%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO902_8 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:42:28 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO902_8 : TPTP v9.0.0. Released v8.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 13:51:11 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(p_type, type, (
% 0.13/0.38 p: |'$ki_world'| > $o)).
% 0.13/0.38 tff(tptp_fun_W1_1_type, type, (
% 0.13/0.38 tptp_fun_W1_1: |'$ki_world'| > |'$ki_world'|)).
% 0.13/0.38 tff(tptp_fun_W_0_type, type, (
% 0.13/0.38 tptp_fun_W_0: |'$ki_world'|)).
% 0.13/0.38 tff(tptp_fun___ki_accessible__type, type, (
% 0.13/0.38 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.13/0.38 tff(tptp_fun___ki_local_world__type, type, (
% 0.13/0.38 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.13/0.38 tff(1,assumption,(~tptp_fun___ki_accessible_(W!0, W!0)), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (^[W: |'$ki_world'|] : refl(tptp_fun___ki_accessible_(W, W) <=> tptp_fun___ki_accessible_(W, W))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.13/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(5,axiom,(![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_reflexive')).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.38 tff(7,plain,(
% 0.13/0.38 ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.13/0.38 inference(skolemize,[status(sab)],[6])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 ((~![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)) | tptp_fun___ki_accessible_(W!0, W!0)),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.13/0.38 tff(11,plain,(tptp_fun___ki_accessible_(W!0, W!0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (^[W0: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0)))))) <=> ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0)))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0)))))) <=> ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (^[W0: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(W!0, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0)) & p(tptp_fun_W1_1(W0)))) <=> ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0)))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0)) & p(tptp_fun_W1_1(W0)))) <=> ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0)) & p(tptp_fun_W1_1(W0))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0)) & p(tptp_fun_W1_1(W0)))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & p(W1)))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & p(W1))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 ((~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & p(W1)))) => ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0))))) <=> (~((~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & p(W1))))) | ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(19,axiom,(~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & p(W1)))) => ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (~((~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & p(W1))))) | ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & p(W1))))),
% 0.13/0.38 inference(or_elim,[status(thm)],[20])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & p(W1))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0)) & p(tptp_fun_W1_1(W0))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0)) & p(tptp_fun_W1_1(W0))))),
% 0.13/0.38 inference(and_elim,[status(thm)],[23])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[24, 15])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[25, 13])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))) | ((~tptp_fun___ki_accessible_(W!0, W!0)) | (~((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))) | (~tptp_fun___ki_accessible_(W!0, W!0)) | (~((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))) | ((~tptp_fun___ki_accessible_(W!0, W!0)) | (~((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0))))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))) | (~tptp_fun___ki_accessible_(W!0, W!0)) | (~((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 ((~tptp_fun___ki_accessible_(W!0, W!0)) | (~((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0)))))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (~((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0))))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[30, 11])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0)))) | p(tptp_fun_W1_1(W!0))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (p(tptp_fun_W1_1(W!0))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 (((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0)))) | tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))),
% 0.13/0.38 inference(transitivity,[status(thm)],[39, 37])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & p(W0)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(42,plain,
% 0.13/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & p(W0)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.13/0.38 tff(43,plain,
% 0.13/0.38 ((~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(44,plain,
% 0.13/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))),
% 0.13/0.38 inference(or_elim,[status(thm)],[20])).
% 0.13/0.38 tff(45,plain,
% 0.13/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.13/0.38 tff(46,plain,
% 0.13/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[45, 43])).
% 0.13/0.38 tff(47,plain,
% 0.13/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.13/0.38 tff(48,plain,
% 0.13/0.38 (^[W: |'$ki_world'|] : nnf_neg(refl($oeq((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)), (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))), nnf_neg(proof_bind(^[W0: |'$ki_world'|] : refl($oeq((~(tptp_fun___ki_accessible_(W, W0) & p(W0))), (~(tptp_fun___ki_accessible_(W, W0) & p(W0)))))), $oeq((~?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0))), ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & p(W0))))), $oeq((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))), ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & p(W0))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(49,plain,(
% 0.13/0.38 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(W, W0) & p(W0))))),
% 0.13/0.38 inference(nnf-neg,[status(sab)],[47, 48])).
% 0.13/0.38 tff(50,plain,
% 0.13/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.13/0.38 tff(51,plain,
% 0.13/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.13/0.38 tff(52,plain,
% 0.13/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)),
% 0.13/0.38 inference(and_elim,[status(thm)],[23])).
% 0.13/0.38 tff(53,plain,
% 0.13/0.38 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(54,plain,
% 0.13/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(55,plain,
% 0.13/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.13/0.38 tff(56,plain,
% 0.13/0.38 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[55, 52, 51])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))) | ((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))) | ((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[59, 56, 35, 33])).
% 0.13/0.39 % SZS output end Proof
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------