%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO887_22 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.17s 0.36s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO887_22 : TPTP v9.0.0. Released v8.2.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n011.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Jun 20 13:50:41 EDT 2025
% 0.17/0.31 % CPUTime :
% 0.17/0.36 % SZS status Theorem
% 0.17/0.36 % SZS output start Proof
% 0.17/0.36 tff(f_type, type, (
% 0.17/0.36 f: ( |'$ki_world'| * $i ) > $o)).
% 0.17/0.36 tff(tptp_fun_X_1_type, type, (
% 0.17/0.36 tptp_fun_X_1: |'$ki_world'| > $i)).
% 0.17/0.36 tff(tptp_fun___ki_local_world__type, type, (
% 0.17/0.36 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.17/0.36 tff(tptp_fun___ki_accessible__type, type, (
% 0.17/0.36 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.17/0.36 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.17/0.36 tptp_fun___ki_exists_in_world__i_: ( |'$ki_world'| * $i ) > $o)).
% 0.17/0.36 tff(1,assumption,(~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)), introduced(assumption)).
% 0.17/0.36 tff(2,plain,
% 0.17/0.36 (^[W: |'$ki_world'|] : refl(tptp_fun___ki_accessible_(W, W) <=> tptp_fun___ki_accessible_(W, W))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(3,plain,
% 0.17/0.36 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.17/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.17/0.36 tff(4,plain,
% 0.17/0.36 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(5,axiom,(![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_reflexive')).
% 0.17/0.36 tff(6,plain,
% 0.17/0.36 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.17/0.36 tff(7,plain,(
% 0.17/0.36 ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.17/0.36 inference(skolemize,[status(sab)],[6])).
% 0.17/0.36 tff(8,plain,
% 0.17/0.36 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.17/0.36 tff(9,plain,
% 0.17/0.36 ((~![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)) | tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)),
% 0.17/0.36 inference(quant_inst,[status(thm)],[])).
% 0.17/0.36 tff(10,plain,
% 0.17/0.36 ($false),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.17/0.36 tff(11,plain,(tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.36 tff(12,plain,
% 0.17/0.36 (^[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_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W)))))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(13,plain,
% 0.17/0.36 (![W: |'$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_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W))))))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.17/0.36 tff(14,plain,
% 0.17/0.36 (^[W: |'$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)))))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(15,plain,
% 0.17/0.36 (![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))))))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.17/0.36 tff(16,plain,
% 0.17/0.36 (![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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(17,plain,
% 0.17/0.36 ((~(![W: |'$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)))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(18,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/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.17/0.36 tff(19,plain,
% 0.17/0.36 (~((~![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))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.17/0.36 tff(20,plain,
% 0.17/0.36 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.17/0.36 inference(or_elim,[status(thm)],[19])).
% 0.17/0.36 tff(21,plain,
% 0.17/0.36 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.17/0.36 tff(22,plain,(
% 0.17/0.36 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W)) & f(W, tptp_fun_X_1(W))))),
% 0.17/0.36 inference(skolemize,[status(sab)],[21])).
% 0.17/0.36 tff(23,plain,
% 0.17/0.36 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W))))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.17/0.36 tff(24,plain,
% 0.17/0.36 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_1(W))) | (~f(W, tptp_fun_X_1(W))))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.17/0.36 tff(25,plain,
% 0.17/0.36 (((~![W: |'$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(|'$ki_local_world'|))))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(26,plain,
% 0.17/0.36 ((~![W: |'$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(|'$ki_local_world'|))))))),
% 0.17/0.36 inference(quant_inst,[status(thm)],[])).
% 0.17/0.36 tff(27,plain,
% 0.17/0.36 ((~![W: |'$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(|'$ki_local_world'|)))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.17/0.36 tff(28,plain,
% 0.17/0.36 ((~tptp_fun___ki_accessible_(|'$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(|'$ki_local_world'|)))))),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.17/0.36 tff(29,plain,
% 0.17/0.36 (~((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))) | (~f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))))),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[28, 11])).
% 0.17/0.36 tff(30,plain,
% 0.17/0.36 (((~tptp_fun___ki_exists_in_world__i_(|'$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(|'$ki_local_world'|))),
% 0.17/0.36 inference(tautology,[status(thm)],[])).
% 0.17/0.36 tff(31,plain,
% 0.17/0.36 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.17/0.36 tff(32,plain,
% 0.17/0.36 (^[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)))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(33,plain,
% 0.17/0.36 (![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))))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[32])).
% 0.17/0.36 tff(34,plain,
% 0.17/0.36 (^[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)))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(35,plain,
% 0.17/0.36 (![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))))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[34])).
% 0.17/0.36 tff(36,plain,
% 0.17/0.36 (![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))))),
% 0.17/0.36 inference(transitivity,[status(thm)],[35, 33])).
% 0.17/0.36 tff(37,plain,
% 0.17/0.36 (^[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)))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(38,plain,
% 0.17/0.36 (![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))))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[37])).
% 0.17/0.36 tff(39,plain,
% 0.17/0.36 ((~?[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))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(40,plain,
% 0.17/0.36 (~?[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)))),
% 0.17/0.36 inference(or_elim,[status(thm)],[19])).
% 0.17/0.36 tff(41,plain,
% 0.17/0.36 (~?[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)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.17/0.36 tff(42,plain,
% 0.17/0.36 (~?[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)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[41, 39])).
% 0.17/0.36 tff(43,plain,
% 0.17/0.36 (~?[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)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[42, 39])).
% 0.17/0.36 tff(44,plain,
% 0.17/0.36 (^[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))))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(45,plain,(
% 0.17/0.36 ![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))))),
% 0.17/0.36 inference(nnf-neg,[status(sab)],[43, 44])).
% 0.17/0.36 tff(46,plain,
% 0.17/0.36 (![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))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.17/0.36 tff(47,plain,
% 0.17/0.36 (![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))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.17/0.36 tff(48,plain,
% 0.17/0.36 (((~![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'|)))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(49,plain,
% 0.17/0.36 ((~![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'|)))))),
% 0.17/0.36 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(50,plain,
% 0.17/0.37 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~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(|'$ki_local_world'|))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.17/0.37 tff(51,plain,
% 0.17/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, tptp_fun_X_1(|'$ki_local_world'|))))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[50, 47, 31])).
% 0.17/0.37 tff(52,plain,
% 0.17/0.37 (((~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'|))),
% 0.17/0.37 inference(tautology,[status(thm)],[])).
% 0.17/0.37 tff(53,plain,
% 0.17/0.37 (f(|'$ki_local_world'|, tptp_fun_X_1(|'$ki_local_world'|))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[52, 29])).
% 0.17/0.37 tff(54,plain,
% 0.17/0.37 (((~![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'|))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(55,plain,
% 0.17/0.37 ((~![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(|'$ki_local_world'|))))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(56,plain,
% 0.17/0.37 ((~![W: |'$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'|)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.17/0.37 tff(57,plain,
% 0.17/0.37 ($false),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[56, 11, 53, 51])).
% 0.17/0.37 % SZS output end Proof
% 0.17/0.37 % E exiting
%------------------------------------------------------------------------------