TSTP Solution File: SYO898_9 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO898_9 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO898_9 : TPTP v8.2.0. Released v8.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.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 13:09:05 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(q_type, type, (
% 0.19/0.39 q: '$ki_world' > $o)).
% 0.19/0.39 tff(tptp_fun_V_0_type, type, (
% 0.19/0.39 tptp_fun_V_0: '$ki_world' > '$ki_world')).
% 0.19/0.39 tff(tptp_fun___ki_local_world__type, type, (
% 0.19/0.39 tptp_fun___ki_local_world_: '$ki_world')).
% 0.19/0.39 tff(p_type, type, (
% 0.19/0.39 p: '$ki_world' > $o)).
% 0.19/0.39 tff(tptp_fun___ki_accessible__type, type, (
% 0.19/0.39 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (![W: '$ki_world'] : ?[V: '$ki_world'] : tptp_fun___ki_accessible_(W, V) <=> ![W: '$ki_world'] : ?[V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(2,axiom,(![W: '$ki_world'] : ?[V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_serial')).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![W: '$ki_world'] : ?[V: '$ki_world'] : tptp_fun___ki_accessible_(W, V)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.19/0.39 tff(4,plain,(
% 0.19/0.39 ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, tptp_fun_V_0(W))),
% 0.19/0.39 inference(skolemize,[status(sab)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 ((~![W: '$ki_world'] : tptp_fun___ki_accessible_(W, tptp_fun_V_0(W))) | tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (^[W: '$ki_world'] : refl((p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))) <=> (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 ((~(![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) => p(W))))) <=> (~((~![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(11,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) => p(W))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (~((~![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | ?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.19/0.39 inference(or_elim,[status(thm)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.19/0.39 tff(15,plain,(
% 0.19/0.39 ![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[14])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (((~![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (p(tptp_fun_V_0(|'$ki_local_world'|)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))))) <=> ((~![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | p(tptp_fun_V_0(|'$ki_local_world'|)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | (p(tptp_fun_V_0(|'$ki_local_world'|)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((~![W: '$ki_world'] : (p(W) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)))) | p(tptp_fun_V_0(|'$ki_local_world'|)) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (p(tptp_fun_V_0(|'$ki_local_world'|))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[19, 16, 6])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|)))) | (~p(tptp_fun_V_0(|'$ki_local_world'|)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (^[W: '$ki_world'] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (^[W: '$ki_world'] : trans(monotonicity(rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W)))) <=> (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))))), ((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))) <=> (~(~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))))))), rewrite((~(~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))), ((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 ((~?[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)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))),
% 0.19/0.39 inference(or_elim,[status(thm)],[12])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (~?[W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 27])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (^[W: '$ki_world'] : refl($oeq((~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W))))), (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(36,plain,(
% 0.19/0.39 ![W: '$ki_world'] : (~(tptp_fun___ki_accessible_(|'$ki_local_world'|, W) & (p(W) | (~q(W)))))),
% 0.19/0.39 inference(nnf-neg,[status(sab)],[34, 35])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[37, 24])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))) | (~(p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|))))))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))) | (~(p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))) | (~(p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~(p(W) | (~q(W)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_V_0(|'$ki_local_world'|))) | (~(p(tptp_fun_V_0(|'$ki_local_world'|)) | (~q(tptp_fun_V_0(|'$ki_local_world'|)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[41, 38, 6, 22])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------