%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO901_11 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:42:27 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SYO901_11 : TPTP v9.0.0. Released v8.2.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:55:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(tptp_fun___ki_accessible__type, type, (
% 0.19/0.37 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.19/0.37 tff(tptp_fun_W0_1_type, type, (
% 0.19/0.37 tptp_fun_W0_1: |'$ki_world'|)).
% 0.19/0.37 tff(tptp_fun___ki_local_world__type, type, (
% 0.19/0.37 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.19/0.37 tff(q_type, type, (
% 0.19/0.37 q: |'$ki_world'| > $o)).
% 0.19/0.37 tff(p_type, type, (
% 0.19/0.37 p: |'$ki_world'| > $o)).
% 0.19/0.37 tff(tptp_fun_W_0_type, type, (
% 0.19/0.37 tptp_fun_W_0: |'$ki_world'|)).
% 0.19/0.37 tff(tptp_fun_W0_2_type, type, (
% 0.19/0.37 tptp_fun_W0_2: |'$ki_world'|)).
% 0.19/0.37 tff(1,assumption,(~q(W0!2)), introduced(assumption)).
% 0.19/0.37 tff(2,assumption,(~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!2)), introduced(assumption)).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (^[W: |'$ki_world'|, V: |'$ki_world'|] : refl(tptp_fun___ki_accessible_(W, V) <=> tptp_fun___ki_accessible_(W, V))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V) <=> ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.19/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V) <=> ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(6,axiom,(![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_universal')).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.37 tff(8,plain,(
% 0.19/0.37 ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.19/0.37 inference(skolemize,[status(sab)],[7])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 ((~![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!2)),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.19/0.37 tff(12,plain,(tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 ((~(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) <=> q(W))) => ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => p(W0)) <=> ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => q(W0)))))) <=> (~((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) <=> ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(17,axiom,(~(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) <=> q(W))) => ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => p(W0)) <=> ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => q(W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (~((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) <=> ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))),
% 0.19/0.37 inference(or_elim,[status(thm)],[18])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.37 tff(21,plain,(
% 0.19/0.37 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[20])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!2)) | (p(W0!2) <=> q(W0!2)))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!2)) | (p(W0!2) <=> q(W0!2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!2)) | (p(W0!2) <=> q(W0!2)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!2)) | (p(W0!2) <=> q(W0!2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (p(W0!2) <=> q(W0!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 ((~(p(W0!2) <=> q(W0!2))) | (~p(W0!2)) | q(W0!2)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 ((~p(W0!2)) | q(W0!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (~p(W0!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[28, 1])).
% 0.19/0.37 tff(30,assumption,(~tptp_fun___ki_accessible_(W!0, W0!2)), introduced(assumption)).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 ((~![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(W!0, W0!2)),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[31, 9, 30])).
% 0.19/0.37 tff(33,plain,(tptp_fun___ki_accessible_(W!0, W0!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(34,assumption,(![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))), introduced(assumption)).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2)))) <=> ((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 ((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 ((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[37, 34, 1, 33])).
% 0.19/0.37 tff(39,plain,((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | q(W0!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[39, 1])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 ((![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) <=> (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & ((![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) & ((~(p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) | (~(q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) & ((~(p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) | (~(q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 ((![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) <=> (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (((![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) & ((~(p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) | (~(q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2)))))) <=> ((![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) & ((~(p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) | (~(q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2))))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & ((![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) & ((~(p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) | (~(q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & ((![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) & ((~(p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) | (~(q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2)))))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & ((![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) & ((~(p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) | (~(q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) & ((~(p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) | (~(q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[45, 42])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) <=> ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) <=> ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) <=> ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.19/0.37 inference(or_elim,[status(thm)],[18])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) <=> ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) <=> ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[49, 47])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) <=> ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) & ((~(p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) | (~(q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[51, 46])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.19/0.37 inference(and_elim,[status(thm)],[52])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[53, 41])).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[54, 40])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 (((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (p(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2)))) <=> ((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | p(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 ((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (p(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(58,plain,
% 0.19/0.37 ((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | p(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.37 tff(59,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[58, 55, 33, 29])).
% 0.19/0.37 tff(60,plain,(q(W0!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(61,plain,
% 0.19/0.37 ((q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2))) | (~q(W0!2))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(62,plain,
% 0.19/0.37 (q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.37 tff(63,plain,
% 0.19/0.37 ((~(p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) | (~(q(W0!2) | (~tptp_fun___ki_accessible_(W!0, W0!2))))),
% 0.19/0.37 inference(and_elim,[status(thm)],[52])).
% 0.19/0.37 tff(64,plain,
% 0.19/0.37 (~(p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.37 tff(65,plain,
% 0.19/0.37 ((p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1))) | tptp_fun___ki_accessible_(W!0, W0!1)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(66,plain,
% 0.19/0.37 (tptp_fun___ki_accessible_(W!0, W0!1)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.37 tff(67,plain,
% 0.19/0.37 ((p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1))) | (~p(W0!1))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(68,plain,
% 0.19/0.37 (~p(W0!1)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[67, 64])).
% 0.19/0.37 tff(69,assumption,(tptp_fun___ki_accessible_(W!0, W0!1)), introduced(assumption)).
% 0.19/0.37 tff(70,assumption,(~p(W0!1)), introduced(assumption)).
% 0.19/0.37 tff(71,assumption,(![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))), introduced(assumption)).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 (((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) <=> ((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 ((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 ((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[74, 71, 70, 69])).
% 0.19/0.38 tff(76,plain,((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | p(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(77,plain,
% 0.19/0.38 (~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[76, 66, 68])).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 (![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[54, 77])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 (((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (q(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) <=> ((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | q(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(80,plain,
% 0.19/0.38 ((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (q(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(81,plain,
% 0.19/0.38 ((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | q(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.38 tff(82,plain,
% 0.19/0.38 (q(W0!1)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[81, 78, 66])).
% 0.19/0.38 tff(83,plain,
% 0.19/0.38 ((~(p(W0!1) <=> q(W0!1))) | p(W0!1) | (~q(W0!1))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(84,plain,
% 0.19/0.38 ((~(p(W0!1) <=> q(W0!1))) | (~q(W0!1))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[83, 68])).
% 0.19/0.38 tff(85,plain,
% 0.19/0.38 (~(p(W0!1) <=> q(W0!1))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[84, 82])).
% 0.19/0.38 tff(86,plain,
% 0.19/0.38 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!1)) | (p(W0!1) <=> q(W0!1)))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!1)) | (p(W0!1) <=> q(W0!1)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(87,plain,
% 0.19/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!1)) | (p(W0!1) <=> q(W0!1)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(88,plain,
% 0.19/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) <=> q(W)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!1)) | (p(W0!1) <=> q(W0!1))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.38 tff(89,plain,
% 0.19/0.38 ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!1)) | (p(W0!1) <=> q(W0!1))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[88, 22])).
% 0.19/0.38 tff(90,plain,
% 0.19/0.38 (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!1)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[89, 85])).
% 0.19/0.38 tff(91,plain,
% 0.19/0.38 ((~![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(|'$ki_local_world'|, W0!1)),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(92,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[91, 9, 90])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------