TSTP Solution File: LCL950_17 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL950_17 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 15:39:15 EDT 2023
% Result : Theorem 0.55s 0.58s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL950_17 : TPTP v8.2.0. Released v8.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 22 11:57:09 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.55/0.58 % SZS status Theorem
% 0.55/0.58 % SZS output start Proof
% 0.55/0.58 tff(tptp_fun___ki_accessible__type, type, (
% 0.55/0.58 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.55/0.58 tff(tptp_fun_W2_4_type, type, (
% 0.55/0.58 tptp_fun_W2_4: ( $i * '$ki_world' * $i ) > '$ki_world')).
% 0.55/0.58 tff(tptp_fun_C_8_type, type, (
% 0.55/0.58 tptp_fun_C_8: $i)).
% 0.55/0.58 tff(tptp_fun_W1_9_type, type, (
% 0.55/0.58 tptp_fun_W1_9: '$ki_world')).
% 0.55/0.58 tff(tptp_fun_B_6_type, type, (
% 0.55/0.58 tptp_fun_B_6: $i)).
% 0.55/0.58 tff(tptp_fun_W2_11_type, type, (
% 0.55/0.58 tptp_fun_W2_11: '$ki_world')).
% 0.55/0.58 tff(member_type, type, (
% 0.55/0.58 member: ( '$ki_world' * $i * $i ) > $o)).
% 0.55/0.58 tff(tptp_fun_D_10_type, type, (
% 0.55/0.58 tptp_fun_D_10: $i)).
% 0.55/0.58 tff(tptp_fun_W2_3_type, type, (
% 0.55/0.58 tptp_fun_W2_3: ( $i * '$ki_world' * $i ) > '$ki_world')).
% 0.55/0.58 tff(intersect_type, type, (
% 0.55/0.58 intersect: ( '$ki_world' * $i * $i ) > $o)).
% 0.55/0.58 tff(tptp_fun_W3_12_type, type, (
% 0.55/0.58 tptp_fun_W3_12: '$ki_world')).
% 0.55/0.58 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.55/0.58 tptp_fun___ki_exists_in_world__i_: ( '$ki_world' * $i ) > $o)).
% 0.55/0.58 tff(tptp_fun_W0_7_type, type, (
% 0.55/0.58 tptp_fun_W0_7: '$ki_world')).
% 0.55/0.58 tff(tptp_fun_W_5_type, type, (
% 0.55/0.58 tptp_fun_W_5: '$ki_world')).
% 0.55/0.58 tff(tptp_fun___ki_local_world__type, type, (
% 0.55/0.58 tptp_fun___ki_local_world_: '$ki_world')).
% 0.55/0.58 tff(tptp_fun_W2_2_type, type, (
% 0.55/0.58 tptp_fun_W2_2: ( '$ki_world' * $i * $i ) > '$ki_world')).
% 0.55/0.58 tff(tptp_fun_D_1_type, type, (
% 0.55/0.58 tptp_fun_D_1: ( '$ki_world' * $i * $i ) > $i)).
% 0.55/0.58 tff(1,assumption,(~tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_3(B!6, W1!9, D!10))), introduced(assumption)).
% 0.55/0.58 tff(2,plain,
% 0.55/0.58 (^[W: '$ki_world', V: '$ki_world'] : refl(tptp_fun___ki_accessible_(W, V) <=> tptp_fun___ki_accessible_(W, V))),
% 0.55/0.58 inference(bind,[status(th)],[])).
% 0.55/0.58 tff(3,plain,
% 0.55/0.58 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V) <=> ![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.55/0.58 inference(quant_intro,[status(thm)],[2])).
% 0.55/0.58 tff(4,plain,
% 0.55/0.58 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V) <=> ![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.55/0.58 inference(rewrite,[status(thm)],[])).
% 0.55/0.58 tff(5,axiom,(![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal')).
% 0.55/0.58 tff(6,plain,
% 0.55/0.58 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.55/0.58 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.55/0.58 tff(7,plain,(
% 0.55/0.58 ![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.55/0.58 inference(skolemize,[status(sab)],[6])).
% 0.55/0.58 tff(8,plain,
% 0.55/0.58 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.55/0.58 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.55/0.58 tff(9,plain,
% 0.55/0.58 ((~![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_3(B!6, W1!9, D!10))),
% 0.55/0.58 inference(quant_inst,[status(thm)],[])).
% 0.55/0.58 tff(10,plain,
% 0.55/0.58 ($false),
% 0.55/0.58 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.55/0.58 tff(11,plain,(tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_3(B!6, W1!9, D!10))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.58 tff(12,plain,
% 0.55/0.58 (^[W3: '$ki_world'] : refl(((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) <=> ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)))),
% 0.55/0.58 inference(bind,[status(th)],[])).
% 0.55/0.58 tff(13,plain,
% 0.55/0.58 (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) <=> ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))),
% 0.55/0.58 inference(quant_intro,[status(thm)],[12])).
