TSTP Solution File: SYO887_22 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO887_22 : 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 15:46:13 EDT 2023
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO887_22 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n020.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 : Mon May 22 13:08:16 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.11/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.34 Usage: tptp [options] [-file:]file
% 0.11/0.34 -h, -? prints this message.
% 0.11/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.34 -m, -model generate model.
% 0.11/0.34 -p, -proof generate proof.
% 0.11/0.34 -c, -core generate unsat core of named formulas.
% 0.11/0.34 -st, -statistics display statistics.
% 0.11/0.34 -t:timeout set timeout (in second).
% 0.11/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.34 -<param>:<value> configuration parameter and value.
% 0.11/0.34 -o:<output-file> file to place output in.
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(f_type, type, (
% 0.11/0.38 f: ( '$ki_world' * $i ) > $o)).
% 0.11/0.38 tff(tptp_fun_X_1_type, type, (
% 0.11/0.38 tptp_fun_X_1: '$ki_world' > $i)).
% 0.11/0.38 tff(tptp_fun___ki_local_world__type, type, (
% 0.11/0.38 tptp_fun___ki_local_world_: '$ki_world')).
% 0.11/0.38 tff(tptp_fun___ki_accessible__type, type, (
% 0.11/0.38 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.11/0.38 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.11/0.38 tptp_fun___ki_exists_in_world__i_: ( '$ki_world' * $i ) > $o)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 (^[W: '$ki_world'] : refl(tptp_fun___ki_accessible_(W, W) <=> tptp_fun___ki_accessible_(W, W))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W) <=> ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W) <=> ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(4,axiom,(![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_reflexive')).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.38 tff(6,plain,(
% 0.11/0.38 ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.11/0.38 inference(skolemize,[status(sab)],[5])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 ((~![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)) | tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (^[W: '$ki_world'] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W)))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W)))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (^[W: '$ki_world'] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W)) & f(W, tptp_fun_X_1(W)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W)) & f(W, tptp_fun_X_1(W)))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 ((~(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X))) => ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X))))) <=> (~((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(16,axiom,(~(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X))) => ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.11/0.39 tff(17,plain,
% 0.11/0.39 (~((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.39 tff(18,plain,
% 0.11/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.11/0.39 inference(or_elim,[status(thm)],[17])).
% 0.11/0.39 tff(19,plain,
% 0.11/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.39 tff(20,plain,(
% 0.11/0.39 ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W)) & f(W, tptp_fun_X_1(W))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[19])).
% 0.11/0.39 tff(21,plain,
% 0.11/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.11/0.39 tff(22,plain,
% 0.11/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.11/0.39 tff(23,plain,
% 0.11/0.39 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | (~((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))))))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | (~((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(24,plain,
% 0.11/0.39 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | (~((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(25,plain,
% 0.11/0.39 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | (~((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.39 tff(26,plain,
% 0.11/0.39 (~((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|)))) | tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (^[X: $i] : refl(((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X)))) <=> ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X)))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (^[X: $i] : rewrite(((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X)))) <=> ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X)))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X)))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[32, 30])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (^[X: $i] : rewrite(((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))) <=> ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ((~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))) <=> (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))),
% 0.19/0.39 inference(or_elim,[status(thm)],[17])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 36])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 36])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[42, 36])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (^[X: $i] : nnf_neg(refl($oeq((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)), (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)))), nnf_neg(proof_bind(^[W: '$ki_world'] : refl($oeq((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X))), (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))))), $oeq((~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X))), ![W: '$ki_world'] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X))))), $oeq((~(tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X)))), ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(45,plain,(
% 0.19/0.39 ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X))))),
% 0.19/0.39 inference(nnf-neg,[status(sab)],[43, 44])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[46, 33])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X))))) | ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, tptp_fun_X_1(|'$ki_local_world'|)))))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X))))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, tptp_fun_X_1(|'$ki_local_world'|)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X))))) | ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, tptp_fun_X_1(|'$ki_local_world'|)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X))))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, tptp_fun_X_1(|'$ki_local_world'|))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, tptp_fun_X_1(|'$ki_local_world'|))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[50, 47, 28])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|)))) | f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[52, 26])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, tptp_fun_X_1(|'$ki_local_world'|))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, tptp_fun_X_1(|'$ki_local_world'|))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, tptp_fun_X_1(|'$ki_local_world'|))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, tptp_fun_X_1(|'$ki_local_world'|))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 9, 53, 51])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------