TSTP Solution File: SYN931+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN931+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 00:01:18 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN931+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 09:43:46 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(p_type, type, (
% 0.20/0.39 p: $i > $o)).
% 0.20/0.39 tff(c_type, type, (
% 0.20/0.39 c: $o)).
% 0.20/0.39 tff(tptp_fun_X_0_type, type, (
% 0.20/0.39 tptp_fun_X_0: $i)).
% 0.20/0.39 tff(tptp_fun_X_1_type, type, (
% 0.20/0.39 tptp_fun_X_1: $i)).
% 0.20/0.39 tff(1,assumption,(![X: $i] : ((~p(X)) | (~c))), introduced(assumption)).
% 0.20/0.39 tff(2,assumption,(p(X!1)), introduced(assumption)).
% 0.20/0.39 tff(3,assumption,(![X: $i] : (~p(X))), introduced(assumption)).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 ((~![X: $i] : (~p(X))) | (~p(X!1))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[4, 2, 3])).
% 0.20/0.39 tff(6,plain,((~![X: $i] : (~p(X))) | (~p(X!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (~![X: $i] : (~p(X))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[6, 2])).
% 0.20/0.39 tff(8,assumption,(~c), introduced(assumption)).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (((~c) | (~p(X!0))) | c),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ((~c) | (~p(X!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (((~c) | (~p(X!1))) | c),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 ((~c) | (~p(X!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (((p(X!0) & c) | (p(X!1) & c)) <=> ((~((~c) | (~p(X!0)))) | (~((~c) | (~p(X!1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 ((((p(X!0) & c) | (p(X!1) & c)) & (![X: $i] : (~(p(X) & c)) | (![X: $i] : (~p(X)) | (~c)))) <=> (((p(X!0) & c) | (p(X!1) & c)) & (![X: $i] : (~(p(X) & c)) | ![X: $i] : (~p(X)) | (~c)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 ((?[X: $i] : p(X) & c) <=> (?[X: $i] : p(X) & c)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 ((~?[X: $i] : (p(X) & c)) <=> (~?[X: $i] : (p(X) & c))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c)) <=> ((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[16, 15])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c)) <=> ((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 ((~(?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c))) <=> ((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 ((?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) <=> (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 ((~(?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c))) <=> (~(?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[20])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 ((~(?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c))) <=> ((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c))),
% 0.20/0.39 inference(transitivity,[status(thm)],[21, 19])).
% 0.20/0.39 tff(23,axiom,(~(?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 ((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 17])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 ((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 ((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 17])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~?[X: $i] : (p(X) & c)) <=> (?[X: $i] : p(X) & c)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[29, 17])).
% 0.20/0.39 tff(31,plain,(
% 0.20/0.39 ((p(X!0) & c) | (p(X!1) & c)) & (![X: $i] : (~(p(X) & c)) | (![X: $i] : (~p(X)) | (~c)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[30])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (((p(X!0) & c) | (p(X!1) & c)) & (![X: $i] : (~(p(X) & c)) | ![X: $i] : (~p(X)) | (~c))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[31, 14])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ((p(X!0) & c) | (p(X!1) & c)),
% 0.20/0.39 inference(and_elim,[status(thm)],[32])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ((~((~c) | (~p(X!0)))) | (~((~c) | (~p(X!1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[33, 13])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[34, 12, 10])).
