%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL961_11 : TPTP v9.3.1. Released v8.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:01:14 PM UTC 2026
% Result : Theorem 0.08s 0.42s
% Output : Proof 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL961_11 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 17:03:46 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.42 % SZS status Theorem
% 0.08/0.42 % SZS output start Proof
% 0.08/0.42 tff(tptp_fun___ki_accessible__type, type, (
% 0.08/0.42 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.08/0.42 tff(tptp_fun_W0_3_type, type, (
% 0.08/0.42 tptp_fun_W0_3: |'$ki_world'|)).
% 0.08/0.42 tff(tptp_fun_W_0_type, type, (
% 0.08/0.42 tptp_fun_W_0: |'$ki_world'|)).
% 0.08/0.42 tff(p_type, type, (
% 0.08/0.42 p: |'$ki_world'| > $o)).
% 0.08/0.42 tff(tptp_fun_W_2_type, type, (
% 0.08/0.42 tptp_fun_W_2: |'$ki_world'|)).
% 0.08/0.42 tff(q_type, type, (
% 0.08/0.42 q: |'$ki_world'| > $o)).
% 0.08/0.42 tff(tptp_fun___ki_local_world__type, type, (
% 0.08/0.42 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.08/0.42 tff(tptp_fun_W0_1_type, type, (
% 0.08/0.42 tptp_fun_W0_1: |'$ki_world'|)).
% 0.08/0.42 tff(1,plain,
% 0.08/0.42 (((~(p(W0!3) | (~tptp_fun___ki_accessible_(W!2, W0!3)))) & tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!2, W0)))) <=> ((~(p(W0!3) | (~tptp_fun___ki_accessible_(W!2, W0!3)))) & tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!2, W0))))),
% 0.08/0.42 inference(rewrite,[status(thm)],[])).
% 0.08/0.42 tff(2,plain,
% 0.08/0.42 ((~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))) <=> (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.08/0.42 inference(rewrite,[status(thm)],[])).
% 0.08/0.42 tff(3,plain,
% 0.08/0.42 ((~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => q(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => p(W0))))) <=> (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.08/0.42 inference(rewrite,[status(thm)],[])).
% 0.08/0.42 tff(4,axiom,(~(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => p(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => q(W0)))) | ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => q(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => p(W0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.08/0.42 tff(5,plain,
% 0.08/0.42 (~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => q(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => p(W0))))),
% 0.08/0.42 inference(or_elim,[status(thm)],[4])).
% 0.08/0.42 tff(6,plain,
% 0.08/0.42 (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[5, 3])).
% 0.08/0.42 tff(7,plain,
% 0.08/0.42 (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.08/0.42 tff(8,plain,
% 0.08/0.42 (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.08/0.42 tff(9,plain,
% 0.08/0.42 (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.08/0.42 tff(10,plain,
% 0.08/0.42 ((~(p(W0!3) | (~tptp_fun___ki_accessible_(W!2, W0!3)))) & tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & ![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W!2, W0)))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.08/0.42 tff(11,plain,
% 0.08/0.42 (~(p(W0!3) | (~tptp_fun___ki_accessible_(W!2, W0!3)))),
% 0.08/0.42 inference(and_elim,[status(thm)],[10])).
% 0.08/0.42 tff(12,plain,
% 0.08/0.42 (~p(W0!3)),
% 0.08/0.42 inference(or_elim,[status(thm)],[11])).
% 0.08/0.42 tff(13,plain,
% 0.08/0.42 (^[W0: |'$ki_world'|] : refl((p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) <=> (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))))),
% 0.08/0.42 inference(bind,[status(th)],[])).
% 0.08/0.42 tff(14,plain,
% 0.08/0.42 (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) <=> ![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.08/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.08/0.42 tff(15,plain,
% 0.08/0.42 (((~(q(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) & ![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) & tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)) <=> ((~(q(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) & ![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) & tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0))),
% 0.08/0.42 inference(rewrite,[status(thm)],[])).
