TSTP Solution File: SYN053+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN053+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 23:53:23 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
% 0.06/0.12 % Problem : SYN053+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n014.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 01:36:14 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.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(big_f_type, type, (
% 0.19/0.39 big_f: $i > $o)).
% 0.19/0.39 tff(tptp_fun_X_0_type, type, (
% 0.19/0.39 tptp_fun_X_0: $i)).
% 0.19/0.39 tff(p_type, type, (
% 0.19/0.39 p: $o)).
% 0.19/0.39 tff(tptp_fun_X1_1_type, type, (
% 0.19/0.39 tptp_fun_X1_1: $i)).
% 0.19/0.39 tff(1,assumption,(~(p | big_f(X1!1))), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 ((p | big_f(X1!1)) | (~big_f(X1!1))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (~big_f(X1!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 ((p | big_f(X1!1)) | (~p)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (~p),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.39 tff(6,assumption,(~big_f(X1!1)), introduced(assumption)).
% 0.19/0.39 tff(7,assumption,(![X1: $i] : big_f(X1)), introduced(assumption)).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![X1: $i] : big_f(X1)) | big_f(X1!1)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7, 6])).
% 0.19/0.39 tff(10,plain,((~![X1: $i] : big_f(X1)) | big_f(X1!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (~![X1: $i] : big_f(X1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[10, 3])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 ((p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (((![X: $i] : (p | big_f(X)) | (p | ![X1: $i] : big_f(X1))) & ((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1))))) <=> ((p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))) & ((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 ((p | ![X1: $i] : big_f(X1)) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) <=> (~![X: $i] : (p | big_f(X)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))) <=> ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[15, 14])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))) <=> ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~(![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1)))) <=> ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1))) <=> (![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ((~(![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1)))) <=> (~(![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[19])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~(![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1)))) <=> ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[20, 18])).
% 0.19/0.39 tff(22,axiom,(~(![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel23')).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 16])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 16])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 16])).
% 0.19/0.39 tff(30,plain,(
% 0.19/0.39 (![X: $i] : (p | big_f(X)) | (p | ![X1: $i] : big_f(X1))) & ((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))) & ((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 13])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))),
% 0.19/0.39 inference(and_elim,[status(thm)],[31])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 12])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![X: $i] : (p | big_f(X))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[33, 11, 5])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (((~![X: $i] : (p | big_f(X))) | (p | big_f(X1!1))) <=> ((~![X: $i] : (p | big_f(X))) | p | big_f(X1!1))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) | (p | big_f(X1!1))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) | p | big_f(X1!1)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[37, 5, 34, 3])).
% 0.19/0.39 tff(39,plain,(p | big_f(X1!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1)))) <=> ((~(p | big_f(X!0))) | (~(p | big_f(X1!1))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1)))),
% 0.19/0.39 inference(and_elim,[status(thm)],[31])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 ((~(p | big_f(X!0))) | (~(p | big_f(X1!1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (~(p | big_f(X!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((p | big_f(X!0)) | (~big_f(X!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (~big_f(X!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,assumption,(![X: $i] : (p | big_f(X))), introduced(assumption)).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((p | big_f(X!0)) | (~p)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (~p),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[47, 43])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (((~![X: $i] : (p | big_f(X))) | (p | big_f(X!0))) <=> ((~![X: $i] : (p | big_f(X))) | p | big_f(X!0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) | (p | big_f(X!0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ((~![X: $i] : (p | big_f(X))) | p | big_f(X!0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[51, 48, 46, 45])).
% 0.19/0.39 tff(53,plain,(~![X: $i] : (p | big_f(X))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[33, 48])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (![X1: $i] : big_f(X1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 ((~![X1: $i] : big_f(X1)) | big_f(X!0)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 55, 45])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------