%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO896_7 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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
% 0.11/0.12 % Problem : SYO896_7 : TPTP v9.0.0. Released v8.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 13:54:51 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(q_type, type, (
% 0.12/0.37 q: |'$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(tptp_fun___ki_accessible__type, type, (
% 0.12/0.37 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.12/0.37 tff(tptp_fun___ki_local_world__type, type, (
% 0.12/0.37 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.12/0.37 tff(p_type, type, (
% 0.12/0.37 p: |'$ki_world'| > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : refl((q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 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) => q(W))) & ![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))))) <=> (~((~?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))) | (~(![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) & ![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))))))),
% 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) => q(W))) & ![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))))), 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) & p(W))) | (~(![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) & ![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) & ![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[7])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.12/0.37 tff(10,plain,(
% 0.12/0.37 ![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W)) <=> ?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (?[W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & p(W))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.37 tff(15,plain,(
% 0.12/0.37 tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0) & p(W!0)),
% 0.12/0.37 inference(skolemize,[status(sab)],[14])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (p(W!0)),
% 0.12/0.37 inference(and_elim,[status(thm)],[15])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)),
% 0.12/0.37 inference(and_elim,[status(thm)],[15])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (((~![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (q(W!0) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))) <=> ((~![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | q(W!0) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (q(W!0) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|] : (q(W) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | q(W!0) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (q(W!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[20, 17, 16, 11])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : refl(((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[7])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.37 tff(27,plain,(
% 0.12/0.37 ![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[26])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (((~![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | ((~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~q(W!0)))) <=> ((~![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~q(W!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (((~q(W!0)) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0))) <=> ((~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~q(W!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (((~![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | ((~q(W!0)) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))) <=> ((~![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | ((~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~q(W!0))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[30])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (((~![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | ((~q(W!0)) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))) <=> ((~![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~q(W!0)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[31, 29])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | ((~q(W!0)) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~![W: |'$ki_world'|] : ((~q(W)) | (~p(W)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (~p(W!0)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) | (~q(W!0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[34, 17, 16, 28, 21])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------