% 0.55/0.58 tff(14,plain,
% 0.55/0.58 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!5) & (tptp_fun___ki_exists_in_world__i_(W!5, B!6) & tptp_fun___ki_accessible_(W!5, W0!7) & tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!5) & tptp_fun___ki_exists_in_world__i_(W!5, B!6) & tptp_fun___ki_accessible_(W!5, W0!7) & tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(15,plain,
% 0.55/0.59 ((tptp_fun___ki_exists_in_world__i_(W!5, B!6) & (tptp_fun___ki_accessible_(W!5, W0!7) & tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))) <=> (tptp_fun___ki_exists_in_world__i_(W!5, B!6) & tptp_fun___ki_accessible_(W!5, W0!7) & tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(16,plain,
% 0.55/0.59 ((tptp_fun___ki_accessible_(W!5, W0!7) & (tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))) <=> (tptp_fun___ki_accessible_(W!5, W0!7) & tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(17,plain,
% 0.55/0.59 ((tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & (tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))) <=> (tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(18,plain,
% 0.55/0.59 ((tptp_fun___ki_accessible_(W0!7, W1!9) & (tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))) <=> (tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(19,plain,
% 0.55/0.59 ((tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & (tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))) <=> (tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(20,plain,
% 0.55/0.59 ((tptp_fun___ki_accessible_(W1!9, W2!11) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))) <=> (tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(21,plain,
% 0.55/0.59 ((![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) <=> (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(22,plain,
% 0.55/0.59 ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) <=> tptp_fun___ki_accessible_(W1!9, W2!11)),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(23,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))) <=> (tptp_fun___ki_accessible_(W1!9, W2!11) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(monotonicity,[status(thm)],[22, 21])).
% 0.55/0.59 tff(24,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))) <=> (tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(transitivity,[status(thm)],[23, 20])).
% 0.55/0.59 tff(25,plain,
% 0.55/0.59 ((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) <=> tptp_fun___ki_exists_in_world__i_(W1!9, D!10)),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(26,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))) <=> (tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & (tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))),
% 0.55/0.59 inference(monotonicity,[status(thm)],[25, 24])).
% 0.55/0.59 tff(27,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))) <=> (tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(transitivity,[status(thm)],[26, 19])).
% 0.55/0.59 tff(28,plain,
% 0.55/0.59 ((~(~tptp_fun___ki_accessible_(W0!7, W1!9))) <=> tptp_fun___ki_accessible_(W0!7, W1!9)),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(29,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_accessible_(W0!7, W1!9))) & ((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))) <=> (tptp_fun___ki_accessible_(W0!7, W1!9) & (tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))),
% 0.55/0.59 inference(monotonicity,[status(thm)],[28, 27])).
% 0.55/0.59 tff(30,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_accessible_(W0!7, W1!9))) & ((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))) <=> (tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(transitivity,[status(thm)],[29, 18])).
% 0.55/0.59 tff(31,plain,
% 0.55/0.59 ((~(~tptp_fun___ki_exists_in_world__i_(W0!7, C!8))) <=> tptp_fun___ki_exists_in_world__i_(W0!7, C!8)),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(32,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_exists_in_world__i_(W0!7, C!8))) & ((~(~tptp_fun___ki_accessible_(W0!7, W1!9))) & ((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))))) <=> (tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & (tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))),
% 0.55/0.59 inference(monotonicity,[status(thm)],[31, 30])).
% 0.55/0.59 tff(33,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_exists_in_world__i_(W0!7, C!8))) & ((~(~tptp_fun___ki_accessible_(W0!7, W1!9))) & ((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))))) <=> (tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(transitivity,[status(thm)],[32, 17])).
% 0.55/0.59 tff(34,plain,
% 0.55/0.59 ((~(~tptp_fun___ki_accessible_(W!5, W0!7))) <=> tptp_fun___ki_accessible_(W!5, W0!7)),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(35,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_accessible_(W!5, W0!7))) & ((~(~tptp_fun___ki_exists_in_world__i_(W0!7, C!8))) & ((~(~tptp_fun___ki_accessible_(W0!7, W1!9))) & ((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))))) <=> (tptp_fun___ki_accessible_(W!5, W0!7) & (tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))),
% 0.55/0.59 inference(monotonicity,[status(thm)],[34, 33])).
% 0.55/0.59 tff(36,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_accessible_(W!5, W0!7))) & ((~(~tptp_fun___ki_exists_in_world__i_(W0!7, C!8))) & ((~(~tptp_fun___ki_accessible_(W0!7, W1!9))) & ((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))))) <=> (tptp_fun___ki_accessible_(W!5, W0!7) & tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(transitivity,[status(thm)],[35, 16])).
% 0.55/0.59 tff(37,plain,
% 0.55/0.59 ((~(~tptp_fun___ki_exists_in_world__i_(W!5, B!6))) <=> tptp_fun___ki_exists_in_world__i_(W!5, B!6)),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(38,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_exists_in_world__i_(W!5, B!6))) & ((~(~tptp_fun___ki_accessible_(W!5, W0!7))) & ((~(~tptp_fun___ki_exists_in_world__i_(W0!7, C!8))) & ((~(~tptp_fun___ki_accessible_(W0!7, W1!9))) & ((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))))))) <=> (tptp_fun___ki_exists_in_world__i_(W!5, B!6) & (tptp_fun___ki_accessible_(W!5, W0!7) & tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))),
% 0.55/0.59 inference(monotonicity,[status(thm)],[37, 36])).
% 0.55/0.59 tff(39,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_exists_in_world__i_(W!5, B!6))) & ((~(~tptp_fun___ki_accessible_(W!5, W0!7))) & ((~(~tptp_fun___ki_exists_in_world__i_(W0!7, C!8))) & ((~(~tptp_fun___ki_accessible_(W0!7, W1!9))) & ((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))))))) <=> (tptp_fun___ki_exists_in_world__i_(W!5, B!6) & tptp_fun___ki_accessible_(W!5, W0!7) & tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(transitivity,[status(thm)],[38, 15])).
