TSTP Solution File: DAT008_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT008_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 14:36:21 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT008_1 : TPTP v8.1.0. Released v5.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n002.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 01:53:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(read_type, type, (
% 0.19/0.38 read: ( array * $int ) > $int)).
% 0.19/0.38 tff(tptp_fun_X_2_type, type, (
% 0.19/0.38 tptp_fun_X_2: $int)).
% 0.19/0.38 tff(tptp_fun_U_1_type, type, (
% 0.19/0.38 tptp_fun_U_1: array)).
% 0.19/0.38 tff(write_type, type, (
% 0.19/0.38 write: ( array * $int * $int ) > array)).
% 0.19/0.38 tff(tptp_fun_V_0_type, type, (
% 0.19/0.38 tptp_fun_V_0: array)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (((![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)) & (U!1 = write(write(V!0, 3, 5), 7, 9))) & $greatereq($sum(X!2, $product(-1, read(U!1, X!2))), 0)) <=> (![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)) & (U!1 = write(write(V!0, 3, 5), 7, 9)) & $greatereq($sum(X!2, $product(-1, read(U!1, X!2))), 0))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 ((~(~$greatereq($sum(X!2, $product(-1, read(U!1, X!2))), 0))) <=> $greatereq($sum(X!2, $product(-1, read(U!1, X!2))), 0)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 ((![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)) & (U!1 = write(write(V!0, 3, 5), 7, 9))) <=> (![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)) & (U!1 = write(write(V!0, 3, 5), 7, 9)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (((![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)) & (U!1 = write(write(V!0, 3, 5), 7, 9))) & (~(~$greatereq($sum(X!2, $product(-1, read(U!1, X!2))), 0)))) <=> ((![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)) & (U!1 = write(write(V!0, 3, 5), 7, 9))) & $greatereq($sum(X!2, $product(-1, read(U!1, X!2))), 0))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[3, 2])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (((![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)) & (U!1 = write(write(V!0, 3, 5), 7, 9))) & (~(~$greatereq($sum(X!2, $product(-1, read(U!1, X!2))), 0)))) <=> (![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)) & (U!1 = write(write(V!0, 3, 5), 7, 9)) & $greatereq($sum(X!2, $product(-1, read(U!1, X!2))), 0))),
% 0.19/0.38 inference(transitivity,[status(thm)],[4, 1])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 ((~![U: array, V: array] : ((~(![W: $int] : (~$greatereq($sum(W, $product(-1, read(V, W))), 0)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$greatereq($sum(X, $product(-1, read(U, X))), 0)))) <=> (~![U: array, V: array] : ((~(![W: $int] : (~$greatereq($sum(W, $product(-1, read(V, W))), 0)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$greatereq($sum(X, $product(-1, read(U, X))), 0))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 ((~![U: array, V: array] : ((~(![W: $int] : (~$lesseq($sum(read(V, W), $product(-1, W)), 0)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$lesseq($sum(read(U, X), $product(-1, X)), 0)))) <=> (~![U: array, V: array] : ((~(![W: $int] : (~$greatereq($sum(W, $product(-1, read(V, W))), 0)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$greatereq($sum(X, $product(-1, read(U, X))), 0))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 ((~![U: array, V: array] : ((~(![W: $int] : (~$lesseq(read(V, W), W)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$lesseq(read(U, X), X)))) <=> (~![U: array, V: array] : ((~(![W: $int] : (~$lesseq($sum(read(V, W), $product(-1, W)), 0)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$lesseq($sum(read(U, X), $product(-1, X)), 0))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 ((~![U: array, V: array] : ((~(![W: $int] : (~$lesseq(read(V, W), W)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$lesseq(read(U, X), X)))) <=> (~![U: array, V: array] : ((~(![W: $int] : (~$lesseq(read(V, W), W)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$lesseq(read(U, X), X))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 ((~![U: array, V: array] : ((![W: $int] : $greater(read(V, W), W) & (U = write(write(V, 3, 5), 7, 9))) => ![X: $int] : $greater(read(U, X), X))) <=> (~![U: array, V: array] : ((~(![W: $int] : (~$lesseq(read(V, W), W)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$lesseq(read(U, X), X))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(11,axiom,(~![U: array, V: array] : ((![W: $int] : $greater(read(V, W), W) & (U = write(write(V, 3, 5), 7, 9))) => ![X: $int] : $greater(read(U, X), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (~![U: array, V: array] : ((~(![W: $int] : (~$lesseq(read(V, W), W)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$lesseq(read(U, X), X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (~![U: array, V: array] : ((~(![W: $int] : (~$lesseq(read(V, W), W)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$lesseq(read(U, X), X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (~![U: array, V: array] : ((~(![W: $int] : (~$lesseq(read(V, W), W)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$lesseq(read(U, X), X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (~![U: array, V: array] : ((~(![W: $int] : (~$lesseq(read(V, W), W)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$lesseq(read(U, X), X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (~![U: array, V: array] : ((~(![W: $int] : (~$lesseq($sum(read(V, W), $product(-1, W)), 0)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$lesseq($sum(read(U, X), $product(-1, X)), 0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (~![U: array, V: array] : ((~(![W: $int] : (~$greatereq($sum(W, $product(-1, read(V, W))), 0)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$greatereq($sum(X, $product(-1, read(U, X))), 0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 7])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~![U: array, V: array] : ((~(![W: $int] : (~$greatereq($sum(W, $product(-1, read(V, W))), 0)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$greatereq($sum(X, $product(-1, read(U, X))), 0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 6])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (~![U: array, V: array] : ((~(![W: $int] : (~$greatereq($sum(W, $product(-1, read(V, W))), 0)) & (U = write(write(V, 3, 5), 7, 9)))) | ![X: $int] : (~$greatereq($sum(X, $product(-1, read(U, X))), 0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 6])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)) & (U!1 = write(write(V!0, 3, 5), 7, 9)) & $greatereq($sum(X!2, $product(-1, read(U!1, X!2))), 0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 5])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ($greatereq($sum(X!2, $product(-1, read(U!1, X!2))), 0)),
% 0.19/0.39 inference(and_elim,[status(thm)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (^[U: array, V: $int, W: $int] : refl(($sum(W, $product(-1, read(write(U, V, W), V))) = 0) <=> ($sum(W, $product(-1, read(write(U, V, W), V))) = 0))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0) <=> ![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (^[U: array, V: $int, W: $int] : trans(monotonicity(rewrite($sum(read(write(U, V, W), V), $product(-1, W)) = $sum($product(-1, W), read(write(U, V, W), V))), (($sum(read(write(U, V, W), V), $product(-1, W)) = 0) <=> ($sum($product(-1, W), read(write(U, V, W), V)) = 0))), rewrite(($sum($product(-1, W), read(write(U, V, W), V)) = 0) <=> ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)), (($sum(read(write(U, V, W), V), $product(-1, W)) = 0) <=> ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![U: array, V: $int, W: $int] : ($sum(read(write(U, V, W), V), $product(-1, W)) = 0) <=> ![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[U: array, V: $int, W: $int] : rewrite((read(write(U, V, W), V) = W) <=> ($sum(read(write(U, V, W), V), $product(-1, W)) = 0))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W) <=> ![U: array, V: $int, W: $int] : ($sum(read(write(U, V, W), V), $product(-1, W)) = 0)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W) <=> ![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(29,axiom,(![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)), file('/export/starexec/sandbox/benchmark/Axioms/DAT001=0.ax','ax1')).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![U: array, V: $int, W: $