TSTP Solution File: DAT061_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT061_1 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 14:36:34 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : DAT061_1 : TPTP v8.1.0. Released v5.5.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 01:55:45 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 tff(tptp_fun_M_2_type, type, (
% 0.13/0.37 tptp_fun_M_2: $int)).
% 0.13/0.37 tff(tptp_fun_N_1_type, type, (
% 0.13/0.37 tptp_fun_N_1: $int)).
% 0.13/0.37 tff(get_type, type, (
% 0.13/0.37 get: ( array * $int ) > data)).
% 0.13/0.37 tff(tptp_fun_Ar_3_type, type, (
% 0.13/0.37 tptp_fun_Ar_3: array)).
% 0.13/0.37 tff(put_type, type, (
% 0.13/0.37 put: ( array * $int * data ) > array)).
% 0.13/0.37 tff(tptp_fun_D_4_type, type, (
% 0.13/0.37 tptp_fun_D_4: data)).
% 0.13/0.37 tff(1,plain,
% 0.13/0.37 ((~((get(put(Ar!3, M!2, D!4), N!1) = get(Ar!3, N!1)) | $lesseq($sum(N!1, $product(-1, M!2)), 0))) <=> (~((get(put(Ar!3, M!2, D!4), N!1) = get(Ar!3, N!1)) | $lesseq($sum(N!1, $product(-1, M!2)), 0)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(2,plain,
% 0.13/0.37 ((~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq($sum(N, $product(-1, M)), 0))) <=> (~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq($sum(N, $product(-1, M)), 0)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(3,plain,
% 0.13/0.37 ((~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq(N, M))) <=> (~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq($sum(N, $product(-1, M)), 0)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(4,plain,
% 0.13/0.37 ((~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq(N, M))) <=> (~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq(N, M)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(5,plain,
% 0.13/0.37 ((~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | (~$less(M, N)))) <=> (~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq(N, M)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(6,axiom,(~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | (~$less(M, N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','th_lem_7')).
% 0.13/0.37 tff(7,plain,
% 0.13/0.37 (~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq(N, M))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.37 tff(8,plain,
% 0.13/0.37 (~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq(N, M))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.13/0.37 tff(9,plain,
% 0.13/0.37 (~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq(N, M))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.37 tff(10,plain,
% 0.13/0.37 (~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq(N, M))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.13/0.37 tff(11,plain,
% 0.13/0.37 (~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq($sum(N, $product(-1, M)), 0))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.13/0.37 tff(12,plain,
% 0.13/0.37 (~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq($sum(N, $product(-1, M)), 0))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.13/0.37 tff(13,plain,
% 0.13/0.37 (~![D: data, Ar: array, M: $int, N: $int] : ((get(put(Ar, M, D), N) = get(Ar, N)) | $lesseq($sum(N, $product(-1, M)), 0))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.13/0.37 tff(14,plain,(
% 0.13/0.37 ~((get(put(Ar!3, M!2, D!4), N!1) = get(Ar!3, N!1)) | $lesseq($sum(N!1, $product(-1, M!2)), 0))),
% 0.13/0.37 inference(skolemize,[status(sab)],[13])).
% 0.13/0.37 tff(15,plain,
% 0.13/0.37 (~((get(put(Ar!3, M!2, D!4), N!1) = get(Ar!3, N!1)) | $lesseq($sum(N!1, $product(-1, M!2)), 0))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[14, 1])).
% 0.13/0.37 tff(16,plain,
% 0.13/0.37 (~$lesseq($sum(N!1, $product(-1, M!2)), 0)),
% 0.13/0.37 inference(or_elim,[status(thm)],[15])).
% 0.13/0.37 tff(17,plain,
% 0.13/0.37 ((~($sum(N!1, $product(-1, M!2)) = 0)) | $lesseq($sum(N!1, $product(-1, M!2)), 0)),
% 0.13/0.37 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.37 tff(18,plain,
% 0.13/0.37 (~($sum(N!1, $product(-1, M!2)) = 0)),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.13/0.37 tff(19,plain,
% 0.13/0.37 (~(get(put(Ar!3, M!2, D!4), N!1) = get(Ar!3, N!1))),
% 0.13/0.37 inference(or_elim,[status(thm)],[15])).
