%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NLP265_17 : 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 05:18:38 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
% 0.07/0.12 % Problem : NLP265_17 : TPTP v9.0.0. Released v8.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.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 : Thu Jun 19 23:57:32 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_: ( |'$ki_index'| * |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.12/0.37 tff(tptp_fun_W0_5_type, type, (
% 0.12/0.37 tptp_fun_W0_5: |'$ki_world'|)).
% 0.12/0.37 tff(tptp_fun___ki_local_world__type, type, (
% 0.12/0.37 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.12/0.37 tff(tptp_fun___idx_b_alice___type, type, (
% 0.12/0.37 tptp_fun___idx_b_alice__: |'$ki_index'|)).
% 0.12/0.37 tff(bigcity_type, type, (
% 0.12/0.37 bigcity: ( |'$ki_world'| * $i ) > $o)).
% 0.12/0.37 tff(portland_type, type, (
% 0.12/0.37 portland: $i)).
% 0.12/0.37 tff(tptp_fun_W_4_type, type, (
% 0.12/0.37 tptp_fun_W_4: |'$ki_world'|)).
% 0.12/0.37 tff(tptp_fun___idx_b_bob___type, type, (
% 0.12/0.37 tptp_fun___idx_b_bob__: |'$ki_index'|)).
% 0.12/0.37 tff(tptp_fun___idx_i_alice___type, type, (
% 0.12/0.37 tptp_fun___idx_i_alice__: |'$ki_index'|)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0)) | bigcity(W0, portland)))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0)) | bigcity(W0, portland))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0) => bigcity(W0, portland)))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0)) | bigcity(W0, portland))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,axiom,(~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W) => ![W0: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0) => bigcity(W0, portland)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0)) | bigcity(W0, portland)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0)) | bigcity(W0, portland)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0)) | bigcity(W0, portland)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W)) | ![W0: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0)) | bigcity(W0, portland)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W!4, W0!5)) | bigcity(W0!5, portland))),
% 0.12/0.37 inference(and_elim,[status(thm)],[7])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~bigcity(W0!5, portland)),
% 0.12/0.37 inference(or_elim,[status(thm)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland)) <=> ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland)) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland)) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[W: |'$ki_world'|] : rewrite((tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W) => bigcity(W, portland)) <=> ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W) => bigcity(W, portland)) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37 tff(15,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W) => bigcity(W, portland))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.37 tff(18,plain,(
% 0.12/0.37 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.12/0.37 inference(skolemize,[status(sab)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))) | ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W0!5)) | bigcity(W0!5, portland))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))) | (~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W0!5)) | bigcity(W0!5, portland))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))) | ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W0!5)) | bigcity(W0!5, portland))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))) | (~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W0!5)) | bigcity(W0!5, portland)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W0!5)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (^[W: |'$ki_world'|, V: |'$ki_world'|] : refl(tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V) <=> tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V) <=> ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V)),
% 0.12/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V) <=> ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(27,axiom,(![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''mrel_universal_#idx(b_alice)'')).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.37 tff(29,plain,(
% 0.12/0.37 ![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V)),
% 0.12/0.37 inference(skolemize,[status(sab)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 ((~![W: |'$ki_world'|, V: |'$ki_world'|] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V)) | tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W0!5)),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------