TSTP Solution File: SYN373+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN373+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 23:55:01 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN373+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.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 : Mon Sep 5 02:58:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(big_q_type, type, (
% 0.12/0.38 big_q: $i > $o)).
% 0.12/0.38 tff(big_p_type, type, (
% 0.12/0.38 big_p: $i > $o)).
% 0.12/0.38 tff(tptp_fun_X_2_type, type, (
% 0.12/0.38 tptp_fun_X_2: $i)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: $i)).
% 0.12/0.38 tff(tptp_fun_X_1_type, type, (
% 0.12/0.38 tptp_fun_X_1: $i)).
% 0.12/0.38 tff(1,assumption,(![X: $i] : (~(big_q(X) | (~big_p(X))))), introduced(assumption)).
% 0.12/0.38 tff(2,assumption,(big_q(X!0) | (~big_p(X!0))), introduced(assumption)).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 ((~![X: $i] : (~(big_q(X) | (~big_p(X))))) | (~(big_q(X!0) | (~big_p(X!0))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[3, 1, 2])).
% 0.12/0.38 tff(5,plain,((~(big_q(X!0) | (~big_p(X!0)))) | (~![X: $i] : (~(big_q(X) | (~big_p(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~(big_q(X!0) | (~big_p(X!0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[5, 1])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 ((big_q(X!0) | (~big_p(X!0))) | (~big_q(X!0))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~big_q(X!0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.12/0.38 tff(9,assumption,(big_q(X!1) | (~big_p(X!1))), introduced(assumption)).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ((~![X: $i] : (~(big_q(X) | (~big_p(X))))) | (~(big_q(X!1) | (~big_p(X!1))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[10, 1, 9])).
% 0.12/0.38 tff(12,plain,((~(big_q(X!1) | (~big_p(X!1)))) | (~![X: $i] : (~(big_q(X) | (~big_p(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (~(big_q(X!1) | (~big_p(X!1)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((big_q(X!1) | (~big_p(X!1))) | big_p(X!1)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (big_p(X!1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 ((big_q(X!0) | (~big_p(X!0))) | big_p(X!0)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (big_p(X!0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[16, 6])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((((big_q(X!0) | (~big_p(X!0))) | ((~big_p(X!1)) | big_q(X!2))) & (![X: $i] : (~(big_q(X) | (~big_p(X)))) | (![X: $i] : big_p(X) & ![X: $i] : (~big_q(X))))) <=> ((big_q(X!0) | (~big_p(X!0)) | (~big_p(X!1)) | big_q(X!2)) & (![X: $i] : (~(big_q(X) | (~big_p(X)))) | (![X: $i] : big_p(X) & ![X: $i] : (~big_q(X)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X)) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> (~?[X: $i] : (big_q(X) | (~big_p(X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X))) <=> ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[20, 19])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X))) <=> ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((~(?[X: $i] : (big_q(X) | (~big_p(X))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X)))) <=> ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((?[X: $i] : (big_p(X) => big_q(X)) <=> (![X: $i] : big_p(X) => ?[X: $i] : big_q(X))) <=> (?[X: $i] : (big_q(X) | (~big_p(X))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~(?[X: $i] : (big_p(X) => big_q(X)) <=> (![X: $i] : big_p(X) => ?[X: $i] : big_q(X)))) <=> (~(?[X: $i] : (big_q(X) | (~big_p(X))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 ((~(?[X: $i] : (big_p(X) => big_q(X)) <=> (![X: $i] : big_p(X) => ?[X: $i] : big_q(X)))) <=> ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[25, 23])).
% 0.12/0.38 tff(27,axiom,(~(?[X: $i] : (big_p(X) => big_q(X)) <=> (![X: $i] : big_p(X) => ?[X: $i] : big_q(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2124')).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 21])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 21])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~?[X: $i] : (big_q(X) | (~big_p(X)))) <=> ((~![X: $i] : big_p(X)) | ?[X: $i] : big_q(X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 21])).
