TSTP Solution File: SYN047+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN047+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Thu Sep 29 23:53:19 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN047+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 01:15:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35 Usage: tptp [options] [-file:]file
% 0.19/0.35 -h, -? prints this message.
% 0.19/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.35 -m, -model generate model.
% 0.19/0.35 -p, -proof generate proof.
% 0.19/0.35 -c, -core generate unsat core of named formulas.
% 0.19/0.35 -st, -statistics display statistics.
% 0.19/0.35 -t:timeout set timeout (in second).
% 0.19/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35 -<param>:<value> configuration parameter and value.
% 0.19/0.35 -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(k!0_type, type, (
% 0.19/0.39 k!0: $o)).
% 0.19/0.39 tff(s_type, type, (
% 0.19/0.39 s: $o)).
% 0.19/0.39 tff(q_type, type, (
% 0.19/0.39 q: $o)).
% 0.19/0.39 tff(r_type, type, (
% 0.19/0.39 r: $o)).
% 0.19/0.39 tff(p_type, type, (
% 0.19/0.39 p: $o)).
% 0.19/0.39 tff(1,assumption,(~s), introduced(assumption)).
% 0.19/0.39 tff(2,assumption,(~q), introduced(assumption)).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 ((r | (~q)) | q),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (r | (~q)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.19/0.39 tff(5,assumption,(~(s | (~r) | k!0)), introduced(assumption)).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (((~(q | s | k!0)) | (~(s | (~r) | k!0))) | (s | (~r) | k!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 ((~(q | s | k!0)) | (~(s | (~r) | k!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.19/0.39 tff(8,assumption,(r | (~q)), introduced(assumption)).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 ((s | (~r) | k!0) | (~k!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (~k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[9, 5])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~(s | (~(r | (~q))) | k!0)) | s | (~(r | (~q))) | k!0),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (~(s | (~(r | (~q))) | k!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[11, 10, 1, 8])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (((s | (~(r | (~q))) | k!0) <=> ((~(q | s | k!0)) | (~(s | (~r) | k!0)))) <=> ((s | (~(r | (~q))) | k!0) <=> ((~(q | s | k!0)) | (~(s | (~r) | k!0))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (((s | k!0 | (~(r | (~q)))) <=> ((~(q | s | k!0)) | (~(s | k!0 | (~r))))) <=> ((s | (~(r | (~q))) | k!0) <=> ((~(q | s | k!0)) | (~(s | (~r) | k!0))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (((s | (~p) | (~(r | (~q)))) <=> ((~(q | s | (~p))) | (~(s | (~p) | (~r))))) <=> ((s | k!0 | (~(r | (~q)))) <=> ((~(q | s | k!0)) | (~(s | k!0 | (~r)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (((~(s | (~p) | (~(r | (~q))))) <=> (~((~(q | s | (~p))) | (~(s | (~p) | (~r)))))) <=> ((s | (~p) | (~(r | (~q)))) <=> ((~(q | s | (~p))) | (~(s | (~p) | (~r)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (((q | s | (~p)) & (s | (~p) | (~r))) <=> (~((~(q | s | (~p))) | (~(s | (~p) | (~r)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~(s | (~(p & (r | (~q)))))) <=> (~(s | (~p) | (~(r | (~q)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (((~(s | (~(p & (r | (~q)))))) <=> ((q | s | (~p)) & (s | (~p) | (~r)))) <=> ((~(s | (~p) | (~(r | (~q))))) <=> (~((~(q | s | (~p))) | (~(s | (~p) | (~r))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (((~(s | (~(p & (r | (~q)))))) <=> ((q | s | (~p)) & (s | (~p) | (~r)))) <=> ((s | (~p) | (~(r | (~q)))) <=> ((~(q | s | (~p))) | (~(s | (~p) | (~r)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[19, 16])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r))))) <=> ((~(s | (~(p & (r | (~q)))))) <=> ((q | s | (~p)) & (s | (~p) | (~r))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((((p & (q => r)) => s) <=> ((((~p) | q) | s) & (((~p) | (~r)) | s))) <=> ((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ((~(((p & (q => r)) => s) <=> ((((~p) | q) | s) & (((~p) | (~r)) | s)))) <=> (~((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 ((~(((p & (q => r)) => s) <=> ((((~p) | q) | s) & (((~p) | (~r)) | s)))) <=> ((~(s | (~(p & (r | (~q)))))) <=> ((q | s | (~p)) & (s | (~p) | (~r))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[23, 21])).
