TSTP Solution File: SYO900_11 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO900_11 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 15:46:14 EDT 2023
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO900_11 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.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 13:31:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(tptp_fun___ki_accessible__type, type, (
% 0.13/0.38 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.13/0.38 tff(tptp_fun_W0_3_type, type, (
% 0.13/0.38 tptp_fun_W0_3: '$ki_world')).
% 0.13/0.38 tff(tptp_fun_W_0_type, type, (
% 0.13/0.38 tptp_fun_W_0: '$ki_world')).
% 0.13/0.38 tff(p_type, type, (
% 0.13/0.38 p: '$ki_world' > $o)).
% 0.13/0.38 tff(tptp_fun_W_2_type, type, (
% 0.13/0.38 tptp_fun_W_2: '$ki_world')).
% 0.13/0.38 tff(q_type, type, (
% 0.13/0.38 q: '$ki_world' > $o)).
% 0.13/0.38 tff(tptp_fun___ki_local_world__type, type, (
% 0.13/0.38 tptp_fun___ki_local_world_: '$ki_world')).
% 0.13/0.38 tff(tptp_fun_W0_1_type, type, (
% 0.13/0.38 tptp_fun_W0_1: '$ki_world')).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 (((~(p(W0!3) | (~tptp_fun___ki_accessible_(W!2, W0!3)))) & (~(~tptp_fun___ki_accessible_(|'$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: '$ki_world'] : (q(W0) | (~tptp_fun___ki_accessible_(W!2, W0))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((~![W: '$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: '$ki_world'] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 ((~![W: '$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: '$ki_world'] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(4,axiom,(~(![W: '$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: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => p(W0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => q(W0)) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => p(W0))))),
% 0.13/0.38 inference(or_elim,[status(thm)],[4])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (~![W: '$ki_world'] : (![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: '$ki_world'] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[5, 3])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (~![W: '$ki_world'] : (![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: '$ki_world'] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (~![W: '$ki_world'] : (![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: '$ki_world'] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (~![W: '$ki_world'] : (![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: '$ki_world'] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (~![W: '$ki_world'] : (![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: '$ki_world'] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (~![W: '$ki_world'] : (![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: '$ki_world'] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~![W: '$ki_world'] : (![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W, W0))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~![W0: '$ki_world'] : (q(W0) | (~tptp_fun___ki_accessible_(W, W0)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ((~(p(W0!3) | (~tptp_fun___ki_accessible_(W!2, W0!3)))) & tptp_fun___ki_accessible_(|'$ki_local_world'|, W!2) & ![W0: '$ki_world'] : (q(W0) | (~tptp_fun___ki_accessible_(W!2, W0)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (~(p(W0!3) | (~tptp_fun___ki_accessible_(W!2, W0!3)))),
% 0.13/0.39 inference(and_elim,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (~p(W0!3)),
% 0.13/0.39 inference(or_elim,[status(thm)],[14])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (^[W0: '$ki_world'] : refl((p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) <=> (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0))) <=> ![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (((~(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))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 ((~![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))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((~![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))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (~![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))))),
% 0.13/0.39 inference(or_elim,[status(thm)],[4])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (~![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (~![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (~![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (~![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (~![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~(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)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.13/0.39 inference(and_elim,[status(thm)],[29])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 17])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (((~![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 ((~![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | (p(W0!3) | (~tptp_fun___ki_accessible_(W!0, W0!3)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 ((~![W0: '$ki_world'] : (p(W0) | (~tptp_fun___ki_accessible_(W!0, W0)))) | p(W0!3) | (~tptp_fun___ki_accessible_(W!0, W0!3))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (~tptp_fun___ki_accessible_(W!0, W0!3)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[34, 31, 15])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (^[W: '$ki_world', V: '$ki_world'] : refl(tptp_fun___ki_accessible_(W, V) <=> tptp_fun___ki_accessible_(W, V))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V) <=> ![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.13/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V) <=> ![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(39,axiom,(![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal')).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.13/0.39 tff(41,plain,(
% 0.13/0.39 ![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.13/0.39 inference(skolemize,[status(sab)],[40])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ((~![W: '$ki_world', V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)) | tptp_fun___ki_accessible_(W!0, W0!3)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[43, 42, 35])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------