TSTP Solution File: DAT024_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT024_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 16 14:36:25 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : DAT024_1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 01:45:19 EDT 2022
% 0.14/0.35 % 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.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(in_type, type, (
% 0.14/0.40 in: ( $int * collection ) > $o)).
% 0.14/0.40 tff(tptp_fun_U_0_type, type, (
% 0.14/0.40 tptp_fun_U_0: collection)).
% 0.14/0.40 tff(tptp_fun_W_1_type, type, (
% 0.14/0.40 tptp_fun_W_1: $int)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (((![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0)) & (~in(0, U!0)) & (~in(1, U!0))) & (~((~in(W!1, U!0)) | $greatereq(W!1, 2)))) <=> (![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0)) & (~in(0, U!0)) & (~in(1, U!0)) & (~((~in(W!1, U!0)) | $greatereq(W!1, 2))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 ((![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0)) & (~in(0, U!0)) & (~in(1, U!0))) <=> (![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0)) & (~in(0, U!0)) & (~in(1, U!0)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (((![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0)) & (~in(0, U!0)) & (~in(1, U!0))) & (~((~in(W!1, U!0)) | $greatereq(W!1, 2)))) <=> ((![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0)) & (~in(0, U!0)) & (~in(1, U!0))) & (~((~in(W!1, U!0)) | $greatereq(W!1, 2))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[2])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (((![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0)) & (~in(0, U!0)) & (~in(1, U!0))) & (~((~in(W!1, U!0)) | $greatereq(W!1, 2)))) <=> (![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0)) & (~in(0, U!0)) & (~in(1, U!0)) & (~((~in(W!1, U!0)) | $greatereq(W!1, 2))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[3, 1])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 ((~![U: collection] : ((~(![V: $int] : ((~in(V, U)) | $greatereq(V, 0)) & (~in(0, U)) & (~in(1, U)))) | ![W: $int] : ((~in(W, U)) | $greatereq(W, 2)))) <=> (~![U: collection] : ((~(![V: $int] : ((~in(V, U)) | $greatereq(V, 0)) & (~in(0, U)) & (~in(1, U)))) | ![W: $int] : ((~in(W, U)) | $greatereq(W, 2))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 ((~![U: collection] : (((![V: $int] : (in(V, U) => $greatereq(V, 0)) & (~in(0, U))) & (~in(1, U))) => ![W: $int] : (in(W, U) => $greatereq(W, 2)))) <=> (~![U: collection] : ((~(![V: $int] : ((~in(V, U)) | $greatereq(V, 0)) & (~in(0, U)) & (~in(1, U)))) | ![W: $int] : ((~in(W, U)) | $greatereq(W, 2))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(7,axiom,(~![U: collection] : (((![V: $int] : (in(V, U) => $greatereq(V, 0)) & (~in(0, U))) & (~in(1, U))) => ![W: $int] : (in(W, U) => $greatereq(W, 2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (~![U: collection] : ((~(![V: $int] : ((~in(V, U)) | $greatereq(V, 0)) & (~in(0, U)) & (~in(1, U)))) | ![W: $int] : ((~in(W, U)) | $greatereq(W, 2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (~![U: collection] : ((~(![V: $int] : ((~in(V, U)) | $greatereq(V, 0)) & (~in(0, U)) & (~in(1, U)))) | ![W: $int] : ((~in(W, U)) | $greatereq(W, 2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (~![U: collection] : ((~(![V: $int] : ((~in(V, U)) | $greatereq(V, 0)) & (~in(0, U)) & (~in(1, U)))) | ![W: $int] : ((~in(W, U)) | $greatereq(W, 2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (~![U: collection] : ((~(![V: $int] : ((~in(V, U)) | $greatereq(V, 0)) & (~in(0, U)) & (~in(1, U)))) | ![W: $int] : ((~in(W, U)) | $greatereq(W, 2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (~![U: collection] : ((~(![V: $int] : ((~in(V, U)) | $greatereq(V, 0)) & (~in(0, U)) & (~in(1, U)))) | ![W: $int] : ((~in(W, U)) | $greatereq(W, 2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (~![U: collection] : ((~(![V: $int] : ((~in(V, U)) | $greatereq(V, 0)) & (~in(0, U)) & (~in(1, U)))) | ![W: $int] : ((~in(W, U)) | $greatereq(W, 2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (~![U: collection] : ((~(![V: $int] : ((~in(V, U)) | $greatereq(V, 0)) & (~in(0, U)) & (~in(1, U)))) | ![W: $int] : ((~in(W, U)) | $greatereq(W, 2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0)) & (~in(0, U!0)) & (~in(1, U!0)) & (~((~in(W!1, U!0)) | $greatereq(W!1, 2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (~((~in(W!1, U!0)) | $greatereq(W!1, 2))),
% 0.14/0.40 inference(and_elim,[status(thm)],[15])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (~$greatereq(W!1, 2)),
% 0.14/0.40 inference(or_elim,[status(thm)],[16])).
% 0.14/0.40 tff(18,assumption,(W!1 = 0), introduced(assumption)).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (in(W!1, U!0) <=> in(0, U!0)),
% 0.14/0.40 inference(monotonicity,[status(thm)],[18])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (in(0, U!0) <=> in(W!1, U!0)),
% 0.14/0.40 inference(symmetry,[status(thm)],[19])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 ((~in(0, U!0)) <=> (~in(W!1, U!0))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 (~in(0, U!0)),
% 0.14/0.40 inference(and_elim,[status(thm)],[15])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (~in(W!1, U!0)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (in(W!1, U!0)),
% 0.14/0.40 inference(or_elim,[status(thm)],[16])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.14/0.40 tff(26,plain,(~(W!1 = 0)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 (^[V: $int] : refl(((~in(V, U!0)) | $greatereq(V, 0)) <=> ((~in(V, U!0)) | $greatereq(V, 0)))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0)) <=> ![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0))),
% 0.14/0.40 inference(and_elim,[status(thm)],[15])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (((~![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0))) | ((~in(W!1, U!0)) | $greatereq(W!1, 0))) <=> ((~![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0))) | (~in(W!1, U!0)) | $greatereq(W!1, 0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 ((~![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0))) | ((~in(W!1, U!0)) | $greatereq(W!1, 0))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 ((~![V: $int] : ((~in(V, U!0)) | $greatereq(V, 0))) | (~in(W!1, U!0)) | $greatereq(W!1, 0)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 ($greatereq(W!1, 0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[33, 30, 24])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 ((W!1 = 0) | (~$lesseq(W!1, 0)) | (~$greatereq(W!1, 0))),
% 0.14/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 ((W!1 = 0) | (~$lesseq(W!1, 0))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 (~$lesseq(W!1, 0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[36, 26])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (W!1 = 1),
% 0.14/0.40 inference(theory_lemma,[status(thm)],[37, 17])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 (in(W!1, U!0) <=> in(1, U!0)),
% 0.14/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (in(1, U!0) <=> in(W!1, U!0)),
% 0.14/0.40 inference(symmetry,[status(thm)],[39])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 ((~in(1, U!0)) <=> (~in(W!1, U!0))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[40])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (~in(1, U!0)),
% 0.14/0.40 inference(and_elim,[status(thm)],[15])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (~in(W!1, U!0)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[24, 43])).
% 0.14/0.40 % SZS output end Proof
%------------------------------------------------------------------------------