TSTP Solution File: PLA053_5 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PLA053_5 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 15:41:28 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
% 0.07/0.13 % Problem : PLA053_5 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 22 12:26:00 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -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_accessible__type, type, (
% 0.22/0.40 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.22/0.40 tff(tptp_fun_W_4_type, type, (
% 0.22/0.40 tptp_fun_W_4: '$ki_world')).
% 0.22/0.40 tff(h_type, type, (
% 0.22/0.40 h: ( '$ki_world' * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun_D_3_type, type, (
% 0.22/0.40 tptp_fun_D_3: ( $i * '$ki_world' ) > $i)).
% 0.22/0.40 tff(tptp_fun_X_5_type, type, (
% 0.22/0.40 tptp_fun_X_5: $i)).
% 0.22/0.40 tff(bomb_type, type, (
% 0.22/0.40 bomb: ( '$ki_world' * $i ) > $o)).
% 0.22/0.40 tff(defused_type, type, (
% 0.22/0.40 defused: ( '$ki_world' * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.22/0.40 tptp_fun___ki_exists_in_world__i_: ( '$ki_world' * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun___ki_local_world__type, type, (
% 0.22/0.40 tptp_fun___ki_local_world_: '$ki_world')).
% 0.22/0.40 tff(1,plain,
% 0.22/0.40 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4) & (tptp_fun___ki_exists_in_world__i_(W!4, X!5) & ![D: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5)))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4) & tptp_fun___ki_exists_in_world__i_(W!4, X!5) & ![D: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5)))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(2,plain,
% 0.22/0.40 (((~(~tptp_fun___ki_exists_in_world__i_(W!4, X!5))) & ![D: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5))))) <=> (tptp_fun___ki_exists_in_world__i_(W!4, X!5) & ![D: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5)))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(3,plain,
% 0.22/0.40 ((~(~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4))) <=> tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(4,plain,
% 0.22/0.40 (((~(~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4))) & ((~(~tptp_fun___ki_exists_in_world__i_(W!4, X!5))) & ![D: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5)))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4) & (tptp_fun___ki_exists_in_world__i_(W!4, X!5) & ![D: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5))))))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[3, 2])).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 (((~(~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4))) & ((~(~tptp_fun___ki_exists_in_world__i_(W!4, X!5))) & ![D: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5)))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4) & tptp_fun___ki_exists_in_world__i_(W!4, X!5) & ![D: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5)))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[4, 1])).
% 0.22/0.40 tff(6,plain,
% 0.22/0.40 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((~(bomb(W, X) & h(W, D))) | defused(W, X)))))) <=> (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((~(bomb(W, X) & h(W, D))) | defused(W, X))))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(7,plain,
% 0.22/0.40 ((~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((bomb(W, X) & h(W, D)) => defused(W, X)))))) <=> (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((~(bomb(W, X) & h(W, D))) | defused(W, X))))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(8,axiom,(~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((bomb(W, X) & h(W, D)) => defused(W, X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.22/0.41 tff(9,plain,
% 0.22/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((~(bomb(W, X) & h(W, D))) | defused(W, X)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.22/0.41 tff(10,plain,
% 0.22/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((~(bomb(W, X) & h(W, D))) | defused(W, X)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.22/0.41 tff(11,plain,
% 0.22/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((~(bomb(W, X) & h(W, D))) | defused(W, X)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((~(bomb(W, X) & h(W, D))) | defused(W, X)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.22/0.41 tff(13,plain,
% 0.22/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((~(bomb(W, X) & h(W, D))) | defused(W, X)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.22/0.41 tff(14,plain,
% 0.22/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((~(bomb(W, X) & h(W, D))) | defused(W, X)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.22/0.41 tff(15,plain,
% 0.22/0.41 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ((~(bomb(W, X) & h(W, D))) | defused(W, X)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.22/0.41 tff(16,plain,
% 0.22/0.41 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4) & tptp_fun___ki_exists_in_world__i_(W!4, X!5) & ![D: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)),
% 0.22/0.41 inference(and_elim,[status(thm)],[16])).
