TSTP Solution File: DAT068_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT068_1 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 14:36:36 EDT 2022
% Result : Theorem 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT068_1 : TPTP v8.1.0. Released v5.5.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n020.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 01:49:45 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.
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 tff(length_type, type, (
% 0.22/0.40 length: heap > $int)).
% 0.22/0.40 tff(tptp_fun_H_0_type, type, (
% 0.22/0.40 tptp_fun_H_0: heap)).
% 0.22/0.40 tff(tptp_fun_M_1_type, type, (
% 0.22/0.40 tptp_fun_M_1: $int)).
% 0.22/0.40 tff(sel_type, type, (
% 0.22/0.40 sel: ( heap * $int ) > $int)).
% 0.22/0.40 tff(app_type, type, (
% 0.22/0.40 app: ( heap * $int ) > heap)).
% 0.22/0.40 tff(tptp_fun_N_2_type, type, (
% 0.22/0.40 tptp_fun_N_2: $int)).
% 0.22/0.40 tff(1,plain,
% 0.22/0.40 ((~![N: $int, M: $int, H: heap] : ($greatereq($sum(M, $product(-1, length(H))), 0) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))) <=> (~![N: $int, M: $int, H: heap] : ($greatereq($sum(M, $product(-1, length(H))), 0) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(2,plain,
% 0.22/0.40 ((~![N: $int, M: $int, H: heap] : (($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = 0) | $lesseq($sum(length(H), $product(-1, M)), 0))) <=> (~![N: $int, M: $int, H: heap] : ($greatereq($sum(M, $product(-1, length(H))), 0) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(3,plain,
% 0.22/0.40 ((~![N: $int, M: $int, H: heap] : ((sel(app(H, N), M) = sel(H, M)) | $lesseq(length(H), M))) <=> (~![N: $int, M: $int, H: heap] : (($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = 0) | $lesseq($sum(length(H), $product(-1, M)), 0)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(4,plain,
% 0.22/0.40 ((~![N: $int, M: $int, H: heap] : ((sel(app(H, N), M) = sel(H, M)) | $lesseq(length(H), M))) <=> (~![N: $int, M: $int, H: heap] : ((sel(app(H, N), M) = sel(H, M)) | $lesseq(length(H), M)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 ((~![N: $int, M: $int, H: heap] : ((sel(app(H, N), M) = sel(H, M)) | (~$less(M, length(H))))) <=> (~![N: $int, M: $int, H: heap] : ((sel(app(H, N), M) = sel(H, M)) | $lesseq(length(H), M)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(6,axiom,(~![N: $int, M: $int, H: heap] : ((sel(app(H, N), M) = sel(H, M)) | (~$less(M, length(H))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','th_3')).
% 0.22/0.40 tff(7,plain,
% 0.22/0.40 (~![N: $int, M: $int, H: heap] : ((sel(app(H, N), M) = sel(H, M)) | $lesseq(length(H), M))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.22/0.40 tff(8,plain,
% 0.22/0.40 (~![N: $int, M: $int, H: heap] : ((sel(app(H, N), M) = sel(H, M)) | $lesseq(length(H), M))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.22/0.40 tff(9,plain,
% 0.22/0.40 (~![N: $int, M: $int, H: heap] : ((sel(app(H, N), M) = sel(H, M)) | $lesseq(length(H), M))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.22/0.40 tff(10,plain,
% 0.22/0.40 (~![N: $int, M: $int, H: heap] : ((sel(app(H, N), M) = sel(H, M)) | $lesseq(length(H), M))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.22/0.40 tff(11,plain,
% 0.22/0.40 (~![N: $int, M: $int, H: heap] : (($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = 0) | $lesseq($sum(length(H), $product(-1, M)), 0))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.22/0.40 tff(12,plain,
% 0.22/0.40 (~![N: $int, M: $int, H: heap] : ($greatereq($sum(M, $product(-1, length(H))), 0) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.22/0.40 tff(13,plain,
% 0.22/0.40 (~![N: $int, M: $int, H: heap] : ($greatereq($sum(M, $product(-1, length(H))), 0) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.22/0.40 tff(14,plain,
% 0.22/0.40 (~![N: $int, M: $int, H: heap] : ($greatereq($sum(M, $product(-1, length(H))), 0) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[13, 1])).
