TSTP Solution File: ARI612_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI612_1 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 : Tue Sep 6 17:02:17 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
% 0.07/0.12 % Problem : ARI612_1 : TPTP v8.1.0. Released v5.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 00:16:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -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(tptp_fun_X_0_type, type, (
% 0.13/0.39 tptp_fun_X_0: $int)).
% 0.13/0.39 tff(p_type, type, (
% 0.13/0.39 p: $int > $o)).
% 0.13/0.39 tff(q_type, type, (
% 0.13/0.39 q: $int > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[X: $int] : refl(((~($lesseq(X, 5) | $greatereq(X, 15))) <=> p(X)) <=> ((~($lesseq(X, 5) | $greatereq(X, 15))) <=> p(X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![X: $int] : ((~($lesseq(X, 5) | $greatereq(X, 15))) <=> p(X)) <=> ![X: $int] : ((~($lesseq(X, 5) | $greatereq(X, 15))) <=> p(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[X: $int] : rewrite((((~$lesseq(X, 5)) & (~$greatereq(X, 15))) <=> p(X)) <=> ((~($lesseq(X, 5) | $greatereq(X, 15))) <=> p(X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 5)) & (~$greatereq(X, 15))) <=> p(X)) <=> ![X: $int] : ((~($lesseq(X, 5) | $greatereq(X, 15))) <=> p(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (^[X: $int] : rewrite((((~$lesseq(X, 5)) & (~$lesseq(15, X))) <=> p(X)) <=> (((~$lesseq(X, 5)) & (~$greatereq(X, 15))) <=> p(X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 5)) & (~$lesseq(15, X))) <=> p(X)) <=> ![X: $int] : (((~$lesseq(X, 5)) & (~$greatereq(X, 15))) <=> p(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 5)) & (~$lesseq(15, X))) <=> p(X)) <=> ![X: $int] : (((~$lesseq(X, 5)) & (~$lesseq(15, X))) <=> p(X))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 ((~((![X: $int] : (($less(5, X) & $less(X, 15)) <=> p(X)) & ![X: $int] : (($less(8, X) & $less(X, 12)) <=> q(X))) => ![X: $int] : (q(X) => p(X)))) <=> (~((~(![X: $int] : (((~$lesseq(X, 5)) & (~$lesseq(15, X))) <=> p(X)) & ![X: $int] : (((~$lesseq(X, 8)) & (~$lesseq(12, X))) <=> q(X)))) | ![X: $int] : (p(X) | (~q(X)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(9,axiom,(~((![X: $int] : (($less(5, X) & $less(X, 15)) <=> p(X)) & ![X: $int] : (($less(8, X) & $less(X, 12)) <=> q(X))) => ![X: $int] : (q(X) => p(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','interv_8_12_subset_5_15')).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~((~(![X: $int] : (((~$lesseq(X, 5)) & (~$lesseq(15, X))) <=> p(X)) & ![X: $int] : (((~$lesseq(X, 8)) & (~$lesseq(12, X))) <=> q(X)))) | ![X: $int] : (p(X) | (~q(X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 5)) & (~$lesseq(15, X))) <=> p(X)) & ![X: $int] : (((~$lesseq(X, 8)) & (~$lesseq(12, X))) <=> q(X))),
% 0.13/0.39 inference(or_elim,[status(thm)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 5)) & (~$lesseq(15, X))) <=> p(X))),
% 0.13/0.39 inference(and_elim,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 5)) & (~$lesseq(15, X))) <=> p(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 5)) & (~$greatereq(X, 15))) <=> p(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.13/0.39 tff(15,plain,(
% 0.13/0.39 ![X: $int] : (((~$lesseq(X, 5)) & (~$greatereq(X, 15))) <=> p(X))),
% 0.13/0.39 inference(skolemize,[status(sab)],[14])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![X: $int] : ((~($lesseq(X, 5) | $greatereq(X, 15))) <=> p(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![X: $int] : ((~($lesseq(X, 5) | $greatereq(X, 15))) <=> p(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 2])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 ((~![X: $int] : ((~($lesseq(X, 5) | $greatereq(X, 15))) <=> p(X))) | ((~($lesseq(X!0, 5) | $greatereq(X!0, 15))) <=> p(X!0))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 ((~($lesseq(X!0, 5) | $greatereq(X!0, 15))) <=> p(X!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((~![X: $int] : (p(X) | (~q(X)))) <=> (~![X: $int] : (p(X) | (~q(X))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (~![X: $int] : (p(X) | (~q(X)))),
% 0.13/0.39 inference(or_elim,[status(thm)],[10])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (~![X: $int] : (p(X) | (~q(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (~![X: $int] : (p(X) | (~q(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (~![X: $int] : (p(X) | (~q(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (~![X: $int] : (p(X) | (~q(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (~![X: $int] : (p(X) | (~q(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~![X: $int] : (p(X) | (~q(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.13/0.39 tff(28,plain,(
