TSTP Solution File: SYO902_8 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO902_8 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Mon May 22 15:46:14 EDT 2023
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYO902_8 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 22 13:13:31 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(tptp_fun___ki_accessible__type, type, (
% 0.14/0.39 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.14/0.39 tff(tptp_fun_W1_1_type, type, (
% 0.14/0.39 tptp_fun_W1_1: '$ki_world' > '$ki_world')).
% 0.14/0.39 tff(tptp_fun_W_0_type, type, (
% 0.14/0.39 tptp_fun_W_0: '$ki_world')).
% 0.14/0.39 tff(p_type, type, (
% 0.14/0.39 p: '$ki_world' > $o)).
% 0.14/0.39 tff(tptp_fun___ki_local_world__type, type, (
% 0.14/0.39 tptp_fun___ki_local_world_: '$ki_world')).
% 0.14/0.39 tff(1,plain,
% 0.14/0.39 (^[W: '$ki_world'] : refl(tptp_fun___ki_accessible_(W, W) <=> tptp_fun___ki_accessible_(W, W))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(2,plain,
% 0.14/0.39 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W) <=> ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.14/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W) <=> ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(4,axiom,(![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_reflexive')).
% 0.14/0.39 tff(5,plain,
% 0.14/0.39 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.39 tff(6,plain,(
% 0.14/0.39 ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.14/0.39 inference(skolemize,[status(sab)],[5])).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 ((~![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)) | tptp_fun___ki_accessible_(W!0, W!0)),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (tptp_fun___ki_accessible_(W!0, W!0)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (^[W0: '$ki_world'] : refl(((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0)))))) <=> ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0)))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 (![W0: '$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: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 (^[W0: '$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)))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(13,plain,
% 0.14/0.39 (![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))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.14/0.39 tff(14,plain,
% 0.14/0.39 ((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)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (?[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))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 ((~(?[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)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(17,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: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) & p(W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 (~((~?[W: '$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))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.14/0.39 tff(19,plain,
% 0.14/0.39 (?[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))))),
% 0.14/0.39 inference(or_elim,[status(thm)],[18])).
% 0.14/0.39 tff(20,plain,
% 0.14/0.39 (?[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))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.14/0.39 tff(21,plain,
% 0.14/0.39 (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))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.14/0.39 tff(22,plain,
% 0.14/0.39 (![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0)) & p(tptp_fun_W1_1(W0))))),
% 0.14/0.39 inference(and_elim,[status(thm)],[21])).
% 0.14/0.39 tff(23,plain,
% 0.14/0.39 (![W0: '$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))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.14/0.39 tff(24,plain,
% 0.14/0.39 (![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[23, 11])).
% 0.14/0.39 tff(25,plain,
% 0.14/0.39 (((~![W0: '$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)) | (~((~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))))))) <=> ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))) | (~tptp_fun___ki_accessible_(W!0, W!0)) | (~((~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(26,plain,
% 0.14/0.39 (((~tptp_fun___ki_accessible_(W!0, W!0)) | (~((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0)))))) <=> ((~tptp_fun___ki_accessible_(W!0, W!0)) | (~((~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(27,plain,
% 0.14/0.39 (((~![W0: '$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: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))) | ((~tptp_fun___ki_accessible_(W!0, W!0)) | (~((~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0)))))))),
% 0.14/0.39 inference(monotonicity,[status(thm)],[26])).
% 0.14/0.39 tff(28,plain,
% 0.14/0.39 (((~![W0: '$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: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))) | (~tptp_fun___ki_accessible_(W!0, W!0)) | (~((~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))))))),
% 0.14/0.39 inference(transitivity,[status(thm)],[27, 25])).
% 0.14/0.39 tff(29,plain,
% 0.14/0.39 ((~![W0: '$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))))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(30,plain,
% 0.14/0.39 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~((~tptp_fun___ki_accessible_(W0, tptp_fun_W1_1(W0))) | (~p(tptp_fun_W1_1(W0))))))) | (~tptp_fun___ki_accessible_(W!0, W!0)) | (~((~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.14/0.39 tff(31,plain,
% 0.14/0.39 (~((~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[30, 24, 9])).
% 0.14/0.39 tff(32,plain,
% 0.14/0.39 (((~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0)))) | tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(33,plain,
% 0.14/0.39 (tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.14/0.39 tff(34,plain,
% 0.14/0.39 (((~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0)))) | p(tptp_fun_W1_1(W!0))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(35,plain,
% 0.14/0.39 (p(tptp_fun_W1_1(W!0))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.14/0.39 tff(36,plain,
% 0.14/0.39 (^[W: '$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)))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(37,plain,
% 0.14/0.39 (![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))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.14/0.39 tff(38,plain,
% 0.14/0.39 (^[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: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0)))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(39,plain,
% 0.14/0.39 (![W: '$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: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.14/0.39 tff(40,plain,
% 0.14/0.39 (![W: '$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: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[39, 37])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (^[W: '$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)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (![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))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 ((~?[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))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))),
% 0.14/0.40 inference(or_elim,[status(thm)],[18])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[45, 43])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[48, 43])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) & p(W0)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[49, 43])).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 (^[W: '$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: '$ki_world'] : (~(tptp_fun___ki_accessible_(W, W0) & p(W0))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(52,plain,(
% 0.14/0.40 ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: '$ki_world'] : (~(tptp_fun___ki_accessible_(W, W0) & p(W0))))),
% 0.14/0.40 inference(nnf-neg,[status(sab)],[50, 51])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.14/0.40 tff(54,plain,
% 0.14/0.40 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | (~p(W0))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[53, 40])).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)),
% 0.14/0.40 inference(and_elim,[status(thm)],[21])).
% 0.14/0.40 tff(56,plain,
% 0.14/0.40 (((~![W: '$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: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(57,plain,
% 0.14/0.40 ((~![W: '$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))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(58,plain,
% 0.14/0.40 ((~![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: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.14/0.40 tff(59,plain,
% 0.14/0.40 (![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[58, 55, 54])).
% 0.14/0.40 tff(60,plain,
% 0.14/0.40 (((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))) | ((~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))))) <=> ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))) | (~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(61,plain,
% 0.14/0.40 (((~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))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(62,plain,
% 0.14/0.40 (((~![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)))) | ((~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0)))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[61])).
% 0.14/0.40 tff(63,plain,
% 0.14/0.40 (((~![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)))) | (~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[62, 60])).
% 0.14/0.40 tff(64,plain,
% 0.14/0.40 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))) | ((~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0))) | (~p(tptp_fun_W1_1(W!0))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(65,plain,
% 0.14/0.40 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!0, W0)) | (~p(W0)))) | (~p(tptp_fun_W1_1(W!0))) | (~tptp_fun___ki_accessible_(W!0, tptp_fun_W1_1(W!0)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.14/0.40 tff(66,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[65, 59, 35, 33])).
% 0.14/0.40 % SZS output end Proof
%------------------------------------------------------------------------------