% 0.22/0.41 tff(18,plain,
% 0.22/0.41 (^[W: '$ki_world'] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W))))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W))))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (^[W: '$ki_world'] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W))))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(21,plain,
% 0.22/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W))))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[20])).
% 0.22/0.41 tff(22,plain,
% 0.22/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W))))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[21, 19])).
% 0.22/0.41 tff(23,plain,
% 0.22/0.41 (^[W: '$ki_world'] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W)) & ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~(bomb(W0, X) & h(W0, tptp_fun_D_3(X, W)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W))))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(24,plain,
% 0.22/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W)) & ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~(bomb(W0, X) & h(W0, tptp_fun_D_3(X, W)))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 (^[W: '$ki_world'] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W)) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, tptp_fun_D_3(X, W)))) | (~tptp_fun___ki_accessible_(W, W0)))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W)) & ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~(bomb(W0, X) & h(W0, tptp_fun_D_3(X, W)))))))))),
% 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: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W)) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, tptp_fun_D_3(X, W)))) | (~tptp_fun___ki_accessible_(W, W0)))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W)) & ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~(bomb(W0, X) & h(W0, tptp_fun_D_3(X, W))))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[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)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0)))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(28,plain,
% 0.22/0.41 (^[W: '$ki_world'] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite((tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ((bomb(W0, X) & h(W0, D)) => defused(W0, X)))) <=> (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0)))))), (?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ((bomb(W0, X) & h(W0, D)) => defused(W0, X)))) <=> ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0)))))), ((tptp_fun___ki_exists_in_world__i_(W, X) => ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ((bomb(W0, X) & h(W0, D)) => defused(W0, X))))) <=> (tptp_fun___ki_exists_in_world__i_(W, X) => ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, X) => ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0)))))), ((tptp_fun___ki_exists_in_world__i_(W, X) => ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ((bomb(W0, X) & h(W0, D)) => defused(W0, X))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0)))))))), (![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ((bomb(W0, X) & h(W0, D)) => defused(W0, X))))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ((bomb(W0, X) & h(W0, D)) => defused(W0, X)))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0)))))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0)))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ((bomb(W0, X) & h(W0, D)) => defused(W0, X)))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 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) => ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ((bomb(W0, X) & h(W0, D)) => defused(W0, X)))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.22/0.41 tff(30,axiom,(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) => ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ((bomb(W0, X) & h(W0, D)) => defused(W0, X))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax3')).
% 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)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.22/0.41 tff(32,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)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W, D) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, D))) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.22/0.41 tff(33,plain,(
% 0.22/0.41 ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W)) & ![W0: '$ki_world'] : (defused(W0, X) | (~(bomb(W0, X) & h(W0, tptp_fun_D_3(X, W)))) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[32])).
% 0.22/0.41 tff(34,plain,
% 0.22/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W)) & ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~(bomb(W0, X) & h(W0, tptp_fun_D_3(X, W))))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.22/0.41 tff(35,plain,
% 0.22/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.22/0.41 tff(36,plain,
% 0.22/0.41 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[35, 22])).
% 0.22/0.41 tff(37,plain,
% 0.22/0.41 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4)))))))))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4)))))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(38,plain,
% 0.22/0.41 (((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4)))))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(39,plain,
% 0.22/0.41 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W!4)))))))))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[38])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W!4)))))))))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4)))))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[39, 37])).
% 0.22/0.42 tff(41,plain,
% 0.22/0.42 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W!4)))))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(42,plain,
% 0.22/0.42 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_D_3(X, W))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | defused(W0, X) | (~bomb(W0, X)) | (~h(W0, tptp_fun_D_3(X, W)))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!4)) | ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.22/0.42 tff(43,plain,
% 0.22/0.42 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[42, 36, 17])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 (tptp_fun___ki_exists_in_world__i_(W!4, X!5)),
% 0.22/0.42 inference(and_elim,[status(thm)],[16])).
