%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO903_10 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:42:28 AM UTC 2025
% Result : Theorem 0.18s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO903_10 : TPTP v9.0.0. Released v8.2.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n002.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 13:52:32 EDT 2025
% 0.18/0.32 % CPUTime :
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(tptp_fun___ki_accessible__type, type, (
% 0.18/0.39 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.18/0.39 tff(tptp_fun___ki_local_world__type, type, (
% 0.18/0.39 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.18/0.39 tff(v1_type, type, (
% 0.18/0.39 v1: |'$ki_world'| > $o)).
% 0.18/0.39 tff(v2_type, type, (
% 0.18/0.39 v2: |'$ki_world'| > $o)).
% 0.18/0.39 tff(v3_type, type, (
% 0.18/0.39 v3: |'$ki_world'| > $o)).
% 0.18/0.39 tff(v4_type, type, (
% 0.18/0.39 v4: |'$ki_world'| > $o)).
% 0.18/0.39 tff(1,assumption,(~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)), introduced(assumption)).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (^[W: |'$ki_world'|] : refl(tptp_fun___ki_accessible_(W, W) <=> tptp_fun___ki_accessible_(W, W))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.18/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(5,axiom,(![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_reflexive')).
% 0.18/0.39 tff(6,plain,
% 0.18/0.39 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.39 tff(7,plain,(
% 0.18/0.39 ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.18/0.39 inference(skolemize,[status(sab)],[6])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 ((~![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)) | tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.39 tff(11,plain,(tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(12,assumption,(~v3(|'$ki_local_world'|)), introduced(assumption)).
% 0.18/0.39 tff(13,assumption,(![W0: |'$ki_world'|] : (v3(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))), introduced(assumption)).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (((~![W0: |'$ki_world'|] : (v3(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | (v3(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)))) <=> ((~![W0: |'$ki_world'|] : (v3(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | v3(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 ((~![W0: |'$ki_world'|] : (v3(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | (v3(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 ((~![W0: |'$ki_world'|] : (v3(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | v3(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[16, 12, 11, 13])).
% 0.18/0.39 tff(18,plain,((~![W0: |'$ki_world'|] : (v3(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | v3(|'$ki_local_world'|)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (~![W0: |'$ki_world'|] : (v3(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[18, 12])).
% 0.18/0.39 tff(20,assumption,(![W0: |'$ki_world'|] : ((~v4(W0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))), introduced(assumption)).
% 0.18/0.39 tff(21,assumption,(~v4(|'$ki_local_world'|)), introduced(assumption)).
% 0.18/0.39 tff(22,assumption,(![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))), introduced(assumption)).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (((~![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | (v4(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)))) <=> ((~![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | v4(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 ((~![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | (v4(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 ((~![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | v4(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[25, 21, 11, 22])).
% 0.18/0.39 tff(27,plain,((~![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | v4(|'$ki_local_world'|)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (~![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[27, 21])).
% 0.18/0.39 tff(29,assumption,(~![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))), introduced(assumption)).
% 0.18/0.39 tff(30,assumption,(![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))), introduced(assumption)).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[33, 30, 11, 29])).
% 0.18/0.39 tff(35,plain,((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[35, 28])).
% 0.18/0.39 tff(37,assumption,(~v1(|'$ki_local_world'|)), introduced(assumption)).
% 0.18/0.39 tff(38,assumption,(![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))), introduced(assumption)).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (((~![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | (v1(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)))) <=> ((~![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | v1(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 ((~![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | (v1(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 ((~![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | v1(|'$ki_local_world'|) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[41, 37, 11, 38])).
% 0.18/0.39 tff(43,plain,((~![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))) | v1(|'$ki_local_world'|)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(44,plain,
% 0.18/0.39 (~![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(46,plain,
% 0.18/0.39 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, |'$ki_local_world'|)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W0)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[47, 44, 11])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 (((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))) <=> ((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))) <=> ((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 ((((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))) <=> ((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (^[W: |'$ki_world'|] : trans(monotonicity(quant_intro(proof_bind(^[W0: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(W, W0) => v4(W0)) <=> (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))), (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v4(W0)) <=> ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v4(W0))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0)))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v4(W0))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v4(W0))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (((v4(|'$ki_local_world'|) | (~v3(|'$ki_local_world'|))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))) <=> ((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (^[W: |'$ki_world'|] : trans(monotonicity(quant_intro(proof_bind(^[W0: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(W, W0) => v1(W0)) <=> (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))), (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v1(W0)) <=> ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v1(W0))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v1(W0))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v1(W0))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (((v4(|'$ki_local_world'|) | (~v3(|'$ki_local_world'|))) | ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v1(W0)))) <=> ((v4(|'$ki_local_world'|) | (~v3(|'$ki_local_world'|))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[56])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (((v4(|'$ki_local_world'|) | (~v3(|'$ki_local_world'|))) | ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v1(W0)))) <=> ((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[57, 54])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 ((((v4(|'$ki_local_world'|) | (~v3(|'$ki_local_world'|))) | ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v1(W0)))) | ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v4(W0)))) <=> (((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[58, 53])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 ((((v4(|'$ki_local_world'|) | (~v3(|'$ki_local_world'|))) | ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v1(W0)))) | ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v4(W0)))) <=> ((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[59, 51])).
% 0.18/0.39 tff(61,axiom,(((v4(|'$ki_local_world'|) | (~v3(|'$ki_local_world'|))) | ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v1(W0)))) | ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => v4(W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','persat31')).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 ((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 ((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[62, 50])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 ((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[63, 50])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 ((~v3(|'$ki_local_world'|)) | v4(|'$ki_local_world'|) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v1(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : (v4(W0) | (~tptp_fun___ki_accessible_(W, W0))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[64, 50])).
% 0.18/0.39 Proof display could not be completed: monotonicity rule is not handled
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------