% 0.55/0.59 tff(40,plain,
% 0.55/0.59 ((~(~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!5))) <=> tptp_fun___ki_accessible_(|'$ki_local_world'|, W!5)),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(41,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!5))) & ((~(~tptp_fun___ki_exists_in_world__i_(W!5, B!6))) & ((~(~tptp_fun___ki_accessible_(W!5, W0!7))) & ((~(~tptp_fun___ki_exists_in_world__i_(W0!7, C!8))) & ((~(~tptp_fun___ki_accessible_(W0!7, W1!9))) & ((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!5) & (tptp_fun___ki_exists_in_world__i_(W!5, B!6) & tptp_fun___ki_accessible_(W!5, W0!7) & tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))),
% 0.55/0.59 inference(monotonicity,[status(thm)],[40, 39])).
% 0.55/0.59 tff(42,plain,
% 0.55/0.59 (((~(~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!5))) & ((~(~tptp_fun___ki_exists_in_world__i_(W!5, B!6))) & ((~(~tptp_fun___ki_accessible_(W!5, W0!7))) & ((~(~tptp_fun___ki_exists_in_world__i_(W0!7, C!8))) & ((~(~tptp_fun___ki_accessible_(W0!7, W1!9))) & ((~(~tptp_fun___ki_exists_in_world__i_(W1!9, D!10))) & ((~(~tptp_fun___ki_accessible_(W1!9, W2!11))) & (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!5) & tptp_fun___ki_exists_in_world__i_(W!5, B!6) & tptp_fun___ki_accessible_(W!5, W0!7) & tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))))),
% 0.55/0.59 inference(transitivity,[status(thm)],[41, 14])).
% 0.55/0.59 tff(43,plain,
% 0.55/0.59 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~(![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, C)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, D)))) | ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | intersect(W3, C, D)))))))))) <=> (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~(![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, C)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, D)))) | ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | intersect(W3, C, D))))))))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(44,plain,
% 0.55/0.59 ((~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => ![D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => ((![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => member(W3, B, C)) & ![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => member(W3, B, D))) => ![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => intersect(W3, C, D))))))))))) <=> (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~(![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, C)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, D)))) | ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | intersect(W3, C, D))))))))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(45,axiom,(~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => ![D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => ((![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => member(W3, B, C)) & ![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => member(W3, B, D))) => ![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => intersect(W3, C, D))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.55/0.60 tff(46,plain,
% 0.55/0.60 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~(![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, C)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, D)))) | ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | intersect(W3, C, D)))))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.55/0.60 tff(47,plain,
% 0.55/0.60 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~(![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, C)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, D)))) | ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | intersect(W3, C, D)))))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.55/0.60 tff(48,plain,
% 0.55/0.60 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~(![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, C)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, D)))) | ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | intersect(W3, C, D)))))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.55/0.60 tff(49,plain,
% 0.55/0.60 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~(![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, C)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, D)))) | ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | intersect(W3, C, D)))))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[48, 43])).
% 0.55/0.60 tff(50,plain,
% 0.55/0.60 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~(![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, C)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, D)))) | ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | intersect(W3, C, D)))))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[49, 43])).
% 0.55/0.60 tff(51,plain,
% 0.55/0.60 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~(![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, C)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, D)))) | ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | intersect(W3, C, D)))))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.55/0.60 tff(52,plain,
% 0.55/0.60 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~(![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, C)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | member(W3, B, D)))) | ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | intersect(W3, C, D)))))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[51, 43])).
% 0.55/0.60 tff(53,plain,
% 0.55/0.60 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!5) & tptp_fun___ki_exists_in_world__i_(W!5, B!6) & tptp_fun___ki_accessible_(W!5, W0!7) & tptp_fun___ki_exists_in_world__i_(W0!7, C!8) & tptp_fun___ki_accessible_(W0!7, W1!9) & tptp_fun___ki_exists_in_world__i_(W1!9, D!10) & tptp_fun___ki_accessible_(W1!9, W2!11) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) & ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10)) & (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10)))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.55/0.60 tff(54,plain,
% 0.55/0.60 (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))),
% 0.55/0.60 inference(and_elim,[status(thm)],[53])).
% 0.55/0.60 tff(55,plain,
% 0.55/0.60 (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[54, 13])).
% 0.55/0.60 tff(56,plain,
% 0.55/0.60 (((~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) | ((~tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_3(B!6, W1!9, D!10))) | member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10))) <=> ((~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) | (~tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_3(B!6, W1!9, D!10))) | member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(57,plain,
% 0.55/0.60 ((~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) | ((~tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_3(B!6, W1!9, D!10))) | member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10))),
% 0.55/0.60 inference(quant_inst,[status(thm)],[])).
% 0.55/0.60 tff(58,plain,
% 0.55/0.60 ((~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, D!10))) | (~tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_3(B!6, W1!9, D!10))) | member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10)),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.55/0.60 tff(59,plain,
% 0.55/0.60 (member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10)),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[58, 55, 11])).
% 0.55/0.60 tff(60,plain,
% 0.55/0.60 (((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(B!6, W1!9, D!10))) | member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10)) | (~member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10))),
% 0.55/0.60 inference(tautology,[status(thm)],[])).
% 0.55/0.60 tff(61,plain,
% 0.55/0.60 ((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(B!6, W1!9, D!10))) | member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10)),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.55/0.60 tff(62,assumption,(~tptp_fun___ki_accessible_(W1!9, W3!12)), introduced(assumption)).
% 0.55/0.60 tff(63,plain,
% 0.55/0.60 ((~![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(W1!9, W3!12)),
% 0.55/0.60 inference(quant_inst,[status(thm)],[])).
