%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO891_16 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO891_16 : TPTP v9.0.0. Released v8.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 13:52:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.12/0.38 tptp_fun___ki_exists_in_world__i_: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_X_1_type, type, (
% 0.12/0.38 tptp_fun_X_1: $i)).
% 0.12/0.38 tff(tptp_fun_W_2_type, type, (
% 0.12/0.38 tptp_fun_W_2: |'$ki_world'|)).
% 0.12/0.38 tff(p_type, type, (
% 0.12/0.38 p: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun___ki_accessible__type, type, (
% 0.12/0.38 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.12/0.38 tff(tptp_fun___ki_local_world__type, type, (
% 0.12/0.38 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.12/0.38 tff(qmltpeq_type, type, (
% 0.12/0.38 qmltpeq: ( |'$ki_world'| * $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1) & (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & p(W!2, X!1))) <=> (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1) & tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & p(W!2, X!1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(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) & p(W, X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 ((~(![X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) => ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[Y: $i] : (tptp_fun___ki_exists_in_world__i_(W, Y) & qmltpeq(W, X, Y)))) => (?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W, X))) => ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))))) <=> (~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(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) & p(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)) | ?[Y: $i] : (tptp_fun___ki_exists_in_world__i_(W, Y) & qmltpeq(W, X, Y)))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 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) => ?[Y: $i] : (tptp_fun___ki_exists_in_world__i_(W, Y) & qmltpeq(W, X, Y)))) => (?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W, X))) => ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(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) & p(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)) | ?[Y: $i] : (tptp_fun___ki_exists_in_world__i_(W, Y) & qmltpeq(W, X, Y))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W, X)))),
% 0.12/0.38 inference(or_elim,[status(thm)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1) & tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & p(W!2, X!1)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)),
% 0.12/0.38 inference(and_elim,[status(thm)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[13, 11])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))),
% 0.12/0.38 inference(or_elim,[status(thm)],[5])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (^[W: |'$ki_world'|] : nnf_neg(refl($oeq((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)), (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))), nnf_neg(proof_bind(^[X: $i] : refl($oeq((~(tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X))), (~(tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))))), $oeq((~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X))), ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X))))), $oeq((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))), ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(23,plain,(
% 0.12/0.38 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X))))),
% 0.12/0.38 inference(nnf-neg,[status(sab)],[21, 22])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[28, 25, 9])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (p(W!2, X!1)),
% 0.12/0.38 inference(and_elim,[status(thm)],[8])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X)))) | ((~tptp_fun___ki_exists_in_world__i_(W!2, X!1)) | (~p(W!2, X!1)))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X)))) | (~tptp_fun___ki_exists_in_world__i_(W!2, X!1)) | (~p(W!2, X!1)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X)))) | ((~tptp_fun___ki_exists_in_world__i_(W!2, X!1)) | (~p(W!2, X!1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X)))) | (~tptp_fun___ki_exists_in_world__i_(W!2, X!1)) | (~p(W!2, X!1))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (~tptp_fun___ki_exists_in_world__i_(W!2, X!1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[33, 30, 29])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)),
% 0.12/0.38 inference(and_elim,[status(thm)],[8])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (^[W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : refl((tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![W: |'$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: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (^[W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) <=> (~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))), ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) <=> (~(~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))))), rewrite((~(~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))) <=> ((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))), ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) <=> ((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))), (((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) | tptp_fun___ki_exists_in_world__i_(V, X)))), rewrite((((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))), (((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![W: |'$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: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![W: |'$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: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (^[W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : rewrite(((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) => tptp_fun___ki_exists_in_world__i_(V, X)) <=> ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (![W: |'$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: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.38 tff(43,axiom,(![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) => tptp_fun___ki_exists_in_world__i_(V, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''$ki_exists_in_world_$i_cumul'')).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.12/0.38 tff(46,plain,(
% 0.12/0.38 ![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.38 inference(skolemize,[status(sab)],[45])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (((~![W: |'$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_(|'$ki_local_world'|, X!1)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1))) <=> ((~![W: |'$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_(|'$ki_local_world'|, X!1)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ((tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_accessible_(|'$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_(|'$ki_local_world'|, X!1)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (((~![W: |'$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_(|'$ki_local_world'|, X!1)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[50])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (((~![W: |'$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_(|'$ki_local_world'|, X!1)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1))),
% 0.12/0.38 inference(transitivity,[status(thm)],[51, 49])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 ((~![W: |'$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_(|'$ki_local_world'|, X!1)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 ((~![W: |'$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_(|'$ki_local_world'|, X!1)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[54, 48, 35, 9, 34])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------