TSTP Solution File: SYO890_16 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO890_16 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 : Mon May 22 15:46:13 EDT 2023
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO890_16 : TPTP v8.2.0. Released v8.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 22 12:37:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.19/0.39 tptp_fun___ki_exists_in_world__i_: ( '$ki_world' * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_X_1_type, type, (
% 0.19/0.39 tptp_fun_X_1: $i)).
% 0.19/0.39 tff(tptp_fun_W_2_type, type, (
% 0.19/0.39 tptp_fun_W_2: '$ki_world')).
% 0.19/0.39 tff(f_type, type, (
% 0.19/0.39 f: ( '$ki_world' * $i ) > $o)).
% 0.19/0.39 tff(e_type, type, (
% 0.19/0.39 e: ( '$ki_world' * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun___ki_accessible__type, type, (
% 0.19/0.39 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.19/0.39 tff(tptp_fun___ki_local_world__type, type, (
% 0.19/0.39 tptp_fun___ki_local_world_: '$ki_world')).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (((~(~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: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!2, X) & f(W!2, X))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 ((~![W: '$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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 ((~(?[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)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 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/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (~((~?[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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.19/0.39 inference(or_elim,[status(thm)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & f(W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!2, X) & f(W!2, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)),
% 0.19/0.39 inference(and_elim,[status(thm)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (^[W: '$ki_world'] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![W: '$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_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (^[W: '$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))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (?[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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (?[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))))),
% 0.19/0.39 inference(or_elim,[status(thm)],[5])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (?[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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1) & ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(W, X!1) & f(W, X!1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (e(W, X!1) & f(W, X!1)))),
% 0.19/0.39 inference(and_elim,[status(thm)],[23])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~e(W, X!1)) | (~f(W, X!1)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 16])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (((~![W: '$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_(|'$ki_local_world'|, W!2)) | (~((~e(W!2, X!1)) | (~f(W!2, X!1)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 ((~![W: '$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)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 ((~![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (~((~e(W!2, X!1)) | (~f(W!2, X!1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[29, 26, 14])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (((~e(W!2, X!1)) | (~f(W!2, X!1))) | f(W!2, X!1)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (f(W!2, X!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!2, X) & f(W!2, X)))),
% 0.19/0.39 inference(and_elim,[status(thm)],[13])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (((~![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((~![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)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~f(W!2, X)))) | (~tptp_fun___ki_exists_in_world__i_(W!2, X!1)) | (~f(W!2, X!1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (~tptp_fun___ki_exists_in_world__i_(W!2, X!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 39, 32])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)),
% 0.19/0.39 inference(and_elim,[status(thm)],[23])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (^[W: '$ki_world', V: '$ki_world', X: $i] : refl((tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (![W: '$ki_world', V: '$ki_world', X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) <=> ![W: '$ki_world', V: '$ki_world', X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (^[W: '$ki_world', V: '$ki_world', X: $i] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) <=> (~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))), ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) <=> (~(~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))))), rewrite((~(~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))) <=> ((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))), ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) <=> ((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))), (((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) | tptp_fun___ki_exists_in_world__i_(V, X)))), rewrite((((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))), (((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![W: '$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: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (![W: '$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: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (^[W: '$ki_world', V: '$ki_world', X: $i] : rewrite(((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) => tptp_fun___ki_exists_in_world__i_(V, X)) <=> ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (![W: '$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: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.40 tff(52,axiom,(![W: '$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_$i_cumul'')).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![W: '$ki_world', V: '$ki_world', X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (![W: '$ki_world', V: '$ki_world', X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.19/0.40 tff(55,plain,(
% 0.19/0.40 ![W: '$ki_world', V: '$ki_world', X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.19/0.40 inference(skolemize,[status(sab)],[54])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![W: '$ki_world', V: '$ki_world', X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![W: '$ki_world', V: '$ki_world', X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (((~![W: '$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_(|'$ki_local_world'|, X!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 ((tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_accessible_(|'$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_(|'$ki_local_world'|, X!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (((~![W: '$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_(|'$ki_local_world'|, X!1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (((~![W: '$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_(|'$ki_local_world'|, X!1)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((~![W: '$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_(|'$ki_local_world'|, X!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 ((~![W: '$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_(|'$ki_local_world'|, X!1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[63, 57, 44, 14, 43])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------