% 0.55/0.60 tff(64,plain,
% 0.55/0.60 ($false),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[63, 8, 62])).
% 0.55/0.60 tff(65,plain,(tptp_fun___ki_accessible_(W1!9, W3!12)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.60 tff(66,assumption,(![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, C!8, D!10))), introduced(assumption)).
% 0.55/0.60 tff(67,plain,
% 0.55/0.60 (~((~tptp_fun___ki_accessible_(W2!11, W3!12)) | intersect(W3!12, C!8, D!10))),
% 0.55/0.60 inference(and_elim,[status(thm)],[53])).
% 0.55/0.60 tff(68,plain,
% 0.55/0.60 (~intersect(W3!12, C!8, D!10)),
% 0.55/0.60 inference(or_elim,[status(thm)],[67])).
% 0.55/0.60 tff(69,plain,
% 0.55/0.60 (((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, C!8, D!10))) | ((~tptp_fun___ki_accessible_(W1!9, W3!12)) | intersect(W3!12, C!8, D!10))) <=> ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, C!8, D!10))) | (~tptp_fun___ki_accessible_(W1!9, W3!12)) | intersect(W3!12, C!8, D!10))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(70,plain,
% 0.55/0.60 ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, C!8, D!10))) | ((~tptp_fun___ki_accessible_(W1!9, W3!12)) | intersect(W3!12, C!8, D!10))),
% 0.55/0.60 inference(quant_inst,[status(thm)],[])).
% 0.55/0.60 tff(71,plain,
% 0.55/0.60 ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, C!8, D!10))) | (~tptp_fun___ki_accessible_(W1!9, W3!12)) | intersect(W3!12, C!8, D!10)),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.55/0.60 tff(72,plain,
% 0.55/0.60 ($false),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[71, 68, 66, 65])).
% 0.55/0.60 tff(73,plain,(~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, C!8, D!10))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.60 tff(74,plain,
% 0.55/0.60 ((~![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(|'$ki_local_world'|, W1!9)),
% 0.55/0.60 inference(quant_inst,[status(thm)],[])).
% 0.55/0.60 tff(75,plain,
% 0.55/0.60 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W1!9)),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[74, 8])).
% 0.55/0.60 tff(76,plain,
% 0.55/0.60 (^[W: '$ki_world'] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))))),
% 0.55/0.60 inference(bind,[status(th)],[])).
% 0.55/0.60 tff(77,plain,
% 0.55/0.60 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))),
% 0.55/0.60 inference(quant_intro,[status(thm)],[76])).
% 0.55/0.60 tff(78,plain,
% 0.55/0.60 (^[W: '$ki_world'] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))))),
% 0.55/0.60 inference(bind,[status(th)],[])).
% 0.55/0.60 tff(79,plain,
% 0.55/0.60 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))),
% 0.55/0.60 inference(quant_intro,[status(thm)],[78])).
% 0.55/0.60 tff(80,plain,
% 0.55/0.60 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))),
% 0.55/0.60 inference(transitivity,[status(thm)],[79, 77])).
% 0.55/0.60 tff(81,plain,
% 0.55/0.60 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(82,plain,
% 0.55/0.60 (^[W: '$ki_world'] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[W0: '$ki_world'] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: '$ki_world'] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W2: '$ki_world'] : rewrite((tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) <=> ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))), (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) <=> ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))), quant_intro(proof_bind(^[W2: '$ki_world'] : rewrite((tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B)) <=> ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))), (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B)) <=> ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))), ((![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B))) <=> (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) => ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))), rewrite((![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) => ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))) <=> ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))), ((![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B))) <=> ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))), ((tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B)))) <=> (tptp_fun___ki_accessible_(W0, W1) => ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))), rewrite((tptp_fun___ki_accessible_(W0, W1) => ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))) <=> ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))), ((tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B)))) <=> ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))), (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B)))) <=> ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))), ((tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B))))) <=> (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))), rewrite((tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))), ((tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))), (![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B))))) <=> ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))), ((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B)))))) <=> (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))), rewrite((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))), ((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B)))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))), (![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B)))))) <=> ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B))))))) <=> (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))))), (![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B))))))) <=> ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B)))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))))),
% 0.55/0.60 inference(bind,[status(th)],[])).
% 0.55/0.60 tff(83,plain,
% 0.55/0.60 (![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B)))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))),
% 0.55/0.60 inference(quant_intro,[status(thm)],[82])).
% 0.55/0.60 tff(84,axiom,(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, C, B))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_of_intersect')).
% 0.55/0.60 tff(85,plain,
% 0.55/0.60 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.55/0.60 tff(86,plain,
% 0.55/0.60 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.55/0.60 tff(87,plain,(
% 0.55/0.60 ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))),
% 0.55/0.60 inference(skolemize,[status(sab)],[86])).
% 0.55/0.60 tff(88,plain,
% 0.55/0.60 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.55/0.60 tff(89,plain,
% 0.55/0.60 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W1!9)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W1!9)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))),
% 0.55/0.61 inference(rewrite,[status(thm)],[])).
% 0.55/0.61 tff(90,plain,
% 0.55/0.61 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W1!9)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))),
% 0.55/0.61 inference(quant_inst,[status(thm)],[])).
% 0.55/0.61 tff(91,plain,
% 0.55/0.61 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W1!9)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))),
% 0.55/0.61 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.55/0.61 tff(92,plain,
% 0.55/0.61 (![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[91, 88, 75])).
% 0.55/0.61 tff(93,plain,
% 0.55/0.61 (tptp_fun___ki_exists_in_world__i_(W1!9, D!10)),
% 0.55/0.61 inference(and_elim,[status(thm)],[53])).