% 0.22/0.42 tff(45,plain,
% 0.22/0.42 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))))))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 (((~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X!5) | (~bomb(W0, X!5)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X!5, W!4)))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(47,plain,
% 0.22/0.42 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X!5) | (~bomb(W0, X!5)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))))))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4)))))))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[46])).
% 0.22/0.42 tff(48,plain,
% 0.22/0.42 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X!5) | (~bomb(W0, X!5)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))))))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[47, 45])).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X!5) | (~bomb(W0, X!5)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(50,plain,
% 0.22/0.42 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, X)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X, W!4))) | (~![W0: '$ki_world'] : (defused(W0, X) | (~bomb(W0, X)) | (~tptp_fun___ki_accessible_(W!4, W0)) | (~h(W0, tptp_fun_D_3(X, W!4))))))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4)))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 (~((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[50, 44, 43])).
% 0.22/0.42 tff(52,plain,
% 0.22/0.42 (((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4)))))) | tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(53,plain,
% 0.22/0.42 (tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 (^[D: $i] : refl(((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D))))) <=> ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.22/0.42 tff(56,plain,
% 0.22/0.42 (^[D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((bomb(W!4, X!5) & h(W!4, D)) <=> (~((~bomb(W!4, X!5)) | (~h(W!4, D))))), ((~(bomb(W!4, X!5) & h(W!4, D))) <=> (~(~((~bomb(W!4, X!5)) | (~h(W!4, D))))))), rewrite((~(~((~bomb(W!4, X!5)) | (~h(W!4, D))))) <=> ((~bomb(W!4, X!5)) | (~h(W!4, D)))), ((~(bomb(W!4, X!5) & h(W!4, D))) <=> ((~bomb(W!4, X!5)) | (~h(W!4, D))))), (((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5)) <=> (((~bomb(W!4, X!5)) | (~h(W!4, D))) | defused(W!4, X!5)))), rewrite((((~bomb(W!4, X!5)) | (~h(W!4, D))) | defused(W!4, X!5)) <=> (defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))), (((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5)) <=> (defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D))))), ((tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5))) <=> (tptp_fun___ki_exists_in_world__i_(W!4, D) & (defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))), rewrite((tptp_fun___ki_exists_in_world__i_(W!4, D) & (defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))) <=> (~((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D))))))), ((tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5))) <=> (~((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))))), ((~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5)))) <=> (~(~((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D))))))))), rewrite((~(~((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))), ((~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5)))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(57,plain,
% 0.22/0.43 (![D: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5)))) <=> ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[56])).
% 0.22/0.43 tff(58,plain,
% 0.22/0.43 (![D: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!4, D) & ((~(bomb(W!4, X!5) & h(W!4, D))) | defused(W!4, X!5))))),
% 0.22/0.43 inference(and_elim,[status(thm)],[16])).
% 0.22/0.43 tff(59,plain,
% 0.22/0.43 (![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.22/0.43 tff(60,plain,
% 0.22/0.43 (![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.22/0.43 tff(61,plain,
% 0.22/0.43 (((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))))))) <=> ((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(62,plain,
% 0.22/0.43 ((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(63,plain,
% 0.22/0.43 ((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.22/0.43 tff(64,plain,
% 0.22/0.43 (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[63, 60, 53])).
