%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO890_16 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:42:26 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO890_16 : TPTP v9.0.0. Released v8.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 13:50:18 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(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_X_1_type, type, (
% 0.12/0.36 tptp_fun_X_1: $i)).
% 0.12/0.36 tff(tptp_fun_W_2_type, type, (
% 0.12/0.36 tptp_fun_W_2: |'$ki_world'|)).
% 0.12/0.36 tff(f_type, type, (
% 0.12/0.36 f: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.36 tff(e_type, type, (
% 0.12/0.36 e: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.36 tff(tptp_fun___ki_accessible__type, type, (
% 0.12/0.36 tptp_fun___ki_accessible_: ( |'$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(1,plain,
% 0.12/0.36 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!2, X) & f(W!2, X)))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!2, X) & f(W!2, X))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 ((~![W: |'$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))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 ((~(?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (e(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))))) <=> (~((~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(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)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(4,axiom,(~(?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (e(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))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (~((~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(W, X) & f(W, X))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.12/0.36 inference(or_elim,[status(thm)],[5])).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!2, X) & f(W!2, X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)),
% 0.12/0.36 inference(and_elim,[status(thm)],[10])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1)))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(W, X!1) & f(W, X!1))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(W, X!1) & f(W, X!1))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1)))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 ((tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(W, X!1) & f(W, X!1)))) <=> (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(W, X!1) & f(W, X!1))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 (?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(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)) | (e(W, X) & f(W, X))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(W, X) & f(W, X))))),
% 0.12/0.36 inference(or_elim,[status(thm)],[5])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 (?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(W, X) & f(W, X))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(W, X!1) & f(W, X!1)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(W, X!1) & f(W, X!1)))),
% 0.12/0.36 inference(and_elim,[status(thm)],[20])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1)))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1)))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.12/0.36 tff(24,plain,
% 0.12/0.36 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~((~e(W!2, X!1)) | (~f(W!2, X!1)))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~((~e(W!2, X!1)) | (~f(W!2, X!1)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(25,plain,
% 0.12/0.36 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~((~e(W!2, X!1)) | (~f(W!2, X!1)))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(26,plain,
% 0.12/0.36 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~((~e(W!2, X!1)) | (~f(W!2, X!1))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (~((~e(W!2, X!1)) | (~f(W!2, X!1)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[26, 23, 11])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (((~e(W!2, X!1)) | (~f(W!2, X!1))) | f(W!2, X!1)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (f(W!2, X!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (^[X: $i] : refl(((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (^[X: $i] : trans(monotonicity(rewrite((tptp_fun___ki_exists_in_world__i_(W!2, X) & f(W!2, X)) <=> (~((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X))))), ((~(tptp_fun___ki_exists_in_world__i_(W!2, X) & f(W!2, X))) <=> (~(~((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X))))))), rewrite((~(~((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))), ((~(tptp_fun___ki_exists_in_world__i_(W!2, X) & f(W!2, X))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!2, X) & f(W!2, X))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[32])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!2, X) & f(W!2, X)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[10])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))) | ((~tptp_fun___ki_exists_in_world__i_(W!2, X!1)) | (~f(W!2, X!1)))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))) | (~tptp_fun___ki_exists_in_world__i_(W!2, X!1)) | (~f(W!2, X!1)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))) | ((~tptp_fun___ki_exists_in_world__i_(W!2, X!1)) | (~f(W!2, X!1)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))) | (~tptp_fun___ki_exists_in_world__i_(W!2, X!1)) | (~f(W!2, X!1))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (~tptp_fun___ki_exists_in_world__i_(W!2, X!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[39, 36, 29])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)),
% 0.12/0.37 inference(and_elim,[status(thm)],[20])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (^[W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : refl((tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) <=> ![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[42])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (^[W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) <=> (~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))), ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) <=> (~(~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))))), rewrite((~(~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))) <=> ((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))), ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) <=> ((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))), (((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) | tptp_fun___ki_exists_in_world__i_(V, X)))), rewrite((((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))), (((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> ![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[44])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> ![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (^[W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : rewrite(((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) => tptp_fun___ki_exists_in_world__i_(V, X)) <=> ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) => tptp_fun___ki_exists_in_world__i_(V, X)) <=> ![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[47])).
% 0.12/0.37 tff(49,axiom,(![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) => tptp_fun___ki_exists_in_world__i_(V, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''$ki_exists_in_world_$i_cumul'')).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.12/0.37 tff(52,plain,(
% 0.12/0.37 ![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.37 inference(skolemize,[status(sab)],[51])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.20/0.37 tff(54,plain,
% 0.20/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.20/0.37 tff(55,plain,
% 0.20/0.37 (((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)))) <=> ((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(56,plain,
% 0.20/0.37 ((tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(57,plain,
% 0.20/0.37 (((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))) | (tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)))) <=> ((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.37 tff(58,plain,
% 0.20/0.37 (((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))) | (tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)))) <=> ((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)))),
% 0.20/0.37 inference(transitivity,[status(thm)],[57, 55])).
% 0.20/0.37 tff(59,plain,
% 0.20/0.37 ((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))) | (tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(60,plain,
% 0.20/0.37 ((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.37 tff(61,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[60, 54, 41, 11, 40])).
% 0.20/0.37 % SZS output end Proof
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------