%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO894_8 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:42:26 AM UTC 2025
% Result : Theorem 0.11s 0.34s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO894_8 : TPTP v9.0.0. Released v8.2.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 13:50:48 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.34 % SZS status Theorem
% 0.11/0.34 % SZS output start Proof
% 0.11/0.34 tff(p_type, type, (
% 0.11/0.34 p: |'$ki_world'| > $o)).
% 0.11/0.34 tff(tptp_fun_W_0_type, type, (
% 0.11/0.34 tptp_fun_W_0: |'$ki_world'|)).
% 0.11/0.34 tff(tptp_fun___ki_accessible__type, type, (
% 0.11/0.34 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.11/0.34 tff(tptp_fun___ki_local_world__type, type, (
% 0.11/0.34 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.11/0.34 tff(tptp_fun_W_1_type, type, (
% 0.11/0.34 tptp_fun_W_1: |'$ki_world'|)).
% 0.11/0.34 tff(1,assumption,(~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))), introduced(assumption)).
% 0.11/0.34 tff(2,plain,
% 0.11/0.34 (((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))) | tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)),
% 0.11/0.34 inference(tautology,[status(thm)],[])).
% 0.11/0.34 tff(3,plain,
% 0.11/0.34 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)),
% 0.11/0.34 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.11/0.34 tff(4,plain,
% 0.11/0.34 (((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))) | p(W!1)),
% 0.11/0.34 inference(tautology,[status(thm)],[])).
% 0.11/0.34 tff(5,plain,
% 0.11/0.34 (p(W!1)),
% 0.11/0.34 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.11/0.34 tff(6,plain,
% 0.11/0.34 (^[W: |'$ki_world'|] : refl(((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.11/0.34 inference(bind,[status(th)],[])).
% 0.11/0.34 tff(7,plain,
% 0.11/0.34 (![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.34 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.34 tff(8,plain,
% 0.11/0.34 ((![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) | ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.34 inference(rewrite,[status(thm)],[])).
% 0.11/0.34 tff(9,plain,
% 0.11/0.34 (^[W: |'$ki_world'|] : trans(monotonicity(rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> (~((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))), ((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) <=> (~(~((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))))), rewrite((~(~((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))) <=> ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))), ((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) <=> ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))))),
% 0.11/0.34 inference(bind,[status(th)],[])).
% 0.11/0.34 tff(10,plain,
% 0.11/0.34 (![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.34 inference(quant_intro,[status(thm)],[9])).
% 0.11/0.34 tff(11,plain,
% 0.11/0.34 ((![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) | ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) <=> (![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) | ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.11/0.34 inference(monotonicity,[status(thm)],[10])).
% 0.11/0.34 tff(12,plain,
% 0.11/0.34 ((![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) | ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.34 inference(transitivity,[status(thm)],[11, 8])).
% 0.11/0.34 tff(13,plain,
% 0.11/0.34 (((![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) | ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) & ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & p(W!0)) | (~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))))) <=> ((![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) | ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) & ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & p(W!0)) | (~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))))))),
% 0.11/0.34 inference(rewrite,[status(thm)],[])).
% 0.11/0.34 tff(14,plain,
% 0.11/0.34 ((?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) <=> (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.11/0.34 inference(rewrite,[status(thm)],[])).
% 0.11/0.34 tff(15,plain,
% 0.11/0.34 ((~(~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))))) <=> (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.11/0.34 inference(rewrite,[status(thm)],[])).
% 0.11/0.34 tff(16,plain,
% 0.11/0.34 ((~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))) <=> (~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(17,plain,
% 0.11/0.35 ((![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)))) <=> (~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(18,plain,
% 0.11/0.35 ((~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(19,plain,
% 0.11/0.35 (^[W: |'$ki_world'|] : trans(monotonicity(rewrite((p(W) => (~p(W))) <=> (~p(W))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) => (~p(W)))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (~p(W))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (~p(W))) <=> ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) => (~p(W)))) <=> ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))))),
% 0.11/0.35 inference(bind,[status(th)],[])).
% 0.11/0.35 tff(20,plain,
% 0.11/0.35 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) => (~p(W)))) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.35 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.35 tff(21,plain,
% 0.11/0.35 ((![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) => (~p(W)))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)))) <=> (![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))))),
% 0.11/0.35 inference(monotonicity,[status(thm)],[20, 18])).
% 0.11/0.35 tff(22,plain,
% 0.11/0.35 ((![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) => (~p(W)))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)))) <=> (~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))))),
% 0.11/0.35 inference(transitivity,[status(thm)],[21, 17])).
% 0.11/0.35 tff(23,plain,
% 0.11/0.35 ((![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) => (~p(W)))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)))) <=> (~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))))),
% 0.11/0.35 inference(transitivity,[status(thm)],[22, 16])).
