%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO893_11 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.12s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO893_11 : TPTP v9.0.0. Released v8.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % 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 13:50:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(tptp_fun___ki_accessible__type, type, (
% 0.12/0.36 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.12/0.36 tff(tptp_fun_W1_2_type, type, (
% 0.12/0.36 tptp_fun_W1_2: |'$ki_world'| > |'$ki_world'|)).
% 0.12/0.36 tff(tptp_fun_W0_5_type, type, (
% 0.12/0.36 tptp_fun_W0_5: |'$ki_world'| > |'$ki_world'|)).
% 0.12/0.36 tff(tptp_fun_W_1_type, type, (
% 0.12/0.36 tptp_fun_W_1: |'$ki_world'|)).
% 0.12/0.36 tff(p_type, type, (
% 0.12/0.36 p: |'$ki_world'| > $o)).
% 0.12/0.36 tff(tptp_fun___ki_local_world__type, type, (
% 0.12/0.36 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.12/0.36 tff(tptp_fun_W0_0_type, type, (
% 0.12/0.36 tptp_fun_W0_0: |'$ki_world'| > |'$ki_world'|)).
% 0.12/0.36 tff(tptp_fun_W1_4_type, type, (
% 0.12/0.36 tptp_fun_W1_4: |'$ki_world'| > |'$ki_world'|)).
% 0.12/0.36 tff(tptp_fun_W_3_type, type, (
% 0.12/0.36 tptp_fun_W_3: |'$ki_world'|)).
% 0.12/0.36 tff(1,assumption,(![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1)))))))), introduced(assumption)).
% 0.12/0.36 tff(2,assumption,(~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))))), introduced(assumption)).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)))))))) | tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1)))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1)))))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1)))))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1))))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (~((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1)))))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[7, 4, 1])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1))))) | tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)))))))) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[11, 2])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))) | ((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))) | (~(p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3)))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))) | (~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))) | (~(p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3)))))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))) | ((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))) | (~(p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3)))))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))) | (~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))) | (~(p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3))))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 (~(p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3)))))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[15, 12, 10])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 ((p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3))))) | tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3)))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3)))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 ((p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3))))) | (~p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 (~p(tptp_fun_W1_4(tptp_fun_W0_0(W!3)))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[19, 16])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 (((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_0(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1))))) | ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1)))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 (![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1)))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[21, 8])).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1)))) | (p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3)))))) <=> ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1)))) | p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1)))) | (p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3)))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), W1)))) | p(tptp_fun_W1_4(tptp_fun_W0_0(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!3), tptp_fun_W1_4(tptp_fun_W0_0(W!3))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[25, 22, 20, 18])).
% 0.12/0.37 tff(27,plain,(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)))))))) | (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[27, 1])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (((~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))))) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)))))))))) <=> ((~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))))) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)) & (~p(tptp_fun_W1_4(W0))))))) <=> ((~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))))) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 ((((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)) & (~p(tptp_fun_W1_4(W0))))))) & (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W)) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W)) & ![W1: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1) & (~p(W1)))))))) <=> (((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)) & (~p(tptp_fun_W1_4(W0))))))) & (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W)) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W)) & ![W1: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1) & (~p(W1))))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 ((![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, W1))))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & (~p(W1)))))) <=> (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, W1))))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & (~p(W1))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 ((~(~(![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, W1))))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & (~p(W1)))))))) <=> (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, W1))))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & (~p(W1))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 ((~(![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, W1))))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & (~p(W1))))))) <=> (~(![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, W1))))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & (~p(W1)))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, W1)))))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & (~p(W1)))))) <=> (~(![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, W1))))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & (~p(W1)))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (^[W: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & (~p(W1))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W, W0)) | ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & (~p(W1))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (?[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)))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[36])).
% 0.18/0.37 tff(38,plain,
% 0.18/0.37 ((~![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'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, W1))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 (((~![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)))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, 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))))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[38, 37])).
% 0.18/0.37 tff(40,plain,
% 0.18/0.37 (((~![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)))))) <=> (~(![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, 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)))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[39, 35])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 (((~![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)))))) <=> (~(![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, 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)))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[40, 34])).
% 0.18/0.37 tff(42,plain,
% 0.18/0.37 ((~((~![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))))))) <=> (~(~(![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, 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))))))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[41])).
% 0.18/0.37 tff(43,plain,
% 0.18/0.37 ((~((~![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))))))) <=> (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, 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))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[42, 33])).
