TSTP Solution File: SYN922+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN922+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 : Fri Sep 30 00:01:16 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN922+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.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 Sep 5 09:30:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(p_type, type, (
% 0.13/0.39 p: $i > $o)).
% 0.13/0.39 tff(tptp_fun_X_1_type, type, (
% 0.13/0.39 tptp_fun_X_1: $i)).
% 0.13/0.39 tff(q_type, type, (
% 0.13/0.39 q: $i > $o)).
% 0.13/0.39 tff(tptp_fun_X_0_type, type, (
% 0.13/0.39 tptp_fun_X_0: $i)).
% 0.13/0.39 tff(tptp_fun_X_2_type, type, (
% 0.13/0.39 tptp_fun_X_2: $i)).
% 0.13/0.39 tff(1,assumption,(~q(X!0)), introduced(assumption)).
% 0.13/0.39 tff(2,assumption,(![X: $i] : (~((~p(X)) | (~q(X))))), introduced(assumption)).
% 0.13/0.39 tff(3,assumption,((~p(X!1)) | (~q(X!1))), introduced(assumption)).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 ((~![X: $i] : (~((~p(X)) | (~q(X))))) | (~((~p(X!1)) | (~q(X!1))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[4, 2, 3])).
% 0.13/0.39 tff(6,plain,((~((~p(X!1)) | (~q(X!1)))) | (~![X: $i] : (~((~p(X)) | (~q(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~((~p(X!1)) | (~q(X!1)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (((~p(X!1)) | (~q(X!1))) | p(X!1)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (p(X!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.39 tff(10,assumption,((~p(X!0)) | (~q(X!0))), introduced(assumption)).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ((~![X: $i] : (~((~p(X)) | (~q(X))))) | (~((~p(X!0)) | (~q(X!0))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[11, 2, 10])).
% 0.13/0.39 tff(13,plain,((~((~p(X!0)) | (~q(X!0)))) | (~![X: $i] : (~((~p(X)) | (~q(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (~((~p(X!0)) | (~q(X!0)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[13, 2])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (((~p(X!0)) | (~q(X!0))) | p(X!0)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (p(X!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (((~p(X!0)) | (~q(X!0))) | q(X!0)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (q(X!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.13/0.39 tff(19,assumption,(~q(X!2)), introduced(assumption)).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (((~p(X!2)) | (~q(X!2))) | q(X!2)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((~p(X!2)) | (~q(X!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.39 tff(22,assumption,(![X: $i] : q(X)), introduced(assumption)).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 ((~![X: $i] : q(X)) | q(X!2)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[23, 22, 19])).
% 0.13/0.39 tff(25,plain,((~![X: $i] : q(X)) | q(X!2)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (~![X: $i] : q(X)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (((~![X: $i] : p(X)) | (~![X: $i] : q(X))) | ![X: $i] : q(X)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 ((~![X: $i] : p(X)) | (~![X: $i] : q(X))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))) <=> ((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) <=> ((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (((![X: $i] : (p(X) & q(X)) | (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(p(X!0) & q(X!0))) | ((~p(X!1)) | (~q(X!2))))) <=> (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!0) & q(X!0))) | (~p(X!1)) | (~q(X!2))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 ((![X: $i] : p(X) & ![X: $i] : q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 ((~![X: $i] : (p(X) & q(X))) <=> (~![X: $i] : (p(X) & q(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) <=> ((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[33, 32])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) <=> ((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))) <=> ((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 ((![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) <=> (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 ((~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))) <=> (~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[37])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 ((~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))) <=> ((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[38, 36])).
% 0.13/0.39 tff(40,axiom,(~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 ((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 ((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[43, 34])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 ((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 ((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[45, 34])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 ((~![X: $i] : (p(X) & q(X))) <=> (![X: $i] : p(X) & ![X: $i] : q(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[46, 34])).
% 0.13/0.39 tff(48,plain,(
% 0.13/0.39 (![X: $i] : (p(X) & q(X)) | (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(p(X!0) & q(X!0))) | ((~p(X!1)) | (~q(X!2))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[47])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!0) & q(X!0))) | (~p(X!1)) | (~q(X!2)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[48, 31])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 ((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))),
% 0.13/0.39 inference(and_elim,[status(thm)],[49])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 ((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[50, 30])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 ((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[51, 29])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 (![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[52, 28])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 ((~![X: $i] : (~((~p(X)) | (~q(X))))) | (~((~p(X!2)) | (~q(X!2))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[54, 53, 21])).
% 0.13/0.39 tff(56,plain,(q(X!2)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 ((((~p(X!0)) | (~q(X!0))) | (~p(X!1)) | (~q(X!2))) <=> ((~p(X!1)) | (~q(X!2)) | (~p(X!0)) | (~q(X!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 ((~(~((~p(X!0)) | (~q(X!0))))) <=> ((~p(X!0)) | (~q(X!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 ((p(X!0) & q(X!0)) <=> (~((~p(X!0)) | (~q(X!0))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 ((~(p(X!0) & q(X!0))) <=> (~(~((~p(X!0)) | (~q(X!0)))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 ((~(p(X!0) & q(X!0))) <=> ((~p(X!0)) | (~q(X!0)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[60, 58])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 (((~(p(X!0) & q(X!0))) | (~p(X!1)) | (~q(X!2))) <=> (((~p(X!0)) | (~q(X!0))) | (~p(X!1)) | (~q(X!2)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[61])).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 (((~(p(X!0) & q(X!0))) | (~p(X!1)) | (~q(X!2))) <=> ((~p(X!1)) | (~q(X!2)) | (~p(X!0)) | (~q(X!0)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[62, 57])).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 ((~(p(X!0) & q(X!0))) | (~p(X!1)) | (~q(X!2))),
% 0.13/0.39 inference(and_elim,[status(thm)],[49])).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 ((~p(X!1)) | (~q(X!2)) | (~p(X!0)) | (~q(X!0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 ((~p(X!1)) | (~p(X!0)) | (~q(X!0))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[65, 56])).
% 0.13/0.39 tff(67,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[66, 18, 16, 9])).
% 0.13/0.39 tff(68,plain,(~![X: $i] : (~((~p(X)) | (~q(X))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 (~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[52, 68])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 (![X: $i] : q(X)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[27, 69])).
% 0.13/0.39 tff(71,plain,
% 0.13/0.39 ((~![X: $i] : q(X)) | q(X!0)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[71, 70, 1])).
% 0.13/0.39 tff(73,plain,(q(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(74,assumption,(~p(X!0)), introduced(assumption)).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 (((~![X: $i] : p(X)) | (~![X: $i] : q(X))) | ![X: $i] : p(X)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(76,plain,
% 0.13/0.39 (![X: $i] : p(X)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[75, 69])).
% 0.13/0.39 tff(77,plain,
% 0.13/0.39 ((~![X: $i] : p(X)) | p(X!0)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(78,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[77, 76, 74])).
% 0.13/0.39 tff(79,plain,(p(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(80,plain,
% 0.13/0.39 (~p(X!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[66, 79, 73])).
% 0.13/0.39 tff(81,plain,
% 0.13/0.39 ((~![X: $i] : p(X)) | p(X!1)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(82,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[81, 76, 80])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------