% 0.11/0.35 tff(24,plain,
% 0.11/0.35 ((~(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) => (~p(W)))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))))) <=> (~(~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))))),
% 0.11/0.35 inference(monotonicity,[status(thm)],[23])).
% 0.11/0.35 tff(25,plain,
% 0.11/0.35 ((~(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) => (~p(W)))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))))) <=> (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.11/0.35 inference(transitivity,[status(thm)],[24, 15])).
% 0.11/0.35 tff(26,axiom,(~(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) => (~p(W)))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.11/0.35 tff(27,plain,
% 0.11/0.35 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.35 tff(28,plain,
% 0.11/0.35 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[27, 14])).
% 0.11/0.35 tff(29,plain,
% 0.11/0.35 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[28, 14])).
% 0.11/0.35 tff(30,plain,
% 0.11/0.35 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[29, 14])).
% 0.11/0.35 tff(31,plain,(
% 0.11/0.35 (![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) | ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) & ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & p(W!0)) | (~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))))),
% 0.11/0.35 inference(skolemize,[status(sab)],[30])).
% 0.11/0.35 tff(32,plain,
% 0.11/0.35 ((![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) | ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) & ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & p(W!0)) | (~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[31, 13])).
% 0.11/0.35 tff(33,plain,
% 0.11/0.35 (![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) | ![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.35 inference(and_elim,[status(thm)],[32])).
% 0.11/0.35 tff(34,plain,
% 0.11/0.35 (![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[33, 12])).
% 0.11/0.35 tff(35,plain,
% 0.11/0.35 (![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[34, 7])).
% 0.11/0.35 tff(36,plain,
% 0.11/0.35 (((~![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | ((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))) <=> ((~![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(37,plain,
% 0.11/0.35 ((~![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | ((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))),
% 0.11/0.35 inference(quant_inst,[status(thm)],[])).
% 0.11/0.35 tff(38,plain,
% 0.11/0.35 ((~![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.35 tff(39,plain,
% 0.11/0.35 ($false),
% 0.11/0.35 inference(unit_resolution,[status(thm)],[38, 35, 5, 3])).
% 0.11/0.35 tff(40,plain,((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.35 tff(41,plain,
% 0.11/0.35 (((~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~p(W!0)))) | (~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))))) <=> ((~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~p(W!0)))))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(42,plain,
% 0.11/0.35 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & p(W!0)) <=> (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~p(W!0))))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(43,plain,
% 0.11/0.35 (((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & p(W!0)) | (~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))))) <=> ((~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~p(W!0)))) | (~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))))),
% 0.11/0.35 inference(monotonicity,[status(thm)],[42])).
% 0.11/0.35 tff(44,plain,
% 0.11/0.35 (((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & p(W!0)) | (~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))))) <=> ((~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~p(W!0)))))),
% 0.11/0.35 inference(transitivity,[status(thm)],[43, 41])).
% 0.11/0.35 tff(45,plain,
% 0.11/0.35 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & p(W!0)) | (~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))))),
% 0.11/0.35 inference(and_elim,[status(thm)],[32])).
% 0.11/0.35 tff(46,plain,
% 0.11/0.35 ((~((~p(W!1)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~p(W!0))))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.11/0.35 tff(47,plain,
% 0.11/0.35 (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~p(W!0)))),
% 0.11/0.35 inference(unit_resolution,[status(thm)],[46, 40])).
% 0.11/0.35 tff(48,plain,
% 0.11/0.35 (((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~p(W!0))) | p(W!0)),
% 0.11/0.35 inference(tautology,[status(thm)],[])).
% 0.11/0.35 tff(49,plain,
% 0.11/0.35 (p(W!0)),
% 0.11/0.35 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.11/0.35 tff(50,plain,
% 0.11/0.35 (((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~p(W!0))) | tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)),
% 0.11/0.35 inference(tautology,[status(thm)],[])).
% 0.11/0.35 tff(51,plain,
% 0.11/0.35 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)),
% 0.11/0.35 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.11/0.35 tff(52,plain,
% 0.11/0.35 (((~![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | ((~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))) <=> ((~![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(53,plain,
% 0.11/0.35 ((~![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | ((~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))),
% 0.11/0.35 inference(quant_inst,[status(thm)],[])).
% 0.11/0.35 tff(54,plain,
% 0.11/0.35 ((~![W: |'$ki_world'|] : ((~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.11/0.35 tff(55,plain,
% 0.11/0.35 ($false),
% 0.11/0.35 inference(unit_resolution,[status(thm)],[54, 35, 51, 49])).
% 0.11/0.35 % SZS output end Proof
% 0.11/0.35 % E exiting
%------------------------------------------------------------------------------