% 0.55/0.61 tff(94,plain,
% 0.55/0.61 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))) | ((~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10))))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))) | (~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10))))))),
% 0.55/0.61 inference(rewrite,[status(thm)],[])).
% 0.55/0.61 tff(95,plain,
% 0.55/0.61 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))) | ((~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10))))))),
% 0.55/0.61 inference(quant_inst,[status(thm)],[])).
% 0.55/0.61 tff(96,plain,
% 0.55/0.61 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, B))))))) | (~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10)))))),
% 0.55/0.61 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.55/0.61 tff(97,plain,
% 0.55/0.61 (![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10)))))),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[96, 93, 92])).
% 0.55/0.61 tff(98,plain,
% 0.55/0.61 ((~![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(W1!9, W0!7)),
% 0.55/0.61 inference(quant_inst,[status(thm)],[])).
% 0.55/0.61 tff(99,plain,
% 0.55/0.61 (tptp_fun___ki_accessible_(W1!9, W0!7)),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[98, 8])).
% 0.55/0.61 tff(100,plain,
% 0.55/0.61 (((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10)))))) | ((~tptp_fun___ki_accessible_(W1!9, W0!7)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10)))))) <=> ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10)))))) | (~tptp_fun___ki_accessible_(W1!9, W0!7)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10)))))),
% 0.55/0.61 inference(rewrite,[status(thm)],[])).
% 0.55/0.61 tff(101,plain,
% 0.55/0.61 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10)))))) | ((~tptp_fun___ki_accessible_(W1!9, W0!7)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10)))))),
% 0.55/0.61 inference(quant_inst,[status(thm)],[])).
% 0.55/0.61 tff(102,plain,
% 0.55/0.61 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10)))))) | (~tptp_fun___ki_accessible_(W1!9, W0!7)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10))))),
% 0.55/0.61 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.55/0.61 tff(103,plain,
% 0.55/0.61 (![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10))))),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[102, 99, 97])).
% 0.55/0.61 tff(104,plain,
% 0.55/0.61 (tptp_fun___ki_exists_in_world__i_(W0!7, C!8)),
% 0.55/0.61 inference(and_elim,[status(thm)],[53])).
% 0.55/0.61 tff(105,plain,
% 0.55/0.61 (((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10))))) | ((~tptp_fun___ki_exists_in_world__i_(W0!7, C!8)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C!8, D!10))))) <=> ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10))))) | (~tptp_fun___ki_exists_in_world__i_(W0!7, C!8)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C!8, D!10))))),
% 0.55/0.61 inference(rewrite,[status(thm)],[])).
% 0.55/0.61 tff(106,plain,
% 0.55/0.61 ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10))))) | ((~tptp_fun___ki_exists_in_world__i_(W0!7, C!8)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C!8, D!10))))),
% 0.55/0.61 inference(quant_inst,[status(thm)],[])).
% 0.55/0.61 tff(107,plain,
% 0.55/0.61 ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C, D!10))))) | (~tptp_fun___ki_exists_in_world__i_(W0!7, C!8)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C!8, D!10)))),
% 0.55/0.61 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.55/0.61 tff(108,plain,
% 0.55/0.61 (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C!8, D!10)))),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[107, 104, 103])).
% 0.55/0.61 tff(109,plain,
% 0.55/0.61 (tptp_fun___ki_accessible_(W0!7, W1!9)),
% 0.55/0.61 inference(and_elim,[status(thm)],[53])).
% 0.55/0.61 tff(110,plain,
% 0.55/0.61 (((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C!8, D!10)))) | ((~tptp_fun___ki_accessible_(W0!7, W1!9)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, C!8, D!10)))) <=> ((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C!8, D!10)))) | (~tptp_fun___ki_accessible_(W0!7, W1!9)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, C!8, D!10)))),
% 0.55/0.61 inference(rewrite,[status(thm)],[])).
% 0.55/0.61 tff(111,plain,
% 0.55/0.61 ((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C!8, D!10)))) | ((~tptp_fun___ki_accessible_(W0!7, W1!9)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, C!8, D!10)))),
% 0.55/0.61 inference(quant_inst,[status(thm)],[])).
% 0.55/0.61 tff(112,plain,
% 0.55/0.61 ((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, C!8, D!10)))) | (~tptp_fun___ki_accessible_(W0!7, W1!9)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, C!8, D!10))),
% 0.55/0.61 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.55/0.61 tff(113,plain,
% 0.55/0.61 ((~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, C!8, D!10))),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[112, 109, 108])).
% 0.55/0.61 tff(114,plain,
% 0.55/0.61 (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8))),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[113, 73])).
% 0.55/0.61 tff(115,plain,
% 0.55/0.61 (((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8)) | (~intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8))),
% 0.55/0.61 inference(tautology,[status(thm)],[])).
% 0.55/0.61 tff(116,plain,
% 0.55/0.61 (~intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8)),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.55/0.61 tff(117,plain,
% 0.55/0.61 (((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8)) | tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))),
% 0.55/0.61 inference(tautology,[status(thm)],[])).
% 0.55/0.61 tff(118,plain,
% 0.55/0.61 (tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[117, 114])).
% 0.55/0.61 tff(119,assumption,(![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, D!10, C!8))), introduced(assumption)).
% 0.55/0.61 tff(120,plain,
% 0.55/0.61 (((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, D!10, C!8))) | ((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8))) <=> ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, D!10, C!8))) | (~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8))),
% 0.55/0.61 inference(rewrite,[status(thm)],[])).
