TSTP Solution File: SYO888_10 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO888_10 : 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 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO888_10 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 22 13:08:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(h_type, type, (
% 0.13/0.39 h: ( '$ki_world' * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_X_1_type, type, (
% 0.13/0.39 tptp_fun_X_1: $i)).
% 0.13/0.39 tff(tptp_fun___ki_accessible__type, type, (
% 0.13/0.39 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.13/0.39 tff(tptp_fun___ki_local_world__type, type, (
% 0.13/0.39 tptp_fun___ki_local_world_: '$ki_world')).
% 0.13/0.39 tff(g_type, type, (
% 0.13/0.39 g: ( '$ki_world' * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.13/0.39 tptp_fun___ki_exists_in_world__i_: ( '$ki_world' * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_W_2_type, type, (
% 0.13/0.39 tptp_fun_W_2: '$ki_world')).
% 0.13/0.39 tff(f_type, type, (
% 0.13/0.39 f: ( '$ki_world' * $i ) > $o)).
% 0.13/0.39 tff(1,assumption,(~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (^[W: '$ki_world'] : refl(tptp_fun___ki_accessible_(W, W) <=> tptp_fun___ki_accessible_(W, W))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W) <=> ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.13/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W) <=> ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,axiom,(![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_reflexive')).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.39 tff(7,plain,(
% 0.13/0.39 ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.13/0.39 inference(skolemize,[status(sab)],[6])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 ((~![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)) | tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.13/0.39 tff(11,plain,(tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (((~(~f(|'$ki_local_world'|, X!1))) & (~(~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1))) & (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | h(W!2, X!1)))) <=> (f(|'$ki_local_world'|, X!1) & tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1) & (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | h(W!2, X!1))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ((~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))) <=> (~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 ((~((![X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) => (f(|'$ki_local_world'|, X) => ![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => g(W, X)))) & ![X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) => (g(|'$ki_local_world'|, X) => ![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => h(W, X))))) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) => (f(|'$ki_local_world'|, X) => ![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => h(W, X)))))) <=> (~((~(![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, 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)) | h(W, X)) | (~g(|'$ki_local_world'|, X))))) | ![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(15,axiom,(~((![X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) => (f(|'$ki_local_world'|, X) => ![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => g(W, X)))) & ![X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) => (g(|'$ki_local_world'|, X) => ![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => h(W, X))))) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) => (f(|'$ki_local_world'|, X) => ![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => h(W, X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (~((~(![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, 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)) | h(W, X)) | (~g(|'$ki_local_world'|, X))))) | ![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))),
% 0.13/0.39 inference(or_elim,[status(thm)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (f(|'$ki_local_world'|, X!1) & tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1) & (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | h(W!2, X!1)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 12])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)),
% 0.13/0.39 inference(and_elim,[status(thm)],[24])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (f(|'$ki_local_world'|, X!1)),
% 0.13/0.39 inference(and_elim,[status(thm)],[24])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (^[X: $i] : rewrite((![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X))) <=> ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X))) <=> ![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (^[X: $i] : refl((![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X))) <=> (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X))) <=> ![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (^[X: $i] : rewrite((![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X))) <=> (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X))) <=> ![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X))) <=> ![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[32, 30])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X))) <=> ![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, 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)) | h(W, X)) | (~g(|'$ki_local_world'|, X)))),
% 0.13/0.39 inference(or_elim,[status(thm)],[16])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)))),
% 0.13/0.39 inference(and_elim,[status(thm)],[35])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.13/0.39 tff(38,plain,(
% 0.13/0.39 ![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[37])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (![X: $i] : (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)) | (~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[39, 28])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (((~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)))) | ((~f(|'$ki_local_world'|, X!1)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1)))) <=> ((~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)))) | (~f(|'$ki_local_world'|, X!1)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)))) | ((~f(|'$ki_local_world'|, X!1)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ((~![X: $i] : ((~f(|'$ki_local_world'|, X)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X)))) | (~f(|'$ki_local_world'|, X!1)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[43, 40, 26, 25])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | g(|'$ki_local_world'|, X!1))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | g(|'$ki_local_world'|, X!1))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | g(|'$ki_local_world'|, X!1))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | g(|'$ki_local_world'|, X!1)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (g(|'$ki_local_world'|, X!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[47, 44, 11])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (^[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)) | h(W, X)) | (~g(|'$ki_local_world'|, X))) <=> ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~g(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)) | (~g(|'$ki_local_world'|, X))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~g(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (^[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)) | h(W, X)) | (~g(|'$ki_local_world'|, X))) <=> ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)) | (~g(|'$ki_local_world'|, X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)) | (~g(|'$ki_local_world'|, 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)) | h(W, X)) | (~g(|'$ki_local_world'|, X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (^[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)) | h(W, X)) | (~g(|'$ki_local_world'|, X))) <=> ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)) | (~g(|'$ki_local_world'|, X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)) | (~g(|'$ki_local_world'|, 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)) | h(W, X)) | (~g(|'$ki_local_world'|, X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)) | (~g(|'$ki_local_world'|, 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)) | h(W, X)) | (~g(|'$ki_local_world'|, X)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[54, 52])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)) | (~g(|'$ki_local_world'|, 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)) | h(W, X)) | (~g(|'$ki_local_world'|, X)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)) | (~g(|'$ki_local_world'|, X)))),
% 0.13/0.40 inference(and_elim,[status(thm)],[35])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)) | (~g(|'$ki_local_world'|, X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.13/0.40 tff(59,plain,(
% 0.13/0.40 ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)) | (~g(|'$ki_local_world'|, X)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[58])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)) | (~g(|'$ki_local_world'|, X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~g(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~g(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))) | ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | (~g(|'$ki_local_world'|, X!1)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1)))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~g(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | (~g(|'$ki_local_world'|, X!1)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~g(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))) | ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | (~g(|'$ki_local_world'|, X!1)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~g(|'$ki_local_world'|, X)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X)))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | (~g(|'$ki_local_world'|, X!1)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 ((~g(|'$ki_local_world'|, X!1)) | ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[64, 61, 25])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[65, 48])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | h(W!2, X!1))),
% 0.13/0.40 inference(and_elim,[status(thm)],[24])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (~h(W!2, X!1)),
% 0.13/0.40 inference(or_elim,[status(thm)],[67])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)),
% 0.13/0.40 inference(or_elim,[status(thm)],[67])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | h(W!2, X!1))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | h(W!2, X!1))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | h(W!2, X!1))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | h(W!2, X!1)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[72, 69, 68, 66])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------