% 0.13/0.39 ~(p(X!0) | (~q(X!0)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[27])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (~p(X!0)),
% 0.13/0.39 inference(or_elim,[status(thm)],[28])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 ((~((~($lesseq(X!0, 5) | $greatereq(X!0, 15))) <=> p(X!0))) | ($lesseq(X!0, 5) | $greatereq(X!0, 15)) | p(X!0)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 ((~((~($lesseq(X!0, 5) | $greatereq(X!0, 15))) <=> p(X!0))) | ($lesseq(X!0, 5) | $greatereq(X!0, 15))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 ($lesseq(X!0, 5) | $greatereq(X!0, 15)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[31, 19])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (^[X: $int] : refl(((~($lesseq(X, 8) | $greatereq(X, 12))) <=> q(X)) <=> ((~($lesseq(X, 8) | $greatereq(X, 12))) <=> q(X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![X: $int] : ((~($lesseq(X, 8) | $greatereq(X, 12))) <=> q(X)) <=> ![X: $int] : ((~($lesseq(X, 8) | $greatereq(X, 12))) <=> q(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (^[X: $int] : rewrite((((~$lesseq(X, 8)) & (~$greatereq(X, 12))) <=> q(X)) <=> ((~($lesseq(X, 8) | $greatereq(X, 12))) <=> q(X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 8)) & (~$greatereq(X, 12))) <=> q(X)) <=> ![X: $int] : ((~($lesseq(X, 8) | $greatereq(X, 12))) <=> q(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (^[X: $int] : rewrite((((~$lesseq(X, 8)) & (~$lesseq(12, X))) <=> q(X)) <=> (((~$lesseq(X, 8)) & (~$greatereq(X, 12))) <=> q(X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 8)) & (~$lesseq(12, X))) <=> q(X)) <=> ![X: $int] : (((~$lesseq(X, 8)) & (~$greatereq(X, 12))) <=> q(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 8)) & (~$lesseq(12, X))) <=> q(X)) <=> ![X: $int] : (((~$lesseq(X, 8)) & (~$lesseq(12, X))) <=> q(X))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 8)) & (~$lesseq(12, X))) <=> q(X))),
% 0.13/0.39 inference(and_elim,[status(thm)],[11])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (![X: $int] : (((~$lesseq(X, 8)) & (~$lesseq(12, X))) <=> 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: $int] : (((~$lesseq(X, 8)) & (~$greatereq(X, 12))) <=> q(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.13/0.39 tff(43,plain,(
% 0.13/0.39 ![X: $int] : (((~$lesseq(X, 8)) & (~$greatereq(X, 12))) <=> q(X))),
% 0.13/0.39 inference(skolemize,[status(sab)],[42])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (![X: $int] : ((~($lesseq(X, 8) | $greatereq(X, 12))) <=> q(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (![X: $int] : ((~($lesseq(X, 8) | $greatereq(X, 12))) <=> 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: $int] : ((~($lesseq(X, 8) | $greatereq(X, 12))) <=> q(X))) | ((~($lesseq(X!0, 8) | $greatereq(X!0, 12))) <=> q(X!0))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 ((~($lesseq(X!0, 8) | $greatereq(X!0, 12))) <=> q(X!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (q(X!0)),
% 0.13/0.39 inference(or_elim,[status(thm)],[28])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 ((~((~($lesseq(X!0, 8) | $greatereq(X!0, 12))) <=> q(X!0))) | (~($lesseq(X!0, 8) | $greatereq(X!0, 12))) | (~q(X!0))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 ((~((~($lesseq(X!0, 8) | $greatereq(X!0, 12))) <=> q(X!0))) | (~($lesseq(X!0, 8) | $greatereq(X!0, 12)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (~($lesseq(X!0, 8) | $greatereq(X!0, 12))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 (($lesseq(X!0, 8) | $greatereq(X!0, 12)) | (~$lesseq(X!0, 8))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 (~$lesseq(X!0, 8)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 ($lesseq(X!0, 8) | (~$lesseq(X!0, 5))),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (~$lesseq(X!0, 5)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 (($lesseq(X!0, 8) | $greatereq(X!0, 12)) | (~$greatereq(X!0, 12))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 (~$greatereq(X!0, 12)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[56, 51])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 ($greatereq(X!0, 12) | (~$greatereq(X!0, 15))),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 (~$greatereq(X!0, 15)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 ((~($lesseq(X!0, 5) | $greatereq(X!0, 15))) | $lesseq(X!0, 5) | $greatereq(X!0, 15)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[60, 59, 55, 32])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------