% 0.22/0.43 tff(65,plain,
% 0.22/0.43 ((defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4)))) | h(W!4, tptp_fun_D_3(X!5, W!4))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(66,plain,
% 0.22/0.43 (h(W!4, tptp_fun_D_3(X!5, W!4))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.22/0.43 tff(67,plain,
% 0.22/0.43 (((~tptp_fun___ki_exists_in_world__i_(W!4, tptp_fun_D_3(X!5, W!4))) | (~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4)))))) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(68,plain,
% 0.22/0.43 (![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[67, 51])).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 (((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, X!5)))))) <=> ((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, X!5)))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 ((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))) | ((~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, X!5)))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 ((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!4, D)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, D)))))) | (~tptp_fun___ki_exists_in_world__i_(W!4, X!5)) | (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, X!5))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.22/0.43 tff(72,plain,
% 0.22/0.43 (~(defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, X!5)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[71, 44, 60])).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 ((defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, X!5))) | bomb(W!4, X!5)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(74,plain,
% 0.22/0.43 (bomb(W!4, X!5)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.22/0.43 tff(75,plain,
% 0.22/0.43 ((defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, X!5))) | (~defused(W!4, X!5))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(76,plain,
% 0.22/0.43 (~defused(W!4, X!5)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[75, 72])).
% 0.22/0.43 tff(77,plain,
% 0.22/0.43 (((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))) | (defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))) | (~tptp_fun___ki_accessible_(W!4, W!4)))) <=> ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))) | defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))) | (~tptp_fun___ki_accessible_(W!4, W!4)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(78,plain,
% 0.22/0.43 (((~tptp_fun___ki_accessible_(W!4, W!4)) | defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4)))) <=> (defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))) | (~tptp_fun___ki_accessible_(W!4, W!4)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(79,plain,
% 0.22/0.43 (((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))) | ((~tptp_fun___ki_accessible_(W!4, W!4)) | defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))))) <=> ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))) | (defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))) | (~tptp_fun___ki_accessible_(W!4, W!4))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[78])).
% 0.22/0.43 tff(80,plain,
% 0.22/0.43 (((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))) | ((~tptp_fun___ki_accessible_(W!4, W!4)) | defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))))) <=> ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))) | defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))) | (~tptp_fun___ki_accessible_(W!4, W!4)))),
% 0.22/0.43 inference(transitivity,[status(thm)],[79, 77])).
% 0.22/0.43 tff(81,plain,
% 0.22/0.43 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))) | ((~tptp_fun___ki_accessible_(W!4, W!4)) | defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(82,plain,
% 0.22/0.43 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!4, W0)) | defused(W0, X!5) | (~bomb(W0, X!5)) | (~h(W0, tptp_fun_D_3(X!5, W!4))))) | defused(W!4, X!5) | (~bomb(W!4, X!5)) | (~h(W!4, tptp_fun_D_3(X!5, W!4))) | (~tptp_fun___ki_accessible_(W!4, W!4))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.22/0.43 tff(83,plain,
% 0.22/0.43 ((~h(W!4, tptp_fun_D_3(X!5, W!4))) | (~tptp_fun___ki_accessible_(W!4, W!4))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[82, 76, 74, 68])).
% 0.22/0.43 tff(84,plain,
% 0.22/0.43 (~tptp_fun___ki_accessible_(W!4, W!4)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[83, 66])).
% 0.22/0.43 tff(85,plain,
% 0.22/0.43 (^[W: '$ki_world', V: '$ki_world'] : refl(tptp_fun___ki_accessible_(W, V) <=> tptp_fun___ki_accessible_(W, V))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(86,plain,
% 0.22/0.43 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V) <=> ![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.22/0.43 inference(quant_intro,[status(thm)],[85])).
% 0.22/0.43 tff(87,plain,
% 0.22/0.43 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V) <=> ![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(88,axiom,(![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal')).
% 0.22/0.43 tff(89,plain,
% 0.22/0.43 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.22/0.43 tff(90,plain,(
% 0.22/0.43 ![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.22/0.43 inference(skolemize,[status(sab)],[89])).
% 0.22/0.43 tff(91,plain,
% 0.22/0.43 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.22/0.43 tff(92,plain,
% 0.22/0.43 ((~![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(W!4, W!4)),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(93,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[92, 91, 84])).
% 0.22/0.43 % SZS output end Proof
%------------------------------------------------------------------------------