ((~(string(W, I) & entry_box(W, B))) | ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, B) => ((~(string(W, I) & entry_box(W, B))) | ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))))) <=> (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2))))))) <=> (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))))), (![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2))))))) <=> ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))), ((tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2)))))))) <=> (tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))), ((tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2)))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))))), (![I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2)))))))) <=> ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))))), ((tptp_fun___ki_exists_in_world__i_(W, S) => ![I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2))))))))) <=> (tptp_fun___ki_exists_in_world__i_(W, S) => ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, S) => ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))))), ((tptp_fun___ki_exists_in_world__i_(W, S) => ![I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))))))), (![S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) => ![I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2))))))))) <=> ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) => ![I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2)))))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) => ![I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2)))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(141,plain,
% 0.18/0.50 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) => ![I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2)))))))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[140])).
% 0.18/0.50 tff(142,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![S: $i] : (tptp_fun___ki_exists_in_world__i_(W, S) => ![I: $i] : (tptp_fun___ki_exists_in_world__i_(W, I) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ((string(W, I) & entry_box(W, B)) => ?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ![S2: $i] : (tptp_fun___ki_exists_in_world__i_(W0, S2) => (do(W0, S, A, S2) => in(W0, I, B, S2))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax3')).
% 0.18/0.50 tff(143,plain,
% 0.18/0.50 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.18/0.50 tff(144,plain,
% 0.18/0.50 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : (?[A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, A, S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.18/0.50 tff(145,plain,(
% 0.18/0.50 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W)) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : (in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)) | (~tptp_fun___ki_exists_in_world__i_(W0, S2))))) | (~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B))))))),
% 0.18/0.50 inference(skolemize,[status(sab)],[144])).
% 0.18/0.50 tff(146,plain,
% 0.18/0.50 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~(string(W, I) & entry_box(W, B))) | (~tptp_fun___ki_exists_in_world__i_(W, B)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W)) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.18/0.50 tff(147,plain,
% 0.18/0.50 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[146, 136])).
% 0.18/0.50 tff(148,plain,
% 0.18/0.50 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[147, 134])).
% 0.18/0.50 tff(149,plain,
% 0.18/0.50 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(150,plain,
% 0.18/0.50 (((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(151,plain,
% 0.18/0.50 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2)))))))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[150])).
% 0.18/0.50 tff(152,plain,
% 0.18/0.50 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2)))))))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B))))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[151, 149])).
% 0.18/0.50 tff(153,plain,
% 0.18/0.50 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2)))))))))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(154,plain,
% 0.18/0.50 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | (~string(W, I)) | (~entry_box(W, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_A_3(B, I, S, W))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W), S2)))))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.18/0.50 tff(155,plain,
% 0.18/0.50 (![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[154, 148, 53])).
% 0.18/0.50 tff(156,plain,
% 0.18/0.50 (((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2))))))))))) <=> ((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2))))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(157,plain,
% 0.18/0.50 (((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2))))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(158,plain,
% 0.18/0.50 (((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))) <=> ((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2)))))))))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[157])).
% 0.18/0.50 tff(159,plain,
% 0.18/0.50 (((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))) <=> ((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2))))))))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[158, 156])).
% 0.18/0.50 tff(160,plain,
% 0.18/0.50 ((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(161,plain,
% 0.18/0.51 ((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, S, W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, S, tptp_fun_A_3(B, I, S, W!4), S2))))))) | (~string(W!4, I)) | (~entry_box(W!4, B)))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2)))))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.18/0.51 tff(162,plain,
% 0.18/0.51 (![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2)))))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[161, 155, 93])).
% 0.18/0.51 tff(163,plain,
% 0.18/0.51 (((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4)))))) <=> ((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2)))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(164,plain,
% 0.18/0.51 (((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, tptp_fun_I_1(W!4))) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(165,plain,
% 0.18/0.51 (((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, tptp_fun_I_1(W!4))) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))))))))) <=> ((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[164])).