% 0.12/0.38 tff(35,plain,(
% 0.12/0.38 ((big_q(X!0) | (~big_p(X!0))) | ((~big_p(X!1)) | big_q(X!2))) & (![X: $i] : (~(big_q(X) | (~big_p(X)))) | (![X: $i] : big_p(X) & ![X: $i] : (~big_q(X))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((big_q(X!0) | (~big_p(X!0)) | (~big_p(X!1)) | big_q(X!2)) & (![X: $i] : (~(big_q(X) | (~big_p(X)))) | (![X: $i] : big_p(X) & ![X: $i] : (~big_q(X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 18])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (big_q(X!0) | (~big_p(X!0)) | (~big_p(X!1)) | big_q(X!2)),
% 0.12/0.38 inference(and_elim,[status(thm)],[36])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (big_q(X!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[37, 17, 15, 8])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 ((big_q(X!2) | (~big_p(X!2))) | (~big_q(X!2))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (big_q(X!2) | (~big_p(X!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ((~![X: $i] : (~(big_q(X) | (~big_p(X))))) | (~(big_q(X!2) | (~big_p(X!2))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[41, 1, 40])).
% 0.12/0.38 tff(43,plain,(~![X: $i] : (~(big_q(X) | (~big_p(X))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 ((![X: $i] : (~(big_q(X) | (~big_p(X)))) | (~((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X)))))) <=> (![X: $i] : (~(big_q(X) | (~big_p(X)))) | (~((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 ((![X: $i] : (~(big_q(X) | (~big_p(X)))) | (~((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X)))))) <=> (![X: $i] : (~(big_q(X) | (~big_p(X)))) | (~((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 ((![X: $i] : big_p(X) & ![X: $i] : (~big_q(X))) <=> (~((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ((![X: $i] : (~(big_q(X) | (~big_p(X)))) | (![X: $i] : big_p(X) & ![X: $i] : (~big_q(X)))) <=> (![X: $i] : (~(big_q(X) | (~big_p(X)))) | (~((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[46])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((![X: $i] : (~(big_q(X) | (~big_p(X)))) | (![X: $i] : big_p(X) & ![X: $i] : (~big_q(X)))) <=> (![X: $i] : (~(big_q(X) | (~big_p(X)))) | (~((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[47, 45])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (![X: $i] : (~(big_q(X) | (~big_p(X)))) | (![X: $i] : big_p(X) & ![X: $i] : (~big_q(X)))),
% 0.12/0.38 inference(and_elim,[status(thm)],[36])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (![X: $i] : (~(big_q(X) | (~big_p(X)))) | (~((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (![X: $i] : (~(big_q(X) | (~big_p(X)))) | (~((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[50, 44])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (~((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[51, 43])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X)))) | ![X: $i] : (~big_q(X))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (![X: $i] : (~big_q(X))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (((~![X: $i] : big_p(X)) | (~![X: $i] : (~big_q(X)))) | ![X: $i] : big_p(X)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (![X: $i] : big_p(X)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.12/0.38 tff(57,assumption,(~big_p(X!0)), introduced(assumption)).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 ((~![X: $i] : big_p(X)) | big_p(X!0)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[58, 57, 56])).
% 0.12/0.38 tff(60,plain,(big_p(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(61,assumption,(~big_p(X!1)), introduced(assumption)).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 ((~![X: $i] : big_p(X)) | big_p(X!1)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[62, 61, 56])).
% 0.12/0.38 tff(64,plain,(big_p(X!1)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(65,assumption,(big_q(X!0)), introduced(assumption)).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 ((~![X: $i] : (~big_q(X))) | (~big_q(X!0))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[66, 65, 54])).
% 0.12/0.38 tff(68,plain,(~big_q(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(69,plain,
% 0.12/0.38 (big_q(X!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[37, 68, 64, 60])).
% 0.12/0.38 tff(70,plain,
% 0.12/0.38 ((~![X: $i] : (~big_q(X))) | (~big_q(X!2))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[70, 69, 54])).
% 0.12/0.39 % SZS output end Proof
%------------------------------------------------------------------------------