%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO888_10 : 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 05:42:25 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO888_10 : TPTP v9.0.0. Released v8.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:54:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(h_type, type, (
% 0.12/0.36 h: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.36 tff(tptp_fun_X_1_type, type, (
% 0.12/0.36 tptp_fun_X_1: $i)).
% 0.12/0.36 tff(tptp_fun___ki_accessible__type, type, (
% 0.12/0.36 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.12/0.36 tff(tptp_fun___ki_local_world__type, type, (
% 0.12/0.36 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.12/0.36 tff(g_type, type, (
% 0.12/0.36 g: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.36 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.12/0.36 tptp_fun___ki_exists_in_world__i_: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.36 tff(tptp_fun_W_2_type, type, (
% 0.12/0.36 tptp_fun_W_2: |'$ki_world'|)).
% 0.12/0.36 tff(f_type, type, (
% 0.12/0.36 f: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.36 tff(1,assumption,(~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)), introduced(assumption)).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (^[W: |'$ki_world'|] : refl(tptp_fun___ki_accessible_(W, W) <=> tptp_fun___ki_accessible_(W, W))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.12/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(5,axiom,(![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_reflexive')).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.36 tff(7,plain,(
% 0.12/0.36 ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.12/0.36 inference(skolemize,[status(sab)],[6])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 ((~![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)) | tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 ($false),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.36 tff(11,plain,(tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 ((~![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))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 ((~((![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)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(14,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')).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (~((~(![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))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (~![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)))),
% 0.12/0.37 inference(or_elim,[status(thm)],[15])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (~![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (~![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (~![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_(|'$ki_local_world'|, W)) | h(W, X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)),
% 0.12/0.37 inference(and_elim,[status(thm)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (f(|'$ki_local_world'|, X!1)),
% 0.12/0.37 inference(and_elim,[status(thm)],[19])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[27, 25])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(or_elim,[status(thm)],[15])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[30])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[31, 29])).
% 0.12/0.37 tff(33,plain,(
% 0.12/0.37 ![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)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[32])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[34, 23])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (((~![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_(|'$ki_local_world'|, W)) | g(W, X)))) | ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | (~f(|'$ki_local_world'|, X!1)) | ![W: |'$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_(|'$ki_local_world'|, W)) | g(W, X)))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | (~f(|'$ki_local_world'|, X!1)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (((~f(|'$ki_local_world'|, X!1)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1))) <=> ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | (~f(|'$ki_local_world'|, X!1)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (((~![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_(|'$ki_local_world'|, W)) | g(W, X)))) | ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | (~f(|'$ki_local_world'|, X!1)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[37])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (((~![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_(|'$ki_local_world'|, W)) | g(W, X)))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | (~f(|'$ki_local_world'|, X!1)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[38, 36])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((~![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)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ((~![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_(|'$ki_local_world'|, W)) | g(W, X)))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)) | (~f(|'$ki_local_world'|, X!1)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | g(W, X!1))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[41, 35, 21, 20])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (((~![W: |'$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(|'$ki_local_world'|, X!1))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 ((~![W: |'$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))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 ((~![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(|'$ki_local_world'|, X!1)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 (g(|'$ki_local_world'|, X!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[45, 42, 11])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[47])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[52, 50])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[30])).
% 0.12/0.37 tff(56,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.37 tff(57,plain,(
% 0.12/0.37 ![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)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[56])).
% 0.12/0.37 tff(58,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.12/0.37 tff(59,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.12/0.37 tff(60,plain,
% 0.12/0.37 (((~![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(61,plain,
% 0.12/0.37 ((~![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)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(62,plain,
% 0.12/0.37 ((~![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_(|'$ki_local_world'|, W)) | h(W, X!1))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.12/0.37 tff(63,plain,
% 0.12/0.37 ((~g(|'$ki_local_world'|, X!1)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[62, 59, 20])).
% 0.12/0.37 tff(64,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[63, 46])).
% 0.12/0.37 tff(65,plain,
% 0.12/0.37 (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | h(W!2, X!1))),
% 0.12/0.37 inference(and_elim,[status(thm)],[19])).
% 0.12/0.37 tff(66,plain,
% 0.12/0.37 (~h(W!2, X!1)),
% 0.12/0.37 inference(or_elim,[status(thm)],[65])).
% 0.12/0.37 tff(67,plain,
% 0.12/0.37 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)),
% 0.12/0.37 inference(or_elim,[status(thm)],[65])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 (((~![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))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(69,plain,
% 0.12/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | h(W, X!1))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | h(W!2, X!1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(70,plain,
% 0.12/0.38 ((~![W: |'$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)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[70, 67, 66, 64])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------