%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO895_9 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:42:26 AM UTC 2025
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO895_9 : TPTP v9.0.0. Released v8.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.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 13:49:55 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 tff(p_type, type, (
% 0.13/0.37 p: |'$ki_world'| > $o)).
% 0.13/0.37 tff(tptp_fun_W_1_type, type, (
% 0.13/0.37 tptp_fun_W_1: |'$ki_world'|)).
% 0.13/0.37 tff(tptp_fun___ki_accessible__type, type, (
% 0.13/0.37 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.13/0.37 tff(tptp_fun___ki_local_world__type, type, (
% 0.13/0.37 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.13/0.37 tff(q_type, type, (
% 0.13/0.37 q: |'$ki_world'| > $o)).
% 0.13/0.37 tff(1,plain,
% 0.13/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(2,plain,
% 0.13/0.37 ((~((![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => p(W)) & ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => q(W))) => ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) & q(W))))) <=> (~((~(![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) & ![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(3,axiom,(~((![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => p(W)) & ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => q(W))) => ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (p(W) & q(W))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.13/0.37 tff(4,plain,
% 0.13/0.37 (~((~(![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) & ![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))) | ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.37 tff(5,plain,
% 0.13/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))),
% 0.13/0.37 inference(or_elim,[status(thm)],[4])).
% 0.13/0.37 tff(6,plain,
% 0.13/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.37 tff(7,plain,
% 0.13/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.37 tff(8,plain,
% 0.13/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.13/0.37 tff(9,plain,(
% 0.13/0.37 ~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (p(W!1) & q(W!1)))),
% 0.13/0.37 inference(skolemize,[status(sab)],[8])).
% 0.13/0.37 tff(10,plain,
% 0.13/0.37 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)),
% 0.13/0.37 inference(or_elim,[status(thm)],[9])).
% 0.13/0.37 tff(11,plain,
% 0.13/0.37 (^[W: |'$ki_world'|] : refl((p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(12,plain,
% 0.13/0.37 (![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)))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.37 tff(13,plain,
% 0.13/0.37 (![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)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(14,plain,
% 0.13/0.37 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) & ![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.13/0.37 inference(or_elim,[status(thm)],[4])).
% 0.13/0.37 tff(15,plain,
% 0.13/0.37 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.13/0.37 inference(and_elim,[status(thm)],[14])).
% 0.13/0.37 tff(16,plain,
% 0.13/0.37 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.13/0.37 tff(17,plain,(
% 0.13/0.37 ![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.13/0.37 inference(skolemize,[status(sab)],[16])).
% 0.13/0.37 tff(18,plain,
% 0.13/0.37 (![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.13/0.37 tff(19,plain,
% 0.13/0.37 (((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (p(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))) <=> ((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | p(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(20,plain,
% 0.13/0.37 ((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (p(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(21,plain,
% 0.13/0.37 ((~![W: |'$ki_world'|] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | p(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.37 tff(22,plain,
% 0.13/0.37 (p(W!1)),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[21, 18, 10])).
% 0.13/0.37 tff(23,plain,
% 0.13/0.37 (^[W: |'$ki_world'|] : refl((q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(24,plain,
% 0.13/0.37 (![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.37 tff(25,plain,
% 0.13/0.37 (![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(26,plain,
% 0.13/0.37 (![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.13/0.37 inference(and_elim,[status(thm)],[14])).
% 0.13/0.37 tff(27,plain,
% 0.13/0.37 (![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.37 tff(28,plain,(
% 0.13/0.37 ![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.13/0.37 inference(skolemize,[status(sab)],[27])).
% 0.13/0.37 tff(29,plain,
% 0.13/0.37 (![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.13/0.37 tff(30,plain,
% 0.13/0.37 (((~![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (q(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))) <=> ((~![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | q(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(31,plain,
% 0.13/0.37 ((~![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (q(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(32,plain,
% 0.13/0.37 ((~![W: |'$ki_world'|] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | q(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.13/0.37 tff(33,plain,
% 0.13/0.37 (q(W!1)),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[32, 29, 10])).
% 0.13/0.37 tff(34,plain,
% 0.13/0.37 ((~(~((~p(W!1)) | (~q(W!1))))) <=> ((~p(W!1)) | (~q(W!1)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(35,plain,
% 0.13/0.37 ((p(W!1) & q(W!1)) <=> (~((~p(W!1)) | (~q(W!1))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(36,plain,
% 0.13/0.37 ((~(p(W!1) & q(W!1))) <=> (~(~((~p(W!1)) | (~q(W!1)))))),
% 0.13/0.37 inference(monotonicity,[status(thm)],[35])).
% 0.13/0.37 tff(37,plain,
% 0.13/0.37 ((~(p(W!1) & q(W!1))) <=> ((~p(W!1)) | (~q(W!1)))),
% 0.13/0.37 inference(transitivity,[status(thm)],[36, 34])).
% 0.13/0.37 tff(38,plain,
% 0.13/0.37 (~(p(W!1) & q(W!1))),
% 0.13/0.37 inference(or_elim,[status(thm)],[9])).
% 0.13/0.37 tff(39,plain,
% 0.13/0.37 ((~p(W!1)) | (~q(W!1))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[39, 33, 22])).
% 0.13/0.38 % SZS output end Proof
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------