TSTP Solution File: SYN934+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN934+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 00:01:19 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN934+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n006.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 09:42:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(p_type, type, (
% 0.21/0.39 p: $i > $o)).
% 0.21/0.39 tff(elem_3_type, type, (
% 0.21/0.39 elem_3: $i)).
% 0.21/0.39 tff(k!0_type, type, (
% 0.21/0.39 k!0: $o)).
% 0.21/0.39 tff(tptp_fun_X_2_type, type, (
% 0.21/0.39 tptp_fun_X_2: $i)).
% 0.21/0.39 tff(tptp_fun_X_1_type, type, (
% 0.21/0.39 tptp_fun_X_1: $i)).
% 0.21/0.39 tff(c_type, type, (
% 0.21/0.39 c: $o)).
% 0.21/0.39 tff(1,assumption,(~k!0), introduced(assumption)).
% 0.21/0.39 tff(2,assumption,(![X: $i] : (~(k!0 | p(X)))), introduced(assumption)).
% 0.21/0.39 tff(3,assumption,(k!0 | p(X!1)), introduced(assumption)).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 ((~![X: $i] : (~(k!0 | p(X)))) | (~(k!0 | p(X!1)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[4, 2, 3])).
% 0.21/0.39 tff(6,plain,((~(k!0 | p(X!1))) | (~![X: $i] : (~(k!0 | p(X))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (~(k!0 | p(X!1))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[6, 2])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((k!0 | p(X!1)) | (~p(X!1))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (~p(X!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 ((((k!0 | p(X!1)) | (k!0 | p(X!2))) & (![X: $i] : (~(k!0 | p(X))) | ((~k!0) & ![X: $i] : (~p(X))))) <=> ((k!0 | p(X!1) | p(X!2)) & (![X: $i] : (~(k!0 | p(X))) | ((~k!0) & ![X: $i] : (~p(X)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 ((k!0 | ?[X: $i] : p(X)) <=> (k!0 | ?[X: $i] : p(X))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 ((~?[X: $i] : (k!0 | p(X))) <=> (~?[X: $i] : (k!0 | p(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (((~?[X: $i] : (k!0 | p(X))) <=> (k!0 | ?[X: $i] : p(X))) <=> ((~?[X: $i] : (k!0 | p(X))) <=> (k!0 | ?[X: $i] : p(X)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[12, 11])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (((~?[X: $i] : ((~c) | p(X))) <=> ((~c) | ?[X: $i] : p(X))) <=> ((~?[X: $i] : (k!0 | p(X))) <=> (k!0 | ?[X: $i] : p(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (((~c) | ?[X: $i] : p(X)) <=> ((~c) | ?[X: $i] : p(X))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 ((~?[X: $i] : ((~c) | p(X))) <=> (~?[X: $i] : ((~c) | p(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (((~?[X: $i] : ((~c) | p(X))) <=> ((~c) | ?[X: $i] : p(X))) <=> ((~?[X: $i] : ((~c) | p(X))) <=> ((~c) | ?[X: $i] : p(X)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[16, 15])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (((~?[X: $i] : ((~c) | p(X))) <=> ((~c) | ?[X: $i] : p(X))) <=> ((~?[X: $i] : ((~c) | p(X))) <=> ((~c) | ?[X: $i] : p(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 ((~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))) <=> ((~?[X: $i] : ((~c) | p(X))) <=> ((~c) | ?[X: $i] : p(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 ((?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X))) <=> (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 ((~(?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X)))) <=> (~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[20])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 ((~(?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X)))) <=> ((~?[X: $i] : ((~c) | p(X))) <=> ((~c) | ?[X: $i] : p(X)))),
% 0.21/0.39 inference(transitivity,[status(thm)],[21, 19])).
% 0.21/0.39 tff(23,axiom,(~(?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 ((~?[X: $i] : ((~c) | p(X))) <=> ((~c) | ?[X: $i] : p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 ((~?[X: $i] : ((~c) | p(X))) <=> ((~c) | ?[X: $i] : p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 ((~?[X: $i] : ((~c) | p(X))) <=> ((~c) | ?[X: $i] : p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 ((~?[X: $i] : ((~c) | p(X))) <=> ((~c) | ?[X: $i] : p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[26, 17])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 ((~?[X: $i] : (k!0 | p(X))) <=> (k!0 | ?[X: $i] : p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[27, 14])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 ((~?[X: $i] : (k!0 | p(X))) <=> (k!0 | ?[X: $i] : p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 13])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 ((~?[X: $i] : (k!0 | p(X))) <=> (k!0 | ?[X: $i] : p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[29, 13])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 ((~?[X: $i] : (k!0 | p(X))) <=> (k!0 | ?[X: $i] : p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[30, 13])).
