%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO889_16 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:42:25 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO889_16 : TPTP v9.0.0. Released v8.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 13:50:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(a_type, type, (
% 0.12/0.37 a: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_X_2_type, type, (
% 0.12/0.37 tptp_fun_X_2: $i)).
% 0.12/0.37 tff(tptp_fun_W0_3_type, type, (
% 0.12/0.37 tptp_fun_W0_3: ( $i * |'$ki_world'| ) > |'$ki_world'|)).
% 0.12/0.37 tff(tptp_fun_W_1_type, type, (
% 0.12/0.37 tptp_fun_W_1: |'$ki_world'|)).
% 0.12/0.37 tff(tptp_fun___ki_accessible__type, type, (
% 0.12/0.37 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.12/0.37 tff(b_type, type, (
% 0.12/0.37 b: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.12/0.37 tptp_fun___ki_exists_in_world__i_: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun___ki_local_world__type, type, (
% 0.12/0.37 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X)))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X)))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X)))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X)))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X)))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X)))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X)))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X))))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W)) & b(tptp_fun_W0_3(X, W), X)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X)))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W)) & b(tptp_fun_W0_3(X, W), X)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & b(W0, X)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & b(W0, X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 ((~((?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => a(W0, X)))) & ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & b(W0, X))))) => ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : ((tptp_fun___ki_accessible_(W, W0) & a(W0, X)) & b(W0, X)))))) <=> (~((~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | a(W0, X)))) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & b(W0, X)))))) | ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(10,axiom,(~((?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => a(W0, X)))) & ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & b(W0, X))))) => ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : ((tptp_fun___ki_accessible_(W, W0) & a(W0, X)) & b(W0, X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (~((~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | a(W0, X)))) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & b(W0, X)))))) | ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | a(W0, X)))) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & b(W0, X))))),
% 0.12/0.38 inference(or_elim,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & b(W0, X))))),
% 0.12/0.38 inference(and_elim,[status(thm)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & b(W0, X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.12/0.38 tff(15,plain,(
% 0.12/0.38 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W)) & b(tptp_fun_W0_3(X, W), X))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 5])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & (tptp_fun___ki_exists_in_world__i_(W!1, X!2) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2)))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & tptp_fun___ki_exists_in_world__i_(W!1, X!2) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ((tptp_fun___ki_exists_in_world__i_(W!1, X!2) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2))) <=> (tptp_fun___ki_exists_in_world__i_(W!1, X!2) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & (tptp_fun___ki_exists_in_world__i_(W!1, X!2) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2)))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & (tptp_fun___ki_exists_in_world__i_(W!1, X!2) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & (tptp_fun___ki_exists_in_world__i_(W!1, X!2) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2)))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & tptp_fun___ki_exists_in_world__i_(W!1, X!2) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[20, 18])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | a(W0, X)))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | a(W0, X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | a(W0, X))))),
% 0.12/0.38 inference(and_elim,[status(thm)],[12])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | a(W0, X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & tptp_fun___ki_exists_in_world__i_(W!1, X!2) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)),
% 0.12/0.38 inference(and_elim,[status(thm)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X, W!1))) | (~b(tptp_fun_W0_3(X, W!1), X))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X, W!1))) | (~b(tptp_fun_W0_3(X, W!1), X))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X, W!1))) | (~b(tptp_fun_W0_3(X, W!1), X))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_3(X, W))) | (~b(tptp_fun_W0_3(X, W), X))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X, W!1))) | (~b(tptp_fun_W0_3(X, W!1), X)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X, W!1))) | (~b(tptp_fun_W0_3(X, W!1), X)))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[29, 26, 17])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (tptp_fun___ki_exists_in_world__i_(W!1, X!2)),