% 0.20/0.39 tff(36,plain,(c), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ((![X: $i] : (~p(X)) | (~c) | ![X: $i] : ((~p(X)) | (~c))) <=> ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 ((![X: $i] : (~p(X)) | (~c) | ![X: $i] : ((~p(X)) | (~c))) <=> (![X: $i] : (~p(X)) | (~c) | ![X: $i] : ((~p(X)) | (~c)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 ((![X: $i] : ((~p(X)) | (~c)) | ![X: $i] : (~p(X)) | (~c)) <=> (![X: $i] : (~p(X)) | (~c) | ![X: $i] : ((~p(X)) | (~c)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (^[X: $i] : trans(monotonicity(rewrite((p(X) & c) <=> (~((~p(X)) | (~c)))), ((~(p(X) & c)) <=> (~(~((~p(X)) | (~c)))))), rewrite((~(~((~p(X)) | (~c)))) <=> ((~p(X)) | (~c))), ((~(p(X) & c)) <=> ((~p(X)) | (~c))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![X: $i] : (~(p(X) & c)) <=> ![X: $i] : ((~p(X)) | (~c))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((![X: $i] : (~(p(X) & c)) | ![X: $i] : (~p(X)) | (~c)) <=> (![X: $i] : ((~p(X)) | (~c)) | ![X: $i] : (~p(X)) | (~c))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((![X: $i] : (~(p(X) & c)) | ![X: $i] : (~p(X)) | (~c)) <=> (![X: $i] : (~p(X)) | (~c) | ![X: $i] : ((~p(X)) | (~c)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[42, 39])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (![X: $i] : (~(p(X) & c)) | ![X: $i] : (~p(X)) | (~c)),
% 0.20/0.39 inference(and_elim,[status(thm)],[32])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (![X: $i] : (~p(X)) | (~c) | ![X: $i] : ((~p(X)) | (~c))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (![X: $i] : (~p(X)) | (~c) | ![X: $i] : ((~p(X)) | (~c))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[46, 37])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[47, 36])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (![X: $i] : ((~p(X)) | (~c))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[48, 7])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (((~![X: $i] : ((~p(X)) | (~c))) | ((~c) | (~p(X!1)))) <=> ((~![X: $i] : ((~p(X)) | (~c))) | (~c) | (~p(X!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (((~p(X!1)) | (~c)) <=> ((~c) | (~p(X!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (((~![X: $i] : ((~p(X)) | (~c))) | ((~p(X!1)) | (~c))) <=> ((~![X: $i] : ((~p(X)) | (~c))) | ((~c) | (~p(X!1))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (((~![X: $i] : ((~p(X)) | (~c))) | ((~p(X!1)) | (~c))) <=> ((~![X: $i] : ((~p(X)) | (~c))) | (~c) | (~p(X!1)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[52, 50])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 ((~![X: $i] : ((~p(X)) | (~c))) | ((~p(X!1)) | (~c))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ((~![X: $i] : ((~p(X)) | (~c))) | (~c) | (~p(X!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[55, 36, 2, 49])).
% 0.20/0.39 tff(57,plain,(~p(X!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (((~c) | (~p(X!1))) | p(X!1)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 ((~c) | (~p(X!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (~((~c) | (~p(X!0)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[34, 59])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (((~c) | (~p(X!0))) | p(X!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (p(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (((~![X: $i] : ((~p(X)) | (~c))) | ((~c) | (~p(X!0)))) <=> ((~![X: $i] : ((~p(X)) | (~c))) | (~c) | (~p(X!0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (((~p(X!0)) | (~c)) <=> ((~c) | (~p(X!0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (((~![X: $i] : ((~p(X)) | (~c))) | ((~p(X!0)) | (~c))) <=> ((~![X: $i] : ((~p(X)) | (~c))) | ((~c) | (~p(X!0))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (((~![X: $i] : ((~p(X)) | (~c))) | ((~p(X!0)) | (~c))) <=> ((~![X: $i] : ((~p(X)) | (~c))) | (~c) | (~p(X!0)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ((~![X: $i] : ((~p(X)) | (~c))) | ((~p(X!0)) | (~c))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 ((~![X: $i] : ((~p(X)) | (~c))) | (~c) | (~p(X!0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[68, 36, 62, 1])).
% 0.20/0.39 tff(70,plain,(~![X: $i] : ((~p(X)) | (~c))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (![X: $i] : (~p(X))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[48, 70])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 ((~![X: $i] : (~p(X))) | (~p(X!0))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[72, 62, 71])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------