% 0.21/0.39 tff(32,plain,(
% 0.21/0.39 ((k!0 | p(X!1)) | (k!0 | p(X!2))) & (![X: $i] : (~(k!0 | p(X))) | ((~k!0) & ![X: $i] : (~p(X))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[31])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 ((k!0 | p(X!1) | p(X!2)) & (![X: $i] : (~(k!0 | p(X))) | ((~k!0) & ![X: $i] : (~p(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[32, 10])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (k!0 | p(X!1) | p(X!2)),
% 0.21/0.39 inference(and_elim,[status(thm)],[33])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (p(X!2)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[34, 9, 1])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 ((k!0 | p(X!2)) | (~p(X!2))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (k!0 | p(X!2)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 ((~![X: $i] : (~(k!0 | p(X)))) | (~(k!0 | p(X!2)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[38, 2, 37])).
% 0.21/0.39 tff(40,plain,((~![X: $i] : (~(k!0 | p(X)))) | k!0), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (~![X: $i] : (~(k!0 | p(X)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[40, 1])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 ((![X: $i] : (~(k!0 | p(X))) | (~(k!0 | (~![X: $i] : (~p(X)))))) <=> (![X: $i] : (~(k!0 | p(X))) | (~(k!0 | (~![X: $i] : (~p(X))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 ((![X: $i] : (~(k!0 | p(X))) | (~(k!0 | (~![X: $i] : (~p(X)))))) <=> (![X: $i] : (~(k!0 | p(X))) | (~(k!0 | (~![X: $i] : (~p(X))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (((~k!0) & ![X: $i] : (~p(X))) <=> (~(k!0 | (~![X: $i] : (~p(X)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 ((![X: $i] : (~(k!0 | p(X))) | ((~k!0) & ![X: $i] : (~p(X)))) <=> (![X: $i] : (~(k!0 | p(X))) | (~(k!0 | (~![X: $i] : (~p(X))))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[44])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 ((![X: $i] : (~(k!0 | p(X))) | ((~k!0) & ![X: $i] : (~p(X)))) <=> (![X: $i] : (~(k!0 | p(X))) | (~(k!0 | (~![X: $i] : (~p(X))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[45, 43])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (![X: $i] : (~(k!0 | p(X))) | ((~k!0) & ![X: $i] : (~p(X)))),
% 0.21/0.39 inference(and_elim,[status(thm)],[33])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (![X: $i] : (~(k!0 | p(X))) | (~(k!0 | (~![X: $i] : (~p(X)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (![X: $i] : (~(k!0 | p(X))) | (~(k!0 | (~![X: $i] : (~p(X)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[48, 42])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (~(k!0 | (~![X: $i] : (~p(X))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[49, 41])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 ((k!0 | (~![X: $i] : (~p(X)))) | ![X: $i] : (~p(X))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (![X: $i] : (~p(X))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.21/0.39 tff(53,assumption,(![X: $i] : (~p(X))), introduced(assumption)).
% 0.21/0.39 tff(54,assumption,(p(X!2)), introduced(assumption)).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 ((~![X: $i] : (~p(X))) | (~p(X!2))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[55, 54, 53])).
% 0.21/0.39 tff(57,plain,((~p(X!2)) | (~![X: $i] : (~p(X)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 (~p(X!2)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[57, 52])).
% 0.21/0.39 tff(59,plain,
% 0.21/0.39 (p(X!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[34, 58, 1])).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 ((~![X: $i] : (~p(X))) | (~p(X!1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[60, 59, 52])).
% 0.21/0.39 tff(62,plain,(k!0), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 ((k!0 | p(elem!3)) | (~k!0)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(64,plain,
% 0.21/0.39 (k!0 | p(elem!3)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.21/0.39 tff(65,plain,
% 0.21/0.39 ((k!0 | (~![X: $i] : (~p(X)))) | (~k!0)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (k!0 | (~![X: $i] : (~p(X)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[65, 62])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (![X: $i] : (~(k!0 | p(X)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[49, 66])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 ((~![X: $i] : (~(k!0 | p(X)))) | (~(k!0 | p(elem!3)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[68, 67, 64])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------