% 0.18/0.51 tff(166,plain,
% 0.18/0.51 (((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, tptp_fun_I_1(W!4))) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))))))))) <=> ((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2)))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4)))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[165, 163])).
% 0.18/0.51 tff(167,plain,
% 0.18/0.51 ((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2)))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, tptp_fun_I_1(W!4))) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))))))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(168,plain,
% 0.18/0.51 ((~![I: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, I)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~string(W!4, I)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, I, B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, I, tptp_fun_I_1(W!4), W!4), S2)))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.18/0.51 tff(169,plain,
% 0.18/0.51 (![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[168, 93, 162])).
% 0.18/0.51 tff(170,plain,
% 0.18/0.51 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | (~((~entry_box(W!4, B!2)) | (~number(W!4, B!2, one)))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | (~((~entry_box(W!4, B!2)) | (~number(W!4, B!2, one)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(171,plain,
% 0.18/0.51 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | (~((~entry_box(W!4, B!2)) | (~number(W!4, B!2, one)))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(172,plain,
% 0.18/0.51 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~entry_box(W, B!2)) | (~number(W, B!2, one)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | (~((~entry_box(W!4, B!2)) | (~number(W!4, B!2, one))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.18/0.51 tff(173,plain,
% 0.18/0.51 (~((~entry_box(W!4, B!2)) | (~number(W!4, B!2, one)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[172, 26, 53])).
% 0.18/0.51 tff(174,plain,
% 0.18/0.51 (((~entry_box(W!4, B!2)) | (~number(W!4, B!2, one))) | entry_box(W!4, B!2)),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(175,plain,
% 0.18/0.51 (entry_box(W!4, B!2)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.18/0.51 tff(176,plain,
% 0.18/0.51 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))) | ((~entry_box(W!4, B!2)) | (~string(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, B!2)))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))) | (~entry_box(W!4, B!2)) | (~string(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, B!2)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(177,plain,
% 0.18/0.51 (((~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | (~entry_box(W!4, B!2)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4)))) <=> ((~entry_box(W!4, B!2)) | (~string(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, B!2)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(178,plain,
% 0.18/0.51 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) <=> (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(179,plain,
% 0.18/0.51 (((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[178])).
% 0.18/0.51 tff(180,plain,
% 0.18/0.51 ((~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) <=> (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[179])).
% 0.18/0.51 tff(181,plain,
% 0.18/0.51 (((~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | (~entry_box(W!4, B!2)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4)))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | (~entry_box(W!4, B!2)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[180])).
% 0.18/0.51 tff(182,plain,
% 0.18/0.51 (((~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | (~entry_box(W!4, B!2)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4)))) <=> ((~entry_box(W!4, B!2)) | (~string(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, B!2)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[181, 177])).
% 0.18/0.51 tff(183,plain,
% 0.18/0.51 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | (~entry_box(W!4, B!2)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))) | ((~entry_box(W!4, B!2)) | (~string(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, B!2))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[182])).
% 0.18/0.51 tff(184,plain,
% 0.18/0.51 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | (~entry_box(W!4, B!2)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))) | (~entry_box(W!4, B!2)) | (~string(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, B!2)))),
% 0.18/0.52 inference(transitivity,[status(thm)],[183, 176])).
% 0.18/0.52 tff(185,plain,
% 0.18/0.52 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, B!2)) | (~entry_box(W!4, B!2)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(186,plain,
% 0.18/0.52 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, B)) | (~entry_box(W!4, B)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~string(W!4, tptp_fun_I_1(W!4))))) | (~entry_box(W!4, B!2)) | (~string(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, B!2))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.18/0.52 tff(187,plain,
% 0.18/0.52 ((~string(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, B!2))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[186, 175, 169])).
% 0.18/0.52 tff(188,plain,
% 0.18/0.52 (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[187, 91, 129])).