% 0.22/0.40 tff(15,plain,(
% 0.22/0.40 ~($greatereq($sum(M!1, $product(-1, length(H!0))), 0) | ($sum(sel(H!0, M!1), $product(-1, sel(app(H!0, N!2), M!1))) = 0))),
% 0.22/0.40 inference(skolemize,[status(sab)],[14])).
% 0.22/0.40 tff(16,plain,
% 0.22/0.40 (~$greatereq($sum(M!1, $product(-1, length(H!0))), 0)),
% 0.22/0.40 inference(or_elim,[status(thm)],[15])).
% 0.22/0.40 tff(17,plain,
% 0.22/0.40 ((~$greatereq($sum(M!1, $product(-1, length(H!0))), 1)) | $greatereq($sum(M!1, $product(-1, length(H!0))), 0)),
% 0.22/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.40 tff(18,plain,
% 0.22/0.40 (~$greatereq($sum(M!1, $product(-1, length(H!0))), 1)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.22/0.40 tff(19,plain,
% 0.22/0.40 ((~($sum(M!1, $product(-1, length(H!0))) = 1)) | $greatereq($sum(M!1, $product(-1, length(H!0))), 1)),
% 0.22/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.40 tff(20,plain,
% 0.22/0.40 (~($sum(M!1, $product(-1, length(H!0))) = 1)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.40 tff(21,plain,
% 0.22/0.40 (~($sum(sel(H!0, M!1), $product(-1, sel(app(H!0, N!2), M!1))) = 0)),
% 0.22/0.40 inference(or_elim,[status(thm)],[15])).
% 0.22/0.40 tff(22,plain,
% 0.22/0.40 (^[N: $int, H: heap, M: $int] : refl((($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0)) <=> (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0)))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(23,plain,
% 0.22/0.40 (![N: $int, H: heap, M: $int] : (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0)) <=> ![N: $int, H: heap, M: $int] : (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.22/0.40 tff(24,plain,
% 0.22/0.40 (^[N: $int, H: heap, M: $int] : trans(monotonicity(trans(monotonicity(rewrite($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = $sum($product(-1, sel(H, M)), sel(app(H, N), M))), (($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = 0) <=> ($sum($product(-1, sel(H, M)), sel(app(H, N), M)) = 0))), rewrite(($sum($product(-1, sel(H, M)), sel(app(H, N), M)) = 0) <=> ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0)), (($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = 0) <=> ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))), ((($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = 0) | ($sum(M, $product(-1, length(H))) = 1)) <=> (($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0) | ($sum(M, $product(-1, length(H))) = 1)))), rewrite((($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0) | ($sum(M, $product(-1, length(H))) = 1)) <=> (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))), ((($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = 0) | ($sum(M, $product(-1, length(H))) = 1)) <=> (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(25,plain,
% 0.22/0.40 (![N: $int, H: heap, M: $int] : (($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = 0) | ($sum(M, $product(-1, length(H))) = 1)) <=> ![N: $int, H: heap, M: $int] : (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.22/0.40 tff(26,plain,
% 0.22/0.40 (^[N: $int, H: heap, M: $int] : rewrite(((sel(app(H, N), M) = sel(H, M)) | (M = $sum(1, length(H)))) <=> (($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = 0) | ($sum(M, $product(-1, length(H))) = 1)))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(27,plain,