% 0.13/0.37 tff(20,plain,
% 0.13/0.37 (^[N: $int, D: data, Ar: array, M: $int] : refl((($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M))) <=> (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(21,plain,
% 0.13/0.37 (![N: $int, D: data, Ar: array, M: $int] : (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M))) <=> ![N: $int, D: data, Ar: array, M: $int] : (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M)))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[20])).
% 0.13/0.37 tff(22,plain,
% 0.13/0.37 (^[N: $int, D: data, Ar: array, M: $int] : rewrite(((M = N) | (get(put(Ar, N, D), M) = get(Ar, M))) <=> (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(23,plain,
% 0.13/0.37 (![N: $int, D: data, Ar: array, M: $int] : ((M = N) | (get(put(Ar, N, D), M) = get(Ar, M))) <=> ![N: $int, D: data, Ar: array, M: $int] : (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M)))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.37 tff(24,plain,
% 0.13/0.37 (![N: $int, D: data, Ar: array, M: $int] : ((M = N) | (get(put(Ar, N, D), M) = get(Ar, M))) <=> ![N: $int, D: data, Ar: array, M: $int] : ((M = N) | (get(put(Ar, N, D), M) = get(Ar, M)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(25,plain,
% 0.13/0.37 (^[N: $int, D: data, Ar: array, M: $int] : rewrite(((~(M = N)) => (get(put(Ar, N, D), M) = get(Ar, M))) <=> ((M = N) | (get(put(Ar, N, D), M) = get(Ar, M))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(26,plain,
% 0.13/0.37 (![N: $int, D: data, Ar: array, M: $int] : ((~(M = N)) => (get(put(Ar, N, D), M) = get(Ar, M))) <=> ![N: $int, D: data, Ar: array, M: $int] : ((M = N) | (get(put(Ar, N, D), M) = get(Ar, M)))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.37 tff(27,axiom,(![N: $int, D: data, Ar: array, M: $int] : ((~(M = N)) => (get(put(Ar, N, D), M) = get(Ar, M)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT004=0.ax','ax_19')).
% 0.13/0.37 tff(28,plain,
% 0.13/0.37 (![N: $int, D: data, Ar: array, M: $int] : ((M = N) | (get(put(Ar, N, D), M) = get(Ar, M)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.37 tff(29,plain,
% 0.13/0.37 (![N: $int, D: data, Ar: array, M: $int] : ((M = N) | (get(put(Ar, N, D), M) = get(Ar, M)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.13/0.37 tff(30,plain,
% 0.13/0.37 (![N: $int, D: data, Ar: array, M: $int] : (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.13/0.37 tff(31,plain,(
% 0.13/0.37 ![N: $int, D: data, Ar: array, M: $int] : (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M)))),
% 0.13/0.37 inference(skolemize,[status(sab)],[30])).
% 0.13/0.37 tff(32,plain,
% 0.13/0.37 (![N: $int, D: data, Ar: array, M: $int] : (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.13/0.37 tff(33,plain,
% 0.13/0.37 (((~![N: $int, D: data, Ar: array, M: $int] : (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M)))) | (($sum(N!1, $product(-1, M!2)) = 0) | (get(put(Ar!3, M!2, D!4), N!1) = get(Ar!3, N!1)))) <=> ((~![N: $int, D: data, Ar: array, M: $int] : (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M)))) | ($sum(N!1, $product(-1, M!2)) = 0) | (get(put(Ar!3, M!2, D!4), N!1) = get(Ar!3, N!1)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(34,plain,
% 0.13/0.37 ((~![N: $int, D: data, Ar: array, M: $int] : (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M)))) | (($sum(N!1, $product(-1, M!2)) = 0) | (get(put(Ar!3, M!2, D!4), N!1) = get(Ar!3, N!1)))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(35,plain,
% 0.13/0.37 ((~![N: $int, D: data, Ar: array, M: $int] : (($sum(M, $product(-1, N)) = 0) | (get(put(Ar, N, D), M) = get(Ar, M)))) | ($sum(N!1, $product(-1, M!2)) = 0) | (get(put(Ar!3, M!2, D!4), N!1) = get(Ar!3, N!1))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.13/0.37 tff(36,plain,
% 0.13/0.37 ($false),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[35, 32, 19, 18])).
% 0.13/0.37 % SZS output end Proof
%------------------------------------------------------------------------------