% 0.19/0.39 tff(25,axiom,(~(((p & (q => r)) => s) <=> ((((~p) | q) | s) & (((~p) | (~r)) | s)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel17')).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 ((~(s | (~(p & (r | (~q)))))) <=> ((q | s | (~p)) & (s | (~p) | (~r)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 ((s | (~p) | (~(r | (~q)))) <=> ((~(q | s | (~p))) | (~(s | (~p) | (~r))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 ((s | k!0 | (~(r | (~q)))) <=> ((~(q | s | k!0)) | (~(s | k!0 | (~r))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 15])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 ((s | (~(r | (~q))) | k!0) <=> ((~(q | s | k!0)) | (~(s | (~r) | k!0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 14])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((s | (~(r | (~q))) | k!0) <=> ((~(q | s | k!0)) | (~(s | (~r) | k!0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 13])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((s | (~(r | (~q))) | k!0) <=> ((~(q | s | k!0)) | (~(s | (~r) | k!0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 13])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 ((s | (~(r | (~q))) | k!0) <=> ((~(q | s | k!0)) | (~(s | (~r) | k!0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 13])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 ((s | (~(r | (~q))) | k!0) | (~((~(q | s | k!0)) | (~(s | (~r) | k!0)))) | (~((s | (~(r | (~q))) | k!0) <=> ((~(q | s | k!0)) | (~(s | (~r) | k!0)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((s | (~(r | (~q))) | k!0) | (~((~(q | s | k!0)) | (~(s | (~r) | k!0))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 12, 7])).
% 0.19/0.39 tff(36,plain,((s | (~r) | k!0) | s | (~(r | (~q)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (s | (~r) | k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[36, 4, 1])).
% 0.19/0.39 tff(38,assumption,(~((~(q | s | k!0)) | (~(s | (~r) | k!0)))), introduced(assumption)).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~(s | (~(r | (~q))) | k!0)) | ((~(q | s | k!0)) | (~(s | (~r) | k!0))) | (~((s | (~(r | (~q))) | k!0) <=> ((~(q | s | k!0)) | (~(s | (~r) | k!0)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ((~(s | (~(r | (~q))) | k!0)) | ((~(q | s | k!0)) | (~(s | (~r) | k!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 32])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~(s | (~(r | (~q))) | k!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 38])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~(q | s | k!0)) | (~(s | (~r) | k!0))) | (q | s | k!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (q | s | k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 38])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~(q | s | k!0)) | q | s | k!0),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[44, 43, 1, 2])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((s | (~(r | (~q))) | k!0) | (~k!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[46, 45, 41])).
% 0.19/0.39 tff(48,plain,(((~(q | s | k!0)) | (~(s | (~r) | k!0))) | s | q), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((~(q | s | k!0)) | (~(s | (~r) | k!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[48, 2, 1])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~((~(q | s | k!0)) | (~(s | (~r) | k!0)))) | (~(q | s | k!0)) | (~(s | (~r) | k!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (~(q | s | k!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[50, 49, 37])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (s | (~(r | (~q))) | k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 49])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[11, 52, 1, 4])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((q | s | k!0) | (~k!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[54, 53, 51])).
% 0.19/0.39 tff(56,plain,(q | s), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (q),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 1])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ((q | s | k!0) | (~q)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (q | s | k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (s | (~r) | k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[6, 38])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (~k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[46, 41])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 ((s | (~(r | (~q))) | k!0) | (r | (~q))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (r | (~q)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[62, 41])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ((~(r | (~q))) | r | (~q)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (r),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[64, 63, 57])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 ((~(s | (~r) | k!0)) | s | (~r) | k!0),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[66, 65, 61, 1, 60])).
% 0.19/0.39 tff(68,plain,(((~(q | s | k!0)) | (~(s | (~r) | k!0))) | s), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 ((~(q | s | k!0)) | (~(s | (~r) | k!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[68, 1])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (~(s | (~r) | k!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[50, 69, 59])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 ((s | (~r) | k!0) | r),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (r),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (~(r | (~q))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[36, 70, 1])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 ((r | (~q)) | (~r)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[74, 73, 72])).
% 0.19/0.39 tff(76,plain,(s), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 ((q | s | k!0) | (~s)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (q | s | k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 ((s | (~r) | k!0) | (~s)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (s | (~r) | k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[79, 76])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 ((s | (~(r | (~q))) | k!0) | (~s)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (s | (~(r | (~q))) | k!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[81, 76])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 ((~(q | s | k!0)) | (~(s | (~r) | k!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 82])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[50, 83, 80, 78])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------