%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO899_8 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:42:27 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO899_8 : TPTP v9.0.0. Released v8.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:50:57 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(tptp_fun___ki_accessible__type, type, (
% 0.12/0.37 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.12/0.37 tff(tptp_fun_W_0_type, type, (
% 0.12/0.37 tptp_fun_W_0: |'$ki_world'|)).
% 0.12/0.37 tff(q_type, type, (
% 0.12/0.37 q: |'$ki_world'| > $o)).
% 0.12/0.37 tff(tptp_fun___ki_local_world__type, type, (
% 0.12/0.37 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.12/0.37 tff(p_type, type, (
% 0.12/0.37 p: |'$ki_world'| > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (((~p(W!0)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) <=> ((~p(W!0)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & ((~p(W!0)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & ((~p(W!0)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ((~p(W)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))))) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ((~p(W)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 ((~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => q(W0)))) => (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => p(W)) => ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W))))) <=> (~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W)) | (~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ((~p(W)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,axiom,(~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => q(W0)))) => (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => p(W)) => ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~(?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W)) | (~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ((~p(W)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ((~p(W)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & ((~p(W)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & ((~p(W!0)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : trans(monotonicity(rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W)) <=> (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W))))), ((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W))) <=> (~(~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W))))))), rewrite((~(~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W)))), ((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W))),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : refl($oeq((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W))), (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(21,plain,(
% 0.12/0.37 ![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & q(W)))),
% 0.12/0.37 inference(nnf-neg,[status(sab)],[19, 20])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~q(W!0)))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~q(W!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W)))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~q(W!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~q(W)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~q(W!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (~q(W!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : refl((p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.37 tff(33,plain,(
% 0.12/0.37 ![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[32])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (p(W!0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))) <=> ((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | p(W!0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (p(W!0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | p(W!0) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (p(W!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[37, 34, 10])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (((~p(W!0)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) <=> ((~p(W!0)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((~p(W!0)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ((~p(W!0)) | ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (q(W!0) | (~tptp_fun___ki_accessible_(W!0, W!0)))) <=> ((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | q(W!0) | (~tptp_fun___ki_accessible_(W!0, W!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 ((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (q(W!0) | (~tptp_fun___ki_accessible_(W!0, W!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 ((~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | q(W!0) | (~tptp_fun___ki_accessible_(W!0, W!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 (~tptp_fun___ki_accessible_(W!0, W!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[45, 42, 27])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : refl(tptp_fun___ki_accessible_(W, W) <=> tptp_fun___ki_accessible_(W, W))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.12/0.37 inference(quant_intro,[status(thm)],[47])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W) <=> ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(50,axiom,(![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_reflexive')).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.12/0.37 tff(52,plain,(
% 0.12/0.37 ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.12/0.37 inference(skolemize,[status(sab)],[51])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, W)) | tptp_fun___ki_accessible_(W!0, W!0)),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[54, 53, 46])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------