% 0.18/0.37 tff(44,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: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => ?[W1: |'$ki_world'|] : (tptp_fun___ki_accessible_(W0, W1) & (~p(W1))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, 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)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, 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)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[45, 32])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, 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)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[46, 32])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(W0, 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)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[47, 32])).
% 0.18/0.37 tff(49,plain,(
% 0.18/0.37 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)) & (~p(tptp_fun_W1_4(W0))))))) & (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W)) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W)) & ![W1: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1) & (~p(W1)))))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[48])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 (((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)) & (~p(tptp_fun_W1_4(W0))))))) & (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W)) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W)) & ![W1: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1) & (~p(W1)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[49, 31])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3) & ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)) & (~p(tptp_fun_W1_4(W0))))))),
% 0.18/0.37 inference(and_elim,[status(thm)],[50])).
% 0.18/0.37 tff(52,plain,
% 0.18/0.37 ((~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))))) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)))))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[51, 30])).
% 0.18/0.37 tff(53,plain,
% 0.18/0.37 ((~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))))) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)))))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[52, 29])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[53, 28])).
% 0.18/0.38 tff(55,plain,
% 0.18/0.38 (((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0)))))))) | tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(56,plain,
% 0.18/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.18/0.38 tff(57,plain,
% 0.18/0.38 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1)))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(58,plain,
% 0.18/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1)))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(59,plain,
% 0.18/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.38 tff(60,plain,
% 0.18/0.38 (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[59, 56, 1])).
% 0.18/0.38 tff(61,plain,
% 0.18/0.38 (((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1))))) | tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(62,plain,
% 0.18/0.38 (tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.18/0.38 tff(63,plain,
% 0.18/0.38 (((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0)))))))) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(64,plain,
% 0.18/0.38 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[63, 54])).
% 0.18/0.38 tff(65,plain,
% 0.18/0.38 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | ((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))) | (~(p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1)))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | (~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))) | (~(p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(66,plain,
% 0.18/0.38 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | ((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))) | (~(p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1)))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(67,plain,
% 0.18/0.38 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | (~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))) | (~(p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.38 tff(68,plain,
% 0.18/0.38 (~(p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[67, 64, 62])).
% 0.18/0.38 tff(69,plain,
% 0.18/0.38 ((p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1))))) | tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1)))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(70,plain,
% 0.18/0.38 (tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.18/0.38 tff(71,plain,
% 0.18/0.38 ((p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1))))) | (~p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(72,plain,
% 0.18/0.38 (~p(tptp_fun_W1_2(tptp_fun_W0_0(W!1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.18/0.38 tff(73,plain,
% 0.18/0.38 (((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_0(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1))))) | ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1)))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(74,plain,
% 0.18/0.38 (![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[73, 60])).
% 0.18/0.38 tff(75,plain,
% 0.18/0.38 (((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1)))) | (p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1)))))) <=> ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1)))) | p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(76,plain,
% 0.18/0.38 ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1)))) | (p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1)))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(77,plain,
% 0.18/0.38 ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), W1)))) | p(tptp_fun_W1_2(tptp_fun_W0_0(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W!1), tptp_fun_W1_2(tptp_fun_W0_0(W!1))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.38 tff(78,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[77, 74, 72, 70])).
% 0.18/0.38 tff(79,plain,(~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(80,plain,
% 0.18/0.38 ((![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))) <=> (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(81,plain,
% 0.18/0.38 ((![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W)) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W)) & ![W1: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1) & (~p(W1))))))) <=> (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(82,plain,
% 0.18/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W)) & ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W)) & ![W1: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1) & (~p(W1))))))),
% 0.18/0.38 inference(and_elim,[status(thm)],[50])).
% 0.18/0.38 tff(83,plain,
% 0.18/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.18/0.38 tff(84,plain,
% 0.18/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_0(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_0(W), W1))))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.18/0.38 tff(85,plain,
% 0.18/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[84, 79])).
% 0.18/0.38 tff(86,plain,
% 0.18/0.38 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1)))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(87,plain,
% 0.18/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1)))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(88,plain,
% 0.18/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.38 tff(89,plain,
% 0.18/0.38 (~((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[88, 4, 85])).