% 0.22/0.40 (![N: $int, H: heap, M: $int] : ((sel(app(H, N), M) = sel(H, M)) | (M = $sum(1, length(H)))) <=> ![N: $int, H: heap, M: $int] : (($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = 0) | ($sum(M, $product(-1, length(H))) = 1))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.40 tff(28,plain,
% 0.22/0.40 (![N: $int, H: heap, M: $int] : ((sel(app(H, N), M) = sel(H, M)) | (M = $sum(1, length(H)))) <=> ![N: $int, H: heap, M: $int] : ((sel(app(H, N), M) = sel(H, M)) | (M = $sum(1, length(H))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(29,plain,
% 0.22/0.40 (^[N: $int, H: heap, M: $int] : rewrite(((~(M = $sum(1, length(H)))) => (sel(app(H, N), M) = sel(H, M))) <=> ((sel(app(H, N), M) = sel(H, M)) | (M = $sum(1, length(H)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(30,plain,
% 0.22/0.40 (![N: $int, H: heap, M: $int] : ((~(M = $sum(1, length(H)))) => (sel(app(H, N), M) = sel(H, M))) <=> ![N: $int, H: heap, M: $int] : ((sel(app(H, N), M) = sel(H, M)) | (M = $sum(1, length(H))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.22/0.40 tff(31,axiom,(![N: $int, H: heap, M: $int] : ((~(M = $sum(1, length(H)))) => (sel(app(H, N), M) = sel(H, M)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT006=0.ax','ax_3')).
% 0.22/0.41 tff(32,plain,
% 0.22/0.41 (![N: $int, H: heap, M: $int] : ((sel(app(H, N), M) = sel(H, M)) | (M = $sum(1, length(H))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.22/0.41 tff(33,plain,
% 0.22/0.41 (![N: $int, H: heap, M: $int] : ((sel(app(H, N), M) = sel(H, M)) | (M = $sum(1, length(H))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.22/0.41 tff(34,plain,
% 0.22/0.41 (![N: $int, H: heap, M: $int] : (($sum(sel(app(H, N), M), $product(-1, sel(H, M))) = 0) | ($sum(M, $product(-1, length(H))) = 1))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[33, 27])).
% 0.22/0.41 tff(35,plain,
% 0.22/0.41 (![N: $int, H: heap, M: $int] : (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[34, 25])).
% 0.22/0.41 tff(36,plain,(
% 0.22/0.41 ![N: $int, H: heap, M: $int] : (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))),
% 0.22/0.41 inference(skolemize,[status(sab)],[35])).
% 0.22/0.41 tff(37,plain,
% 0.22/0.41 (![N: $int, H: heap, M: $int] : (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[36, 23])).
% 0.22/0.41 tff(38,plain,
% 0.22/0.41 (((~![N: $int, H: heap, M: $int] : (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))) | (($sum(M!1, $product(-1, length(H!0))) = 1) | ($sum(sel(H!0, M!1), $product(-1, sel(app(H!0, N!2), M!1))) = 0))) <=> ((~![N: $int, H: heap, M: $int] : (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))) | ($sum(M!1, $product(-1, length(H!0))) = 1) | ($sum(sel(H!0, M!1), $product(-1, sel(app(H!0, N!2), M!1))) = 0))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(39,plain,
% 0.22/0.41 ((~![N: $int, H: heap, M: $int] : (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))) | (($sum(M!1, $product(-1, length(H!0))) = 1) | ($sum(sel(H!0, M!1), $product(-1, sel(app(H!0, N!2), M!1))) = 0))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(40,plain,
% 0.22/0.41 ((~![N: $int, H: heap, M: $int] : (($sum(M, $product(-1, length(H))) = 1) | ($sum(sel(H, M), $product(-1, sel(app(H, N), M))) = 0))) | ($sum(M!1, $product(-1, length(H!0))) = 1) | ($sum(sel(H!0, M!1), $product(-1, sel(app(H!0, N!2), M!1))) = 0)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.22/0.41 tff(41,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[40, 37, 21, 20])).
% 0.22/0.41 % SZS output end Proof
%------------------------------------------------------------------------------