%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN047+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 : Sat Jun 21 05:38:02 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN047+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:30:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(r_type, type, (
% 0.11/0.37 r: $o)).
% 0.11/0.37 tff(k!0_type, type, (
% 0.11/0.37 k!0: $o)).
% 0.11/0.37 tff(s_type, type, (
% 0.11/0.37 s: $o)).
% 0.11/0.37 tff(q_type, type, (
% 0.11/0.37 q: $o)).
% 0.11/0.37 tff(p_type, type, (
% 0.11/0.37 p: $o)).
% 0.11/0.37 tff(1,assumption,(~((~(q | s | k!0)) | (~(s | (~r) | k!0)))), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 ((((~(q | s | k!0)) | (~(s | (~r) | k!0))) <=> (s | (k!0 | (~(r | (~q)))))) <=> (((~(q | s | k!0)) | (~(s | (~r) | k!0))) <=> (s | (~(r | (~q))) | k!0))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 ((~(s | (~r) | k!0)) <=> (~(s | (~r) | k!0))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 ((~(q | s | k!0)) <=> (~(q | s | k!0))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (((~(q | s | k!0)) | (~(s | (~r) | k!0))) <=> ((~(q | s | k!0)) | (~(s | (~r) | k!0)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[4, 3])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 ((((~(q | s | k!0)) | (~(s | (~r) | k!0))) <=> (s | (k!0 | (~(r | (~q)))))) <=> (((~(q | s | k!0)) | (~(s | (~r) | k!0))) <=> (s | (k!0 | (~(r | (~q))))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[5])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 ((((~(q | s | k!0)) | (~(s | k!0 | (~r)))) <=> (s | (k!0 | (~(r | (~q)))))) <=> (((~(q | s | k!0)) | (~(s | (~r) | k!0))) <=> (s | (k!0 | (~(r | (~q))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 ((((~(q | s | (~p))) | (~(s | (~p) | (~r)))) <=> (s | ((~p) | (~(r | (~q)))))) <=> (((~(q | s | k!0)) | (~(s | k!0 | (~r)))) <=> (s | (k!0 | (~(r | (~q))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 ((~(~(((~(q | s | (~p))) | (~(s | (~p) | (~r)))) <=> (s | ((~p) | (~(r | (~q)))))))) <=> (((~(q | s | (~p))) | (~(s | (~p) | (~r)))) <=> (s | ((~p) | (~(r | (~q))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 ((~(((~(q | s | (~p))) | (~(s | (~p) | (~r)))) <=> (s | ((~p) | (~(r | (~q))))))) <=> (~(((~(q | s | (~p))) | (~(s | (~p) | (~r)))) <=> (s | ((~p) | (~(r | (~q)))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (((s | ((~p) | (~(r | (~q))))) <=> (~((~(q | s | (~p))) | (~(s | (~p) | (~r)))))) <=> (~(((~(q | s | (~p))) | (~(s | (~p) | (~r)))) <=> (s | ((~p) | (~(r | (~q)))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (((q | s | (~p)) & (s | (~p) | (~r))) <=> (~((~(q | s | (~p))) | (~(s | (~p) | (~r)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 ((s | (~(p & (r | (~q))))) <=> (s | ((~p) | (~(r | (~q)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r)))) <=> ((s | ((~p) | (~(r | (~q))))) <=> (~((~(q | s | (~p))) | (~(s | (~p) | (~r))))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[13, 12])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r)))) <=> (~(((~(q | s | (~p))) | (~(s | (~p) | (~r)))) <=> (s | ((~p) | (~(r | (~q)))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[14, 11])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r)))) <=> (~(((~(q | s | (~p))) | (~(s | (~p) | (~r)))) <=> (s | ((~p) | (~(r | (~q)))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[15, 10])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 ((~((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r))))) <=> (~(~(((~(q | s | (~p))) | (~(s | (~p) | (~r)))) <=> (s | ((~p) | (~(r | (~q))))))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[16])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 ((~((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r))))) <=> (((~(q | s | (~p))) | (~(s | (~p) | (~r)))) <=> (s | ((~p) | (~(r | (~q))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[17, 9])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 ((~((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r))))) <=> (~((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((((p & (q => r)) => s) <=> ((((~p) | q) | s) & (((~p) | (~r)) | s))) <=> ((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 ((~(((p & (q => r)) => s) <=> ((((~p) | q) | s) & (((~p) | (~r)) | s)))) <=> (~((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r)))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 ((~(((p & (q => r)) => s) <=> ((((~p) | q) | s) & (((~p) | (~r)) | s)))) <=> (~((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r)))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[21, 19])).
% 0.19/0.37 tff(23,axiom,(~(((p & (q => r)) => s) <=> ((((~p) | q) | s) & (((~p) | (~r)) | s)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel17')).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (~((s | (~(p & (r | (~q))))) <=> ((q | s | (~p)) & (s | (~p) | (~r))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (((~(q | s | (~p))) | (~(s | (~p) | (~r)))) <=> (s | ((~p) | (~(r | (~q)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (((~(q | s | k!0)) | (~(s | k!0 | (~r)))) <=> (s | (k!0 | (~(r | (~q)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[25, 8])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (((~(q | s | k!0)) | (~(s | (~r) | k!0))) <=> (s | (k!0 | (~(r | (~q)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 7])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (((~(q | s | k!0)) | (~(s | (~r) | k!0))) <=> (s | (k!0 | (~(r | (~q)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[27, 6])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (((~(q | s | k!0)) | (~(s | (~r) | k!0))) <=> (s | (~(r | (~q))) | k!0)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[28, 2])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (((~(q | s | k!0)) | (~(s | (~r) | k!0))) | (~(s | (~(r | (~q))) | k!0)) | (~(((~(q | s | k!0)) | (~(s | (~r) | k!0))) <=> (s | (~(r | (~q))) | k!0)))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (((~(q | s | k!0)) | (~(s | (~r) | k!0))) | (~(s | (~(r | (~q))) | k!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (~(s | (~(r | (~q))) | k!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[31, 1])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 ((s | (~(r | (~q))) | k!0) | (r | (~q))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (r | (~q)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (((~(q | s | k!0)) | (~(s | (~r) | k!0))) | (s | (~r) | k!0)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (s | (~r) | k!0),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[35, 1])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 ((s | (~(r | (~q))) | k!0) | (~s)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (~s),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[37, 32])).