% 0.18/0.38 tff(90,plain,
% 0.18/0.38 (((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1))))) | tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(91,plain,
% 0.18/0.38 (tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.18/0.38 tff(92,plain,
% 0.18/0.38 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))) | ((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))) | (~(p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3)))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))) | (~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))) | (~(p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(93,plain,
% 0.18/0.38 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))) | ((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))) | (~(p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3)))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(94,plain,
% 0.18/0.38 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0))))))) | (~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))) | (~(p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.38 tff(95,plain,
% 0.18/0.38 (~(p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[94, 12, 91])).
% 0.18/0.38 tff(96,plain,
% 0.18/0.38 ((p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3))))) | tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3)))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(97,plain,
% 0.18/0.38 (tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.18/0.38 tff(98,plain,
% 0.18/0.38 ((p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3))))) | (~p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(99,plain,
% 0.18/0.38 (~p(tptp_fun_W1_4(tptp_fun_W0_5(W!3)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[98, 95])).
% 0.18/0.38 tff(100,plain,
% 0.18/0.38 (((~tptp_fun___ki_accessible_(W!3, tptp_fun_W0_5(W!3))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1))))) | ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1)))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(101,plain,
% 0.18/0.38 (![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[100, 89])).
% 0.18/0.38 tff(102,plain,
% 0.18/0.38 (((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1)))) | (p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3)))))) <=> ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1)))) | p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(103,plain,
% 0.18/0.38 ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1)))) | (p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3)))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(104,plain,
% 0.18/0.38 ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), W1)))) | p(tptp_fun_W1_4(tptp_fun_W0_5(W!3))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!3), tptp_fun_W1_4(tptp_fun_W0_5(W!3))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.18/0.38 tff(105,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[104, 101, 99, 97])).
% 0.18/0.38 tff(106,plain,((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!3, W0)) | (~(p(tptp_fun_W1_4(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_4(W0)))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(107,plain,
% 0.18/0.38 (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[53, 106])).
% 0.18/0.38 tff(108,plain,
% 0.18/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[55, 107])).
% 0.18/0.38 tff(109,plain,
% 0.18/0.38 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1)))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(110,plain,
% 0.18/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1)))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(111,plain,
% 0.18/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_accessible_(W, tptp_fun_W0_5(W))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W), W1)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.38 tff(112,plain,
% 0.18/0.38 (~((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[111, 108, 85])).
% 0.18/0.38 tff(113,plain,
% 0.18/0.38 (((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1))))) | tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(114,plain,
% 0.18/0.38 (tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.18/0.38 tff(115,plain,
% 0.18/0.38 (![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[63, 107])).
% 0.18/0.38 tff(116,plain,
% 0.18/0.38 (((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | ((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))) | (~(p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1)))))))) <=> ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | (~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))) | (~(p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(117,plain,
% 0.18/0.38 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | ((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))) | (~(p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1)))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(118,plain,
% 0.18/0.38 ((~![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(W!1, W0)) | (~(p(tptp_fun_W1_2(W0)) | (~tptp_fun___ki_accessible_(W0, tptp_fun_W1_2(W0))))))) | (~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))) | (~(p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.18/0.38 tff(119,plain,
% 0.18/0.38 (~(p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[118, 115, 114])).
% 0.18/0.38 tff(120,plain,
% 0.18/0.38 ((p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1))))) | tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(121,plain,
% 0.18/0.39 (tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.18/0.39 tff(122,plain,
% 0.18/0.39 ((p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1))))) | (~p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(123,plain,
% 0.18/0.39 (~p(tptp_fun_W1_2(tptp_fun_W0_5(W!1)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[122, 119])).
% 0.18/0.39 tff(124,plain,
% 0.18/0.39 (((~tptp_fun___ki_accessible_(W!1, tptp_fun_W0_5(W!1))) | (~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1))))) | ![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(125,plain,
% 0.18/0.39 (![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[124, 112])).
% 0.18/0.39 tff(126,plain,
% 0.18/0.39 (((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1)))) | (p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1)))))) <=> ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1)))) | p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(127,plain,
% 0.18/0.39 ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1)))) | (p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(128,plain,
% 0.18/0.39 ((~![W1: |'$ki_world'|] : (p(W1) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), W1)))) | p(tptp_fun_W1_2(tptp_fun_W0_5(W!1))) | (~tptp_fun___ki_accessible_(tptp_fun_W0_5(W!1), tptp_fun_W1_2(tptp_fun_W0_5(W!1))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.18/0.39 tff(129,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[128, 125, 123, 121])).
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------