TSTP Solution File: NLP265_17 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NLP265_17 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n024.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 : Mon May 22 15:40:04 EDT 2023

% Result   : Theorem 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NLP265_17 : TPTP v8.2.0. Released v8.2.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n024.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 : Mon May 22 12:07:50 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.39  % SZS status Theorem
% 0.20/0.39  % SZS output start Proof
% 0.20/0.39  tff(tptp_fun___ki_accessible__type, type, (
% 0.20/0.39     tptp_fun___ki_accessible_: ( '$ki_index' * '$ki_world' * '$ki_world' ) > $o)).
% 0.20/0.39  tff(tptp_fun_W0_5_type, type, (
% 0.20/0.39     tptp_fun_W0_5: '$ki_world')).
% 0.20/0.39  tff(tptp_fun___ki_local_world__type, type, (
% 0.20/0.39     tptp_fun___ki_local_world_: '$ki_world')).
% 0.20/0.39  tff(tptp_fun___idx_b_alice___type, type, (
% 0.20/0.39     tptp_fun___idx_b_alice__: '$ki_index')).
% 0.20/0.39  tff(bigcity_type, type, (
% 0.20/0.39     bigcity: ( '$ki_world' * $i ) > $o)).
% 0.20/0.39  tff(portland_type, type, (
% 0.20/0.39     portland: $i)).
% 0.20/0.39  tff(tptp_fun_W_4_type, type, (
% 0.20/0.39     tptp_fun_W_4: '$ki_world')).
% 0.20/0.39  tff(tptp_fun___idx_b_bob___type, type, (
% 0.20/0.39     tptp_fun___idx_b_bob__: '$ki_index')).
% 0.20/0.39  tff(tptp_fun___idx_i_alice___type, type, (
% 0.20/0.39     tptp_fun___idx_i_alice__: '$ki_index')).
% 0.20/0.39  tff(1,plain,
% 0.20/0.39      (((~(~tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W!4))) & (~((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W!4, W0!5)) | bigcity(W0!5, portland)))) <=> (tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W!4) & (~((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W!4, W0!5)) | bigcity(W0!5, portland))))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(2,plain,
% 0.20/0.39      ((~![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))))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(3,plain,
% 0.20/0.39      ((~![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))))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(4,axiom,(~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0) => bigcity(W0, portland)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.20/0.39  tff(5,plain,
% 0.20/0.39      (~![W: '$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)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.39  tff(6,plain,
% 0.20/0.39      (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0)) | bigcity(W0, portland)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.39  tff(7,plain,
% 0.20/0.39      (~![W: '$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)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.39  tff(8,plain,
% 0.20/0.39      (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0)) | bigcity(W0, portland)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.39  tff(9,plain,
% 0.20/0.39      (~![W: '$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)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[8, 2])).
% 0.20/0.39  tff(10,plain,
% 0.20/0.39      (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W, W0)) | bigcity(W0, portland)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.39  tff(11,plain,
% 0.20/0.39      (~![W: '$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)))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.40  tff(12,plain,
% 0.20/0.40      (tptp_fun___ki_accessible_(|'#idx(i_alice)'|, |'$ki_local_world'|, W!4) & (~((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W!4, W0!5)) | bigcity(W0!5, portland)))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[11, 1])).
% 0.20/0.40  tff(13,plain,
% 0.20/0.40      (~((~tptp_fun___ki_accessible_(|'#idx(b_bob)'|, W!4, W0!5)) | bigcity(W0!5, portland))),
% 0.20/0.40      inference(and_elim,[status(thm)],[12])).
% 0.20/0.40  tff(14,plain,
% 0.20/0.40      (~bigcity(W0!5, portland)),
% 0.20/0.40      inference(or_elim,[status(thm)],[13])).
% 0.20/0.40  tff(15,plain,
% 0.20/0.40      (^[W: '$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)))),
% 0.20/0.40      inference(bind,[status(th)],[])).
% 0.20/0.40  tff(16,plain,
% 0.20/0.40      (![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))),
% 0.20/0.40      inference(quant_intro,[status(thm)],[15])).
% 0.20/0.40  tff(17,plain,
% 0.20/0.40      (![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))),
% 0.20/0.40      inference(rewrite,[status(thm)],[])).
% 0.20/0.40  tff(18,plain,
% 0.20/0.40      (^[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)'|, |'$ki_local_world'|, W)) | bigcity(W, portland)))),
% 0.20/0.40      inference(bind,[status(th)],[])).
% 0.20/0.40  tff(19,plain,
% 0.20/0.40      (![W: '$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)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.20/0.40      inference(quant_intro,[status(thm)],[18])).
% 0.20/0.40  tff(20,axiom,(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W) => bigcity(W, portland))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.20/0.40  tff(21,plain,
% 0.20/0.40      (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.40  tff(22,plain,
% 0.20/0.40      (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.40  tff(23,plain,(
% 0.20/0.40      ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.20/0.40      inference(skolemize,[status(sab)],[22])).
% 0.20/0.40  tff(24,plain,
% 0.20/0.40      (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.40  tff(25,plain,
% 0.20/0.40      (((~![W: '$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)'|, |'$ki_local_world'|, W0!5)) | bigcity(W0!5, portland))),
% 0.20/0.40      inference(rewrite,[status(thm)],[])).
% 0.20/0.40  tff(26,plain,
% 0.20/0.40      ((~![W: '$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))),
% 0.20/0.40      inference(quant_inst,[status(thm)],[])).
% 0.20/0.40  tff(27,plain,
% 0.20/0.40      ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W)) | bigcity(W, portland))) | (~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W0!5)) | bigcity(W0!5, portland)),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.40  tff(28,plain,
% 0.20/0.40      (~tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W0!5)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.20/0.40  tff(29,plain,
% 0.20/0.40      (^[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))),
% 0.20/0.40      inference(bind,[status(th)],[])).
% 0.20/0.40  tff(30,plain,
% 0.20/0.40      (![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)),
% 0.20/0.40      inference(quant_intro,[status(thm)],[29])).
% 0.20/0.40  tff(31,plain,
% 0.20/0.40      (![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)),
% 0.20/0.40      inference(rewrite,[status(thm)],[])).
% 0.20/0.40  tff(32,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)'')).
% 0.20/0.40  tff(33,plain,
% 0.20/0.40      (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V)),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.40  tff(34,plain,(
% 0.20/0.40      ![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V)),
% 0.20/0.40      inference(skolemize,[status(sab)],[33])).
% 0.20/0.40  tff(35,plain,
% 0.20/0.40      (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V)),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.40  tff(36,plain,
% 0.20/0.40      ((~![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(|'#idx(b_alice)'|, W, V)) | tptp_fun___ki_accessible_(|'#idx(b_alice)'|, |'$ki_local_world'|, W0!5)),
% 0.20/0.40      inference(quant_inst,[status(thm)],[])).
% 0.20/0.40  tff(37,plain,
% 0.20/0.40      ($false),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[36, 35, 28])).
% 0.20/0.40  % SZS output end Proof
%------------------------------------------------------------------------------