TSTP Solution File: SYO891_16 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 22 13:08:45 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.22/0.40 tptp_fun___ki_exists_in_world__i_: ( '$ki_world' * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun_X_1_type, type, (
% 0.22/0.40 tptp_fun_X_1: $i)).
% 0.22/0.40 tff(tptp_fun_W_2_type, type, (
% 0.22/0.40 tptp_fun_W_2: '$ki_world')).
% 0.22/0.40 tff(p_type, type, (
% 0.22/0.40 p: ( '$ki_world' * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun___ki_accessible__type, type, (
% 0.22/0.40 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.22/0.40 tff(tptp_fun___ki_local_world__type, type, (
% 0.22/0.40 tptp_fun___ki_local_world_: '$ki_world')).
% 0.22/0.40 tff(qmltpeq_type, type, (
% 0.22/0.40 qmltpeq: ( '$ki_world' * $i * $i ) > $o)).
% 0.22/0.40 tff(1,plain,
% 0.22/0.40 ((tptp_fun___ki_exists_in_world__i_(|'$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))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(2,plain,
% 0.22/0.40 (?[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)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(3,plain,
% 0.22/0.40 ((~(![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)))))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 (~(?[W: '$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))))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.40 tff(6,plain,
% 0.22/0.40 (?[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)))),
% 0.22/0.40 inference(or_elim,[status(thm)],[5])).
% 0.22/0.40 tff(7,plain,
% 0.22/0.40 (?[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)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.40 tff(8,plain,
% 0.22/0.41 (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)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.22/0.41 tff(9,plain,
% 0.22/0.41 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2)),
% 0.22/0.41 inference(and_elim,[status(thm)],[8])).
% 0.22/0.41 tff(10,plain,
% 0.22/0.41 (^[W: '$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: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(11,plain,
% 0.22/0.41 (![W: '$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: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 (^[W: '$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: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(13,plain,
% 0.22/0.41 (![W: '$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: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.22/0.41 tff(14,plain,
% 0.22/0.41 (![W: '$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: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[13, 11])).
% 0.22/0.41 tff(15,plain,
% 0.22/0.41 (^[W: '$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: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(16,plain,
% 0.22/0.41 (![W: '$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: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 ((~?[W: '$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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(18,plain,
% 0.22/0.41 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))),
% 0.22/0.41 inference(or_elim,[status(thm)],[5])).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.22/0.41 tff(21,plain,
% 0.22/0.41 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.22/0.41 tff(22,plain,
% 0.22/0.41 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.22/0.41 tff(23,plain,
% 0.22/0.41 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.22/0.41 tff(24,plain,
% 0.22/0.41 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[23, 17])).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 (^[W: '$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: $i] : (~(tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(26,plain,(
% 0.22/0.41 ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W, X) & p(W, X))))),
% 0.22/0.41 inference(nnf-neg,[status(sab)],[24, 25])).
% 0.22/0.41 tff(27,plain,
% 0.22/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.22/0.41 tff(28,plain,
% 0.22/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~p(W, X))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[27, 14])).
% 0.22/0.41 tff(29,plain,
% 0.22/0.41 (((~![W: '$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: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(30,plain,
% 0.22/0.41 ((~![W: '$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: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(31,plain,
% 0.22/0.41 ((~![W: '$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)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.22/0.41 tff(32,plain,
% 0.22/0.41 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[31, 28, 9])).
% 0.22/0.41 tff(33,plain,
% 0.22/0.41 (p(W!2, X!1)),
% 0.22/0.41 inference(and_elim,[status(thm)],[8])).
% 0.22/0.41 tff(34,plain,
% 0.22/0.41 (((~![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)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(35,plain,
% 0.22/0.41 ((~![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)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(36,plain,
% 0.22/0.41 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!2, X)) | (~p(W!2, X)))) | (~tptp_fun___ki_exists_in_world__i_(W!2, X!1)) | (~p(W!2, X!1))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.22/0.41 tff(37,plain,
% 0.22/0.41 (~tptp_fun___ki_exists_in_world__i_(W!2, X!1)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[36, 33, 32])).
% 0.22/0.41 tff(38,plain,
% 0.22/0.41 (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X!1)),
% 0.22/0.41 inference(and_elim,[status(thm)],[8])).
% 0.22/0.41 tff(39,plain,
% 0.22/0.41 (^[W: '$ki_world', V: '$ki_world', X: $i] : refl((tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(40,plain,
% 0.22/0.41 (![W: '$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: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.22/0.41 tff(41,plain,
% 0.22/0.41 (^[W: '$ki_world', V: '$ki_world', X: $i] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) <=> (~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))), ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) <=> (~(~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))))), rewrite((~(~((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))) <=> ((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))), ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) <=> ((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))))), (((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) | tptp_fun___ki_exists_in_world__i_(V, X)))), rewrite((((~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))), (((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)) <=> (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(42,plain,
% 0.22/0.41 (![W: '$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: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.22/0.41 tff(43,plain,
% 0.22/0.41 (![W: '$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: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(44,plain,
% 0.22/0.41 (^[W: '$ki_world', V: '$ki_world', X: $i] : rewrite(((tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V)) => tptp_fun___ki_exists_in_world__i_(V, X)) <=> ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(45,plain,
% 0.22/0.41 (![W: '$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: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.22/0.41 tff(46,axiom,(![W: '$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_$i_cumul'')).
% 0.22/0.41 tff(47,plain,
% 0.22/0.41 (![W: '$ki_world', V: '$ki_world', X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.22/0.41 tff(48,plain,
% 0.22/0.41 (![W: '$ki_world', V: '$ki_world', X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.22/0.41 tff(49,plain,(
% 0.22/0.41 ![W: '$ki_world', V: '$ki_world', X: $i] : ((~(tptp_fun___ki_exists_in_world__i_(W, X) & tptp_fun___ki_accessible_(W, V))) | tptp_fun___ki_exists_in_world__i_(V, X))),
% 0.22/0.41 inference(skolemize,[status(sab)],[48])).
% 0.22/0.41 tff(50,plain,
% 0.22/0.41 (![W: '$ki_world', V: '$ki_world', X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.22/0.41 tff(51,plain,
% 0.22/0.41 (![W: '$ki_world', V: '$ki_world', X: $i] : (tptp_fun___ki_exists_in_world__i_(V, X) | (~tptp_fun___ki_accessible_(W, V)) | (~tptp_fun___ki_exists_in_world__i_(W, X)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.22/0.41 tff(52,plain,
% 0.22/0.41 (((~![W: '$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_(|'$ki_local_world'|, X!1)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(53,plain,
% 0.22/0.41 ((tptp_fun___ki_exists_in_world__i_(W!2, X!1) | (~tptp_fun___ki_accessible_(|'$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_(|'$ki_local_world'|, X!1)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(54,plain,
% 0.22/0.41 (((~![W: '$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_(|'$ki_local_world'|, X!1)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1)))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[53])).
% 0.22/0.41 tff(55,plain,
% 0.22/0.41 (((~![W: '$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_(|'$ki_local_world'|, X!1)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1))),
% 0.22/0.41 inference(transitivity,[status(thm)],[54, 52])).
% 0.22/0.41 tff(56,plain,
% 0.22/0.41 ((~![W: '$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_(|'$ki_local_world'|, X!1)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(57,plain,
% 0.22/0.41 ((~![W: '$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_(|'$ki_local_world'|, X!1)) | tptp_fun___ki_exists_in_world__i_(W!2, X!1)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.22/0.41 tff(58,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[57, 51, 38, 9, 37])).
% 0.22/0.41 % SZS output end Proof
%------------------------------------------------------------------------------