% 0.08/0.42 tff(16,plain,
% 0.08/0.42 ((~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) <=> (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.08/0.42 inference(rewrite,[status(thm)],[])).
% 0.08/0.42 tff(17,plain,
% 0.08/0.42 ((~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => p(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => q(W0))))) <=> (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.08/0.42 inference(rewrite,[status(thm)],[])).
% 0.08/0.42 tff(18,plain,
% 0.08/0.42 (~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => p(W0)) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(W, W0) => q(W0))))),
% 0.08/0.42 inference(or_elim,[status(thm)],[4])).
% 0.08/0.42 tff(19,plain,
% 0.08/0.42 (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.08/0.42 tff(20,plain,
% 0.08/0.42 (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.08/0.42 tff(21,plain,
% 0.08/0.42 (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.08/0.42 tff(22,plain,
% 0.08/0.42 (~![W: |'$ki_world'|] : (![W0: |'$ki_world'|] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0)))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.08/0.42 tff(23,plain,
% 0.08/0.42 ((~(q(W0!1) | (~tptp_fun___ki_accessible_(W!0, W0!1)))) & ![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) & tptp_fun___ki_accessible_(|'$ki_local_world'|, W!0)),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.08/0.42 tff(24,plain,
% 0.08/0.42 (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.08/0.42 inference(and_elim,[status(thm)],[23])).
% 0.08/0.43 tff(25,plain,
% 0.08/0.43 (![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.08/0.43 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.08/0.43 tff(26,plain,
% 0.08/0.43 (((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (p(W0!3) | (~tptp_fun___ki_accessible_(W!0, W0!3)))) <=> ((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | p(W0!3) | (~tptp_fun___ki_accessible_(W!0, W0!3)))),
% 0.08/0.43 inference(rewrite,[status(thm)],[])).
% 0.08/0.43 tff(27,plain,
% 0.08/0.43 ((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (p(W0!3) | (~tptp_fun___ki_accessible_(W!0, W0!3)))),
% 0.08/0.43 inference(quant_inst,[status(thm)],[])).
% 0.08/0.43 tff(28,plain,
% 0.08/0.43 ((~![W0: |'$ki_world'|] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | p(W0!3) | (~tptp_fun___ki_accessible_(W!0, W0!3))),
% 0.08/0.43 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.08/0.43 tff(29,plain,
% 0.08/0.43 (~tptp_fun___ki_accessible_(W!0, W0!3)),
% 0.08/0.43 inference(unit_resolution,[status(thm)],[28, 25, 12])).
% 0.08/0.43 tff(30,plain,
% 0.08/0.43 (^[W: |'$ki_world'|, V: |'$ki_world'|] : refl(tptp_fun___ki_accessible_(W, V) <=> tptp_fun___ki_accessible_(W, V))),
% 0.08/0.43 inference(bind,[status(th)],[])).
% 0.08/0.43 tff(31,plain,
% 0.08/0.43 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V) <=> ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.08/0.43 inference(quant_intro,[status(thm)],[30])).
% 0.08/0.43 tff(32,plain,
% 0.08/0.43 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V) <=> ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.08/0.43 inference(rewrite,[status(thm)],[])).
% 0.08/0.43 tff(33,axiom,(![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal')).
% 0.08/0.43 tff(34,plain,
% 0.08/0.43 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.08/0.43 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.08/0.43 tff(35,plain,(
% 0.08/0.43 ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.08/0.43 inference(skolemize,[status(sab)],[34])).
% 0.08/0.43 tff(36,plain,
% 0.08/0.43 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)),
% 0.08/0.43 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.08/0.43 tff(37,plain,
% 0.08/0.43 ((~![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(W!0, W0!3)),
% 0.08/0.43 inference(quant_inst,[status(thm)],[])).
% 0.08/0.43 tff(38,plain,
% 0.08/0.43 ($false),
% 0.08/0.43 inference(unit_resolution,[status(thm)],[37, 36, 29])).
% 0.08/0.43 % SZS output end Proof
% 0.08/0.43 % E exiting
%------------------------------------------------------------------------------