% 0.55/0.61 tff(121,plain,
% 0.55/0.61 ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, D!10, C!8))) | ((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8))),
% 0.55/0.61 inference(quant_inst,[status(thm)],[])).
% 0.55/0.61 tff(122,plain,
% 0.55/0.61 ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, D!10, C!8))) | (~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_2(W1!9, C!8, D!10))) | intersect(tptp_fun_W2_2(W1!9, C!8, D!10), D!10, C!8)),
% 0.55/0.61 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.55/0.61 tff(123,plain,
% 0.55/0.61 ($false),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[122, 119, 118, 116])).
% 0.55/0.61 tff(124,plain,(~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, D!10, C!8))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.61 tff(125,plain,
% 0.55/0.61 (^[W: '$ki_world'] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))))),
% 0.55/0.61 inference(bind,[status(th)],[])).
% 0.55/0.61 tff(126,plain,
% 0.55/0.61 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))),
% 0.55/0.61 inference(quant_intro,[status(thm)],[125])).
% 0.55/0.61 tff(127,plain,
% 0.55/0.61 (^[W: '$ki_world'] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))))),
% 0.55/0.61 inference(bind,[status(th)],[])).
% 0.55/0.61 tff(128,plain,
% 0.55/0.61 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))),
% 0.55/0.61 inference(quant_intro,[status(thm)],[127])).
% 0.55/0.61 tff(129,plain,
% 0.55/0.61 (^[W: '$ki_world'] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))))),
% 0.55/0.61 inference(bind,[status(th)],[])).
% 0.55/0.61 tff(130,plain,
% 0.55/0.61 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))),
% 0.55/0.61 inference(quant_intro,[status(thm)],[129])).
% 0.55/0.61 tff(131,plain,
% 0.55/0.61 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))),
% 0.55/0.61 inference(transitivity,[status(thm)],[130, 128])).
% 0.55/0.61 tff(132,plain,
% 0.55/0.61 (^[W: '$ki_world'] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))))),
% 0.55/0.62 inference(bind,[status(th)],[])).
% 0.55/0.62 tff(133,plain,
% 0.55/0.62 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))),
% 0.55/0.62 inference(quant_intro,[status(thm)],[132])).
% 0.55/0.62 tff(134,plain,
% 0.55/0.62 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C)))))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))))),
% 0.55/0.62 inference(rewrite,[status(thm)],[])).
% 0.55/0.62 tff(135,plain,
% 0.55/0.62 (^[W: '$ki_world'] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[W0: '$ki_world'] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C))))) <=> (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))), ((tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)))))) <=> (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C)))))))), ((tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C)))))))))), (![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)))))) <=> ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))), ((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C))))))) <=> (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C)))))))))), rewrite((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C)))))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))), ((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C))))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))))), (![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C))))))) <=> ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C)))))))))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)))))))) <=> (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C)))))))))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C)))))))))))), (![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)))))))) <=> ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C))))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C)))))))))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C)))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))))))),
% 0.55/0.62 inference(bind,[status(th)],[])).
% 0.55/0.62 tff(136,plain,
% 0.55/0.62 (![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C))))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))))),
% 0.55/0.62 inference(quant_intro,[status(thm)],[135])).
% 0.55/0.62 tff(137,axiom,(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)) => ?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))))) & ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (?[D: $i] : ((tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, B))) & ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => member(W2, D, C))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => intersect(W2, B, C)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersect_defn')).
% 0.55/0.62 tff(138,plain,
% 0.55/0.62 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))))),
% 0.55/0.62 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.55/0.62 tff(139,plain,
% 0.55/0.62 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | (~?[D: $i] : (tptp_fun___ki_exists_in_world__i_(W1, D) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, D, C))))))))))),
% 0.55/0.62 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.55/0.62 tff(140,plain,(
% 0.55/0.62 ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B)) & ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C)))) & ![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))),
% 0.55/0.62 inference(skolemize,[status(sab)],[139])).
% 0.55/0.62 tff(141,plain,
% 0.55/0.62 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))),
% 0.55/0.62 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.55/0.62 tff(142,plain,
% 0.55/0.62 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | (~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))),
% 0.55/0.62 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.55/0.62 tff(143,plain,
% 0.55/0.62 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))),
% 0.55/0.62 inference(modus_ponens,[status(thm)],[142, 126])).
% 0.55/0.62 tff(144,plain,
% 0.55/0.62 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W1!9)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W1!9)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(145,plain,
% 0.60/0.63 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W1!9)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))),
% 0.60/0.63 inference(quant_inst,[status(thm)],[])).
% 0.60/0.63 tff(146,plain,
% 0.60/0.63 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W1!9)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.60/0.63 tff(147,plain,
% 0.60/0.63 (![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[146, 143, 75])).
% 0.60/0.63 tff(148,plain,
% 0.60/0.63 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)))))))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) | (~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)))))))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(149,plain,
% 0.60/0.63 (((~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C))))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)))))))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(150,plain,
% 0.60/0.63 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C))))))))))),
% 0.60/0.63 inference(monotonicity,[status(thm)],[149])).
% 0.60/0.63 tff(151,plain,
% 0.60/0.63 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) | (~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)))))))))),
% 0.60/0.63 inference(transitivity,[status(thm)],[150, 148])).
% 0.60/0.63 tff(152,plain,
% 0.60/0.63 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) | ((~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))),
% 0.60/0.63 inference(quant_inst,[status(thm)],[])).