% 0.19/0.37 tff(39,assumption,(k!0), introduced(assumption)).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 ((s | (~(r | (~q))) | k!0) | (~k!0)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (s | (~(r | (~q))) | k!0),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 ((q | s | k!0) | (~k!0)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (q | s | k!0),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 ((s | (~r) | k!0) | (~k!0)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (s | (~r) | k!0),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[44, 39])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 ((~((~(q | s | k!0)) | (~(s | (~r) | k!0)))) | (~(q | s | k!0)) | (~(s | (~r) | k!0))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 (~((~(q | s | k!0)) | (~(s | (~r) | k!0)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[46, 45, 43])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[31, 47, 41])).
% 0.19/0.37 tff(49,plain,(~k!0), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 ((~(s | (~r) | k!0)) | s | (~r) | k!0),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 ((~(s | (~r) | k!0)) | s | (~r)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (~r),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[51, 38, 36])).
% 0.19/0.37 tff(53,assumption,(~q), introduced(assumption)).
% 0.19/0.37 tff(54,assumption,(~k!0), introduced(assumption)).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 (((~(q | s | k!0)) | (~(s | (~r) | k!0))) | (q | s | k!0)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 (q | s | k!0),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[55, 1])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 ((~(q | s | k!0)) | q | s | k!0),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(58,plain,
% 0.19/0.37 (s),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[57, 56, 53, 54])).
% 0.19/0.37 tff(59,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[37, 58, 32])).
% 0.19/0.37 tff(60,plain,(((~(q | s | k!0)) | (~(s | (~r) | k!0))) | q | k!0), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(61,plain,
% 0.19/0.37 ((~(q | s | k!0)) | (~(s | (~r) | k!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[60, 54, 53])).
% 0.19/0.37 tff(62,plain,
% 0.19/0.37 ((r | (~q)) | q),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(63,plain,
% 0.19/0.37 (r | (~q)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[62, 53])).
% 0.19/0.37 tff(64,plain,
% 0.19/0.37 ((~((~(q | s | k!0)) | (~(s | (~r) | k!0)))) | (s | (~(r | (~q))) | k!0) | (~(((~(q | s | k!0)) | (~(s | (~r) | k!0))) <=> (s | (~(r | (~q))) | k!0)))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(65,plain,
% 0.19/0.37 ((~((~(q | s | k!0)) | (~(s | (~r) | k!0)))) | (s | (~(r | (~q))) | k!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[64, 29])).
% 0.19/0.37 tff(66,plain,
% 0.19/0.37 (s | (~(r | (~q))) | k!0),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[65, 61])).
% 0.19/0.37 tff(67,plain,
% 0.19/0.37 ((~(s | (~(r | (~q))) | k!0)) | s | (~(r | (~q))) | k!0),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(68,plain,
% 0.19/0.37 (s),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[67, 66, 63, 54])).
% 0.19/0.37 tff(69,plain,
% 0.19/0.37 ((q | s | k!0) | (~s)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(70,plain,
% 0.19/0.37 (q | s | k!0),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.37 tff(71,plain,
% 0.19/0.37 ((s | (~r) | k!0) | (~s)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(72,plain,
% 0.19/0.37 (s | (~r) | k!0),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.19/0.37 tff(73,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[46, 72, 70, 61])).
% 0.19/0.37 tff(74,plain,(k!0 | q), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(75,plain,
% 0.19/0.37 (q),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[74, 49])).
% 0.19/0.37 tff(76,plain,
% 0.19/0.37 ((~(r | (~q))) | r | (~q)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(77,plain,
% 0.19/0.37 ((~(r | (~q))) | r),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.37 tff(78,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[77, 52, 34])).
% 0.19/0.37 tff(79,plain,((~(q | s | k!0)) | (~(s | (~r) | k!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(80,plain,
% 0.19/0.37 ((q | s | k!0) | (~q)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(81,plain,
% 0.19/0.37 (q | s | k!0),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.19/0.37 tff(82,plain,
% 0.19/0.37 ((~((~(q | s | k!0)) | (~(s | (~r) | k!0)))) | (~(s | (~r) | k!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[46, 81])).
% 0.19/0.37 tff(83,plain,
% 0.19/0.37 (~(s | (~r) | k!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.19/0.37 tff(84,plain,
% 0.19/0.37 ((s | (~r) | k!0) | r),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(85,plain,
% 0.19/0.37 (r),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.37 tff(86,plain,
% 0.19/0.37 (s | (~(r | (~q))) | k!0),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[65, 79])).
% 0.19/0.37 tff(87,plain,
% 0.19/0.37 (~s),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[71, 83])).
% 0.19/0.37 tff(88,plain,
% 0.19/0.37 ((~(s | (~(r | (~q))) | k!0)) | s | (~(r | (~q)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[67, 49])).
% 0.19/0.37 tff(89,plain,
% 0.19/0.37 (~(r | (~q))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[88, 87, 86])).
% 0.19/0.37 tff(90,plain,
% 0.19/0.37 ((r | (~q)) | (~r)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(91,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[90, 89, 85])).
% 0.19/0.37 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------