%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN045+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:38:01 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN045+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:27:02 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(r_type, type, (
% 0.18/0.37 r: $o)).
% 0.18/0.37 tff(q_type, type, (
% 0.18/0.37 q: $o)).
% 0.18/0.37 tff(p_type, type, (
% 0.18/0.37 p: $o)).
% 0.18/0.37 tff(1,assumption,(~p), introduced(assumption)).
% 0.18/0.37 tff(2,assumption,(~(p | q)), introduced(assumption)).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 ((p | q) | (~q)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (~q),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (((~q) | (~r)) | q),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 ((~q) | (~r)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (((~(p | q)) | (~(p | r))) | (p | q)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 ((~(p | q)) | (~(p | r))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[7, 2])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 ((~(~(((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r))))))) <=> (((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r)))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 ((~(((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r)))))) <=> (~(((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (((p | (~((~q) | (~r)))) <=> (~((~(p | q)) | (~(p | r))))) <=> (~(((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (((p | q) & (p | r)) <=> (~((~(p | q)) | (~(p | r))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 ((p | (q & r)) <=> (p | (~((~q) | (~r))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (((p | (q & r)) <=> ((p | q) & (p | r))) <=> ((p | (~((~q) | (~r)))) <=> (~((~(p | q)) | (~(p | r)))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[13, 12])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (((p | (q & r)) <=> ((p | q) & (p | r))) <=> (~(((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[14, 11])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (((p | (q & r)) <=> ((p | q) & (p | r))) <=> (~(((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[15, 10])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 ((~((p | (q & r)) <=> ((p | q) & (p | r)))) <=> (~(~(((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r)))))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[16])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 ((~((p | (q & r)) <=> ((p | q) & (p | r)))) <=> (((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r)))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[17, 9])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 ((~((p | (q & r)) <=> ((p | q) & (p | r)))) <=> (~((p | (q & r)) <=> ((p | q) & (p | r))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(20,axiom,(~((p | (q & r)) <=> ((p | q) & (p | r)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel13')).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (~((p | (q & r)) <=> ((p | q) & (p | r)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 ((~((~(p | q)) | (~(p | r)))) | (p | (~((~q) | (~r)))) | (~(((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r))))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 ((~((~(p | q)) | (~(p | r)))) | (p | (~((~q) | (~r))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (p | (~((~q) | (~r)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[24, 8])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 ((~(p | (~((~q) | (~r))))) | p | (~((~q) | (~r)))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[26, 25, 6, 1])).
% 0.18/0.37 tff(28,plain,((p | q) | p), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (p | q),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[28, 1])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 ((~(p | q)) | p | q),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (q),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[30, 29, 1])).
% 0.18/0.37 tff(32,assumption,(~(p | (~((~q) | (~r))))), introduced(assumption)).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 ((p | (~((~q) | (~r)))) | ((~q) | (~r))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 ((~q) | (~r)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 ((~((~q) | (~r))) | (~q) | (~r)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (~r),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[35, 34, 31])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (~((~(p | q)) | (~(p | r)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[24, 32])).
% 0.18/0.37 tff(38,plain,
% 0.18/0.37 (((~(p | q)) | (~(p | r))) | (p | r)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 (p | r),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.18/0.37 tff(40,plain,
% 0.18/0.37 ((~(p | r)) | p | r),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[40, 39, 36, 1])).
% 0.18/0.37 tff(42,plain,((p | (~((~q) | (~r)))) | p), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(43,plain,
% 0.18/0.37 (p | (~((~q) | (~r)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[42, 1])).
% 0.18/0.37 tff(44,plain,
% 0.18/0.37 (((~(p | q)) | (~(p | r))) | (~(p | (~((~q) | (~r))))) | (~(((~(p | q)) | (~(p | r))) <=> (p | (~((~q) | (~r))))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 (((~(p | q)) | (~(p | r))) | (~(p | (~((~q) | (~r)))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[44, 22])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 ((~(p | q)) | (~(p | r))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[45, 43])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 ((~((~(p | q)) | (~(p | r)))) | (~(p | q)) | (~(p | r))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 (~(p | r)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[47, 46, 29])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 (~((~q) | (~r))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[26, 43, 1])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 (((~q) | (~r)) | r),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 (r),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.18/0.37 tff(52,plain,
% 0.18/0.37 ((p | r) | (~r)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(53,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[52, 51, 48])).
% 0.18/0.37 tff(54,plain,(p), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(55,plain,
% 0.18/0.37 ((p | (~((~q) | (~r)))) | (~p)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(56,plain,
% 0.18/0.37 (p | (~((~q) | (~r)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 ((p | q) | (~p)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 (p | q),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.18/0.37 tff(59,plain,
% 0.18/0.37 ((p | r) | (~p)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 (p | r),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[59, 54])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 (~((~(p | q)) | (~(p | r)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[47, 60, 58])).
% 0.18/0.37 tff(62,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[45, 61, 56])).
% 0.18/0.37 % SZS output end Proof
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------