% 0.60/0.63 tff(153,plain,
% 0.60/0.63 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, B))) | intersect(tptp_fun_W2_2(W1, C, B), B, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), B))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, B), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, B, C)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, B))) | member(tptp_fun_W2_3(D, W1, B), D, B))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))))))))))) | (~tptp_fun___ki_exists_in_world__i_(W1!9, D!10)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C))))))))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.60/0.63 tff(154,plain,
% 0.60/0.63 (![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C))))))))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[153, 93, 147])).
% 0.60/0.63 tff(155,plain,
% 0.60/0.63 (((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C))))))))) | ((~tptp_fun___ki_accessible_(W1!9, W0!7)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C))))))))) <=> ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C))))))))) | (~tptp_fun___ki_accessible_(W1!9, W0!7)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C))))))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(156,plain,
% 0.60/0.63 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C))))))))) | ((~tptp_fun___ki_accessible_(W1!9, W0!7)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C))))))))),
% 0.60/0.63 inference(quant_inst,[status(thm)],[])).
% 0.60/0.63 tff(157,plain,
% 0.60/0.63 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C))))))))) | (~tptp_fun___ki_accessible_(W1!9, W0!7)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)))))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.60/0.64 tff(158,plain,
% 0.60/0.64 (![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)))))))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[157, 99, 154])).
% 0.60/0.64 tff(159,plain,
% 0.60/0.64 (((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)))))))) | ((~tptp_fun___ki_exists_in_world__i_(W0!7, C!8)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C!8, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), C!8))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8)))))))) <=> ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)))))))) | (~tptp_fun___ki_exists_in_world__i_(W0!7, C!8)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C!8, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), C!8))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8)))))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(160,plain,
% 0.60/0.64 ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)))))))) | ((~tptp_fun___ki_exists_in_world__i_(W0!7, C!8)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C!8, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), C!8))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8)))))))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(161,plain,
% 0.60/0.64 ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0!7, C)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C, D!10))) | intersect(tptp_fun_W2_2(W1, C, D!10), D!10, C))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C, D!10), C))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C))) | member(tptp_fun_W2_4(D, W1, C), D, C)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C)))))))) | (~tptp_fun___ki_exists_in_world__i_(W0!7, C!8)) | (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C!8, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), C!8))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8))))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.60/0.64 tff(162,plain,
% 0.60/0.64 (~((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C!8, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), C!8))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8)))))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[161, 104, 158])).
% 0.60/0.64 tff(163,plain,
% 0.60/0.64 (((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_2(W1, C!8, D!10))) | intersect(tptp_fun_W2_2(W1, C!8, D!10), D!10, C!8))) | (~((~tptp_fun___ki_exists_in_world__i_(W1, tptp_fun_D_1(W1, C!8, D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), D!10))) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | member(W2, tptp_fun_D_1(W1, C!8, D!10), C!8))))))) | (~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8))))) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8)))),
% 0.60/0.64 inference(tautology,[status(thm)],[])).
% 0.60/0.64 tff(164,plain,
% 0.60/0.64 (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8)))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.60/0.64 tff(165,plain,
% 0.60/0.64 (((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8)))) | ((~tptp_fun___ki_accessible_(W0!7, W1!9)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, D)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(D, W1!9, D!10))) | member(tptp_fun_W2_3(D, W1!9, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(D, W1!9, C!8))) | member(tptp_fun_W2_4(D, W1!9, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, D!10, C!8)))) <=> ((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8)))) | (~tptp_fun___ki_accessible_(W0!7, W1!9)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, D)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(D, W1!9, D!10))) | member(tptp_fun_W2_3(D, W1!9, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(D, W1!9, C!8))) | member(tptp_fun_W2_4(D, W1!9, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, D!10, C!8)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(166,plain,
% 0.60/0.64 ((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8)))) | ((~tptp_fun___ki_accessible_(W0!7, W1!9)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, D)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(D, W1!9, D!10))) | member(tptp_fun_W2_3(D, W1!9, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(D, W1!9, C!8))) | member(tptp_fun_W2_4(D, W1!9, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, D!10, C!8)))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(167,plain,
% 0.61/0.64 ((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0!7, W1)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1, D)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_3(D, W1, D!10))) | member(tptp_fun_W2_3(D, W1, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_4(D, W1, C!8))) | member(tptp_fun_W2_4(D, W1, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | intersect(W2, D!10, C!8)))) | (~tptp_fun___ki_accessible_(W0!7, W1!9)) | ![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, D)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(D, W1!9, D!10))) | member(tptp_fun_W2_3(D, W1!9, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(D, W1!9, C!8))) | member(tptp_fun_W2_4(D, W1!9, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, D!10, C!8))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.61/0.64 tff(168,plain,
% 0.61/0.64 (![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, D)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(D, W1!9, D!10))) | member(tptp_fun_W2_3(D, W1!9, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(D, W1!9, C!8))) | member(tptp_fun_W2_4(D, W1!9, C!8), D, C!8)))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1!9, W2)) | intersect(W2, D!10, C!8))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[167, 109, 164])).
% 0.61/0.64 tff(169,plain,
% 0.61/0.64 (![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, D)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(D, W1!9, D!10))) | member(tptp_fun_W2_3(D, W1!9, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(D, W1!9, C!8))) | member(tptp_fun_W2_4(D, W1!9, C!8), D, C!8))))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[168, 124])).
