%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO898_9 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.21s 0.37s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO898_9 : TPTP v9.0.0. Released v8.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 13:51:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.37 % SZS status Theorem
% 0.21/0.37 % SZS output start Proof
% 0.21/0.37 tff(q_type, type, (
% 0.21/0.37 q: |'$ki_world'| > $o)).
% 0.21/0.37 tff(tptp_fun_V_0_type, type, (
% 0.21/0.37 tptp_fun_V_0: |'$ki_world'| > |'$ki_world'|)).
% 0.21/0.37 tff(tptp_fun___ki_local_world__type, type, (
% 0.21/0.37 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.21/0.37 tff(p_type, type, (
% 0.21/0.37 p: |'$ki_world'| > $o)).
% 0.21/0.37 tff(tptp_fun___ki_accessible__type, type, (
% 0.21/0.37 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.21/0.37 tff(1,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ?[V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V) <=> ![W: |'$ki_world'|] : ?[V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(2,axiom,(![W: |'$ki_world'|] : ?[V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_serial')).
% 0.21/0.37 tff(3,plain,
% 0.21/0.37 (![W: |'$ki_world'|] : ?[V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.37 tff(4,plain,(
% 0.21/0.37 ![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, tptp_fun_V_0(W))),
% 0.21/0.38 inference(skolemize,[status(sab)],[3])).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 ((~![W: |'$ki_world'|] : tptp_fun___ki_accessible_(W, tptp_fun_V_0(W))) | tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (^[W: |'$ki_world'|] : refl((p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(8,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 ((~(![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) => p(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) | (~q(W))))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(11,axiom,(~(![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) => p(W))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 (~((~![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) | (~q(W)))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.21/0.38 inference(or_elim,[status(thm)],[12])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.38 tff(15,plain,(
% 0.21/0.38 ![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[14])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (p(tptp_fun_V_0(|'$ki_local_world'|)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))))) <=> ((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | p(tptp_fun_V_0(|'$ki_local_world'|)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 ((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (p(tptp_fun_V_0(|'$ki_local_world'|)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 ((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | p(tptp_fun_V_0(|'$ki_local_world'|)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 (p(tptp_fun_V_0(|'$ki_local_world'|))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[19, 16, 6])).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 ((p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|)))) | (~p(tptp_fun_V_0(|'$ki_local_world'|)))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 (p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|)))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 (^[W: |'$ki_world'|] : trans(monotonicity(rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W)))) <=> (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))))), ((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))) <=> (~(~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))))))), rewrite((~(~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))), ((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.38 tff(27,plain,
% 0.21/0.38 ((~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))) <=> (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W)))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(28,plain,
% 0.21/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))),
% 0.21/0.38 inference(or_elim,[status(thm)],[12])).
% 0.21/0.38 tff(29,plain,
% 0.21/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.38 tff(30,plain,
% 0.21/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.21/0.38 tff(31,plain,
% 0.21/0.38 (~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.21/0.38 tff(32,plain,
% 0.21/0.38 (^[W: |'$ki_world'|] : refl($oeq((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))), (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W)))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(33,plain,(
% 0.21/0.38 ![W: |'$ki_world'|] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W)))))),
% 0.21/0.38 inference(nnf-neg,[status(sab)],[31, 32])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.21/0.38 tff(35,plain,
% 0.21/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.21/0.38 tff(36,plain,
% 0.21/0.38 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))) | (~(p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|))))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))) | (~(p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|))))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))) | (~(p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|))))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(38,plain,
% 0.21/0.38 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))) | (~(p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|)))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.38 tff(39,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[38, 35, 6, 22])).
% 0.21/0.38 % SZS output end Proof
% 0.21/0.38 % E exiting
%------------------------------------------------------------------------------