TSTP Solution File: SYO895_9 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO895_9 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 15:46:13 EDT 2023
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO895_9 : TPTP v8.2.0. Released v8.2.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 22 13:19:46 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(p_type, type, (
% 0.20/0.40 p: '$ki_world' > $o)).
% 0.20/0.40 tff(tptp_fun_W_1_type, type, (
% 0.20/0.40 tptp_fun_W_1: '$ki_world')).
% 0.20/0.40 tff(tptp_fun___ki_accessible__type, type, (
% 0.20/0.40 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.20/0.40 tff(tptp_fun___ki_local_world__type, type, (
% 0.20/0.40 tptp_fun___ki_local_world_: '$ki_world')).
% 0.20/0.40 tff(q_type, type, (
% 0.20/0.40 q: '$ki_world' > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))) <=> (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 ((~((![W: '$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_(|'$ki_local_world'|, W)) | (p(W) & q(W)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(3,axiom,(~((![W: '$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_(|'$ki_local_world'|, W) => (p(W) & q(W))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (~((~(![W: '$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_(|'$ki_local_world'|, W)) | (p(W) & q(W))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))),
% 0.20/0.40 inference(or_elim,[status(thm)],[4])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (p(W) & q(W)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.20/0.40 tff(12,plain,(
% 0.20/0.40 ~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)) | (p(W!1) & q(W!1)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[11])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)),
% 0.20/0.40 inference(or_elim,[status(thm)],[12])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (^[W: '$ki_world'] : refl((p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(or_elim,[status(thm)],[4])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.20/0.40 inference(and_elim,[status(thm)],[17])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 16])).
% 0.20/0.40 tff(20,plain,(
% 0.20/0.40 ![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[19])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((~![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (p(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ((~![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | p(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (p(W!1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[24, 21, 13])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (^[W: '$ki_world'] : refl((q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![W: '$ki_world'] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ![W: '$ki_world'] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![W: '$ki_world'] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> ![W: '$ki_world'] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (![W: '$ki_world'] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.20/0.40 inference(and_elim,[status(thm)],[17])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![W: '$ki_world'] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.40 tff(31,plain,(
% 0.20/0.40 ![W: '$ki_world'] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![W: '$ki_world'] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (((~![W: '$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_(|'$ki_local_world'|, W!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~![W: '$ki_world'] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (q(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((~![W: '$ki_world'] : (q(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | q(W!1) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (q(W!1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[35, 32, 13])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ((~(~((~p(W!1)) | (~q(W!1))))) <=> ((~p(W!1)) | (~q(W!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ((p(W!1) & q(W!1)) <=> (~((~p(W!1)) | (~q(W!1))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ((~(p(W!1) & q(W!1))) <=> (~(~((~p(W!1)) | (~q(W!1)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ((~(p(W!1) & q(W!1))) <=> ((~p(W!1)) | (~q(W!1)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[39, 37])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (~(p(W!1) & q(W!1))),
% 0.20/0.40 inference(or_elim,[status(thm)],[12])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 ((~p(W!1)) | (~q(W!1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[42, 36, 25])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------