% 0.61/0.64 tff(170,plain,
% 0.61/0.64 (^[W: '$ki_world', X: $i] : refl(tptp_fun___ki_exists_in_world__i_(W, X) <=> tptp_fun___ki_exists_in_world__i_(W, X))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(171,plain,
% 0.61/0.64 (![W: '$ki_world', X: $i] : tptp_fun___ki_exists_in_world__i_(W, X) <=> ![W: '$ki_world', X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.61/0.64 inference(quant_intro,[status(thm)],[170])).
% 0.61/0.64 tff(172,plain,
% 0.61/0.64 (![W: '$ki_world', X: $i] : tptp_fun___ki_exists_in_world__i_(W, X) <=> ![W: '$ki_world', X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(173,axiom,(![W: '$ki_world', X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''$ki_exists_in_world_$i_const'')).
% 0.61/0.64 tff(174,plain,
% 0.61/0.64 (![W: '$ki_world', X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.61/0.64 tff(175,plain,(
% 0.61/0.64 ![W: '$ki_world', X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.61/0.64 inference(skolemize,[status(sab)],[174])).
% 0.61/0.64 tff(176,plain,
% 0.61/0.64 (![W: '$ki_world', X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.61/0.64 tff(177,plain,
% 0.61/0.64 ((~![W: '$ki_world', X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)) | tptp_fun___ki_exists_in_world__i_(W1!9, B!6)),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(178,plain,
% 0.61/0.64 (tptp_fun___ki_exists_in_world__i_(W1!9, B!6)),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.61/0.64 tff(179,plain,
% 0.61/0.64 (((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, D)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(D, W1!9, D!10))) | member(tptp_fun_W2_3(D, W1!9, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(D, W1!9, C!8))) | member(tptp_fun_W2_4(D, W1!9, C!8), D, C!8))))) | ((~tptp_fun___ki_exists_in_world__i_(W1!9, B!6)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(B!6, W1!9, D!10))) | member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(B!6, W1!9, C!8))) | member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8))))) <=> ((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, D)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(D, W1!9, D!10))) | member(tptp_fun_W2_3(D, W1!9, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(D, W1!9, C!8))) | member(tptp_fun_W2_4(D, W1!9, C!8), D, C!8))))) | (~tptp_fun___ki_exists_in_world__i_(W1!9, B!6)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(B!6, W1!9, D!10))) | member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(B!6, W1!9, C!8))) | member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(180,plain,
% 0.61/0.64 ((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, D)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(D, W1!9, D!10))) | member(tptp_fun_W2_3(D, W1!9, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(D, W1!9, C!8))) | member(tptp_fun_W2_4(D, W1!9, C!8), D, C!8))))) | ((~tptp_fun___ki_exists_in_world__i_(W1!9, B!6)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(B!6, W1!9, D!10))) | member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(B!6, W1!9, C!8))) | member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8))))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(181,plain,
% 0.61/0.64 ((~![D: $i] : ((~tptp_fun___ki_exists_in_world__i_(W1!9, D)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(D, W1!9, D!10))) | member(tptp_fun_W2_3(D, W1!9, D!10), D, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(D, W1!9, C!8))) | member(tptp_fun_W2_4(D, W1!9, C!8), D, C!8))))) | (~tptp_fun___ki_exists_in_world__i_(W1!9, B!6)) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(B!6, W1!9, D!10))) | member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(B!6, W1!9, C!8))) | member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.61/0.64 tff(182,plain,
% 0.61/0.64 ((~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_3(B!6, W1!9, D!10))) | member(tptp_fun_W2_3(B!6, W1!9, D!10), B!6, D!10))) | (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(B!6, W1!9, C!8))) | member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8)))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[181, 178, 169])).
% 0.61/0.64 tff(183,plain,
% 0.61/0.64 (~((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(B!6, W1!9, C!8))) | member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[182, 61])).
% 0.61/0.64 tff(184,plain,
% 0.61/0.64 (((~tptp_fun___ki_accessible_(W1!9, tptp_fun_W2_4(B!6, W1!9, C!8))) | member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8)) | (~member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8))),
% 0.61/0.64 inference(tautology,[status(thm)],[])).
% 0.61/0.64 tff(185,plain,
% 0.61/0.64 (~member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8)),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.61/0.64 tff(186,plain,
% 0.61/0.64 (^[W3: '$ki_world'] : refl(((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) <=> ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(187,plain,
% 0.61/0.64 (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8)) <=> ![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[186])).
% 0.61/0.64 tff(188,plain,
% 0.61/0.64 (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8))),
% 0.61/0.64 inference(and_elim,[status(thm)],[53])).
% 0.61/0.64 tff(189,plain,
% 0.61/0.64 (![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.61/0.64 tff(190,plain,
% 0.61/0.64 (((~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8))) | ((~tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_4(B!6, W1!9, C!8))) | member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8))) <=> ((~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8))) | (~tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_4(B!6, W1!9, C!8))) | member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(191,plain,
% 0.61/0.65 ((~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8))) | ((~tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_4(B!6, W1!9, C!8))) | member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(192,plain,
% 0.61/0.65 ((~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2!11, W3)) | member(W3, B!6, C!8))) | (~tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_4(B!6, W1!9, C!8))) | member(tptp_fun_W2_4(B!6, W1!9, C!8), B!6, C!8)),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.61/0.65 tff(193,plain,
% 0.61/0.65 (~tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_4(B!6, W1!9, C!8))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[192, 189, 185])).
% 0.61/0.65 tff(194,plain,
% 0.61/0.65 ((~![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(W2!11, tptp_fun_W2_4(B!6, W1!9, C!8))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(195,plain,
% 0.61/0.65 ($false),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[194, 8, 193])).
% 0.61/0.65 % SZS output end Proof
%------------------------------------------------------------------------------