%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO892_15 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO892_15 : TPTP v9.0.0. Released v8.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.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 13:50:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.12/0.37 tptp_fun___ki_exists_in_world__i_: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_X_3_type, type, (
% 0.12/0.37 tptp_fun_X_3: $i)).
% 0.12/0.37 tff(tptp_fun_W_2_type, type, (
% 0.12/0.37 tptp_fun_W_2: |'$ki_world'|)).
% 0.12/0.37 tff(f_type, type, (
% 0.12/0.37 f: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun___ki_accessible__type, type, (
% 0.12/0.37 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.12/0.37 tff(tptp_fun___ki_local_world__type, type, (
% 0.12/0.37 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : trans(monotonicity(rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X!3)) <=> (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3))))), ((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X!3))) <=> (~(~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3))))))), rewrite((~(~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3)))), ((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X!3))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X!3))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 ((tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3) & ![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X!3)))) <=> (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3) & ![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X!3))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(6,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) & 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))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 ((~(?[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)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(8,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/sandbox/benchmark/theBenchmark.p','verify')).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~((~?[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))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,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) & f(W, X)))),
% 0.12/0.37 inference(or_elim,[status(thm)],[9])).
% 0.12/0.37 tff(11,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) & f(W, X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.12/0.37 tff(12,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) & f(W, X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.12/0.37 tff(13,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) & f(W, X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3) & ![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X!3)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & f(W, X!3)))),
% 0.12/0.38 inference(and_elim,[status(thm)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 2])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((tptp_fun___ki_accessible_(|'$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: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | f(W!2, X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | f(W, X))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | f(W, X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | f(W, X)))),
% 0.12/0.38 inference(or_elim,[status(thm)],[9])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | f(W, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | f(W!2, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)),
% 0.12/0.38 inference(and_elim,[status(thm)],[22])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~f(W!2, X!3)))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~f(W!2, X!3)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~f(W!2, X!3)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~f(W, X!3)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | (~f(W!2, X!3))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~f(W!2, X!3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[26, 23, 17])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (^[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)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![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))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | f(W!2, X))),
% 0.12/0.38 inference(and_elim,[status(thm)],[22])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | f(W!2, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (((~![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!3)) | f(W!2, X!3))) <=> ((~![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!3)) | f(W!2, X!3))),
% 0.12/0.38 inference(rewrite,[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)) | f(W!2, X))) | ((~tptp_fun___ki_exists_in_world__i_(W!2, X!3)) | f(W!2, X!3))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | f(W!2, X))) | (~tptp_fun___ki_exists_in_world__i_(W!2, X!3)) | f(W!2, X!3)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (~tptp_fun___ki_exists_in_world__i_(W!2, X!3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[34, 31, 27])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)),
% 0.12/0.38 inference(and_elim,[status(thm)],[14])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (^[W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : refl((tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V))) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V))) <=> ![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (^[W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) <=> (~((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V))))), ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) <=> (~(~((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V))))))), rewrite((~(~((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))), ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V))))), (((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)))), rewrite((((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))), (((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![W: |'$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: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![W: |'$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: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (^[W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : rewrite(((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) => tptp_fun___ki_exists_in_world__i_(V, X)) <=> ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (![W: |'$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: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.12/0.38 tff(44,axiom,(![W: |'$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_$i_cumul'')).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.12/0.38 tff(47,plain,(
% 0.12/0.38 ![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.12/0.38 inference(skolemize,[status(sab)],[46])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))) | ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!3))) <=> ((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!3))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 ((tptp_fun___ki_exists_in_world__i_(W!2, X!3) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2))) <=> ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!3))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))) | (tptp_fun___ki_exists_in_world__i_(W!2, X!3) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)))) <=> ((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))) | ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!3)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))) | (tptp_fun___ki_exists_in_world__i_(W!2, X!3) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)))) <=> ((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!3))),
% 0.19/0.38 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 ((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))) | (tptp_fun___ki_exists_in_world__i_(W!2, X!3) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 ((~![W: |'$ki_world'|, V: |'$ki_world'|, X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_exists_in_world__i_(W, X)) | (~tptp_fun___ki_accessible_(W, V)))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | tptp_fun___ki_exists_in_world__i_(W!2, X!3)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[55, 49, 23, 36, 35])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------