TSTP Solution File: NLP265_17 by Z3---4.8.9.0
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- 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
%------------------------------------------------------------------------------