% 0.12/0.38 inference(and_elim,[status(thm)],[25])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X, W!1))) | (~b(tptp_fun_W0_3(X, W!1), X)))))) | ((~tptp_fun___ki_exists_in_world__i_(W!1, X!2)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | (~b(tptp_fun_W0_3(X!2, W!1), X!2)))))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X, W!1))) | (~b(tptp_fun_W0_3(X, W!1), X)))))) | (~tptp_fun___ki_exists_in_world__i_(W!1, X!2)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | (~b(tptp_fun_W0_3(X!2, W!1), X!2)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X, W!1))) | (~b(tptp_fun_W0_3(X, W!1), X)))))) | ((~tptp_fun___ki_exists_in_world__i_(W!1, X!2)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | (~b(tptp_fun_W0_3(X!2, W!1), X!2)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X, W!1))) | (~b(tptp_fun_W0_3(X, W!1), X)))))) | (~tptp_fun___ki_exists_in_world__i_(W!1, X!2)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | (~b(tptp_fun_W0_3(X!2, W!1), X!2))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | (~b(tptp_fun_W0_3(X!2, W!1), X!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[34, 31, 30])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | (~b(tptp_fun_W0_3(X!2, W!1), X!2))) | tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (^[W0: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2)) <=> ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2)) <=> ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2))),
% 0.12/0.38 inference(and_elim,[status(thm)],[25])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2))) | ((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | a(tptp_fun_W0_3(X!2, W!1), X!2))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2))) | (~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | a(tptp_fun_W0_3(X!2, W!1), X!2))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2))) | ((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | a(tptp_fun_W0_3(X!2, W!1), X!2))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | a(W0, X!2))) | (~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | a(tptp_fun_W0_3(X!2, W!1), X!2)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (a(tptp_fun_W0_3(X!2, W!1), X!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[44, 41, 37])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[48])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X)))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[49, 47])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 ((~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))))),
% 0.12/0.38 inference(or_elim,[status(thm)],[11])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[55, 53])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[56, 53])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (^[W: |'$ki_world'|] : nnf_neg(refl($oeq((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)), (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))), nnf_neg(proof_bind(^[X: $i] : nnf_neg(refl($oeq((~tptp_fun___ki_exists_in_world__i_(W, X)), (~tptp_fun___ki_exists_in_world__i_(W, X)))), nnf_neg(proof_bind(^[W0: |'$ki_world'|] : refl($oeq((~(tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))), (~(tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X)))))), $oeq((~?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))), ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))))), $oeq((~(tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X)))), ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))))))), $oeq((~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X)))), ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X)))))), $oeq((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X))))), ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(59,plain,(
% 0.12/0.39 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & a(W0, X) & b(W0, X)))))),
% 0.12/0.39 inference(nnf-neg,[status(sab)],[57, 58])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X)) | (~b(W0, X)))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X)) | (~b(W0, X)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X)) | (~b(W0, X)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~a(W0, X)) | (~b(W0, X)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X)) | (~b(W0, X))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X)) | (~b(W0, X))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[64, 26, 61])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X)) | (~b(W0, X))))) | ((~tptp_fun___ki_exists_in_world__i_(W!1, X!2)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X!2)) | (~b(W0, X!2))))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X)) | (~b(W0, X))))) | (~tptp_fun___ki_exists_in_world__i_(W!1, X!2)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X!2)) | (~b(W0, X!2))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X)) | (~b(W0, X))))) | ((~tptp_fun___ki_exists_in_world__i_(W!1, X!2)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X!2)) | (~b(W0, X!2))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!1, X)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X)) | (~b(W0, X))))) | (~tptp_fun___ki_exists_in_world__i_(W!1, X!2)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X!2)) | (~b(W0, X!2)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X!2)) | (~b(W0, X!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[68, 31, 65])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | (~b(tptp_fun_W0_3(X!2, W!1), X!2))) | b(tptp_fun_W0_3(X!2, W!1), X!2)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (b(tptp_fun_W0_3(X!2, W!1), X!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[70, 35])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X!2)) | (~b(W0, X!2)))) | ((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | (~a(tptp_fun_W0_3(X!2, W!1), X!2)) | (~b(tptp_fun_W0_3(X!2, W!1), X!2)))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X!2)) | (~b(W0, X!2)))) | (~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | (~a(tptp_fun_W0_3(X!2, W!1), X!2)) | (~b(tptp_fun_W0_3(X!2, W!1), X!2)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X!2)) | (~b(W0, X!2)))) | ((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | (~a(tptp_fun_W0_3(X!2, W!1), X!2)) | (~b(tptp_fun_W0_3(X!2, W!1), X!2)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~a(W0, X!2)) | (~b(W0, X!2)))) | (~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_3(X!2, W!1))) | (~a(tptp_fun_W0_3(X!2, W!1), X!2)) | (~b(tptp_fun_W0_3(X!2, W!1), X!2))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[74, 37, 71, 69, 45])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------