% 0.18/0.52 tff(189,plain,
% 0.18/0.52 (((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))))) | tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(190,plain,
% 0.18/0.52 (tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.18/0.52 tff(191,plain,
% 0.18/0.52 (((~![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))))))))) <=> ((~![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(192,plain,
% 0.18/0.52 ((~![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))))))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(193,plain,
% 0.18/0.52 ((~![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, A)) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, A, B!2, tptp_fun_I_1(W!4)), S, A, tptp_fun_S2_7(S, A, B!2, tptp_fun_I_1(W!4))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | ![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.18/0.52 tff(194,plain,
% 0.18/0.52 (![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[193, 190, 115])).
% 0.18/0.52 tff(195,plain,
% 0.18/0.52 (((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))))) <=> ((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(196,plain,
% 0.18/0.53 ((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(197,plain,
% 0.18/0.53 ((~![S: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, S)) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(S, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_I_1(W!4))) | (~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.18/0.53 tff(198,plain,
% 0.18/0.53 ((~((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)))) | (~((~userid(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), u, tptp_fun_I_1(W!4))) | (~entry_box(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2)) | (~number(tptp_fun_W0_5(B!2, tptp_fun_I_1(W!4)), B!2, one)))))) | (~(in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[197, 93, 194])).
% 0.18/0.53 tff(199,plain,
% 0.18/0.53 (~(in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[198, 80])).
% 0.18/0.53 tff(200,plain,
% 0.18/0.53 ((in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))))) | tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(201,plain,
% 0.18/0.53 (tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.18/0.53 tff(202,plain,
% 0.18/0.53 (((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4))) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))))) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(203,plain,
% 0.18/0.53 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[202, 188])).
% 0.18/0.53 tff(204,plain,
% 0.18/0.53 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) | ((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | ![S2: $i] : (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | ![S2: $i] : (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(205,plain,
% 0.18/0.53 (((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))) <=> ((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | ![S2: $i] : (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(206,plain,
% 0.18/0.53 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) | ((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) | ((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | ![S2: $i] : (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[205])).
% 0.18/0.53 tff(207,plain,
% 0.18/0.53 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) | ((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | ![S2: $i] : (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))),
% 0.18/0.53 inference(transitivity,[status(thm)],[206, 204])).
% 0.18/0.53 tff(208,plain,
% 0.18/0.53 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) | ((~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(209,plain,
% 0.18/0.53 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!4, W0)) | ![S2: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, S2)) | in(W0, tptp_fun_I_1(W!4), B!2, S2) | (~do(W0, tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2))))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | ![S2: $i] : (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.18/0.53 tff(210,plain,
% 0.18/0.53 (![S2: $i] : (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[209, 203, 201])).
% 0.18/0.54 tff(211,plain,
% 0.18/0.54 ((in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))))) | do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(212,plain,
% 0.18/0.54 (do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[211, 199])).
% 0.18/0.54 tff(213,plain,
% 0.18/0.54 ((in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))))) | tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(214,plain,
% 0.18/0.54 (tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[213, 199])).
% 0.18/0.54 tff(215,plain,
% 0.18/0.54 ((in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_accessible_(W!4, tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))))) | (~in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(216,plain,
% 0.18/0.54 (~in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[215, 199])).
% 0.18/0.54 tff(217,plain,
% 0.18/0.54 (((~![S2: $i] : (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))) | (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))) <=> ((~![S2: $i] : (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))) | in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(218,plain,
% 0.18/0.54 ((~![S2: $i] : (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))) | (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(219,plain,
% 0.18/0.54 ((~![S2: $i] : (in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, S2) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), S2)) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), S2)))) | in(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), B!2, tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)))) | (~do(tptp_fun_W0_6(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4)), tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), tptp_fun_S2_7(tptp_fun_I_1(W!4), tptp_fun_A_3(B!2, tptp_fun_I_1(W!4), tptp_fun_I_1(W!4), W!4), B!2, tptp_fun_I_1(W!4))))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.18/0.54 tff(220,plain,
% 0.18/0.54 ($false),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[219, 216, 214, 212, 210])).
% 0.18/0.54 % SZS output end Proof
% 0.18/0.54 % E exiting
%------------------------------------------------------------------------------