%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO886_6 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO886_6 : TPTP v9.0.0. Released v8.2.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 13:50:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(f_type, type, (
% 0.11/0.36 f: ( |'$ki_world'| * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_X_3_type, type, (
% 0.11/0.36 tptp_fun_X_3: $i)).
% 0.11/0.36 tff(tptp_fun___ki_accessible__type, type, (
% 0.11/0.36 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.11/0.36 tff(tptp_fun___ki_local_world__type, type, (
% 0.11/0.36 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.11/0.36 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.11/0.36 tptp_fun___ki_exists_in_world__i_: ( |'$ki_world'| * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_W_2_type, type, (
% 0.11/0.36 tptp_fun_W_2: |'$ki_world'|)).
% 0.11/0.36 tff(1,assumption,(~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (^[W: |'$ki_world'|, X: $i] : refl(tptp_fun___ki_exists_in_world__i_(W, X) <=> tptp_fun___ki_exists_in_world__i_(W, X))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X) <=> ![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.11/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X) <=> ![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(5,axiom,(![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''$ki_exists_in_world_$i_const'')).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.36 tff(7,plain,(
% 0.11/0.36 ![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.11/0.36 inference(skolemize,[status(sab)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 ((~![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)) | tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.36 tff(11,plain,(tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (^[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))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (^[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))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(transitivity,[status(thm)],[15, 13])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 ((~(![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))) => ![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)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(19,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) => 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/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (~((~![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)))) | ![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))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(or_elim,[status(thm)],[20])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.11/0.36 tff(23,plain,(
% 0.11/0.36 ![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)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[22])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (((~![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_(|'$ki_local_world'|, X!3)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | f(W, X!3)))) <=> ((~![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_(|'$ki_local_world'|, X!3)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | f(W, X!3)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 ((~![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_(|'$ki_local_world'|, X!3)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | f(W, X!3)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 ((~![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_(|'$ki_local_world'|, X!3)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | f(W, X!3))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!3)) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | f(W, X!3))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | f(W, X!3))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[28, 11])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | f(W, X)))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | f(W, X))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | f(W, X)))),
% 0.11/0.37 inference(or_elim,[status(thm)],[20])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | f(W, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | f(W, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[32, 30])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | f(W, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (~((~tptp_fun___ki_exists_in_world__i_(W!2, X!3)) | f(W!2, X!3))),
% 0.11/0.37 inference(and_elim,[status(thm)],[34])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (~f(W!2, X!3)),
% 0.11/0.37 inference(or_elim,[status(thm)],[35])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)),
% 0.11/0.37 inference(and_elim,[status(thm)],[34])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (((~![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))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | f(W, X!3))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)) | f(W!2, X!3))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 ((~![W: |'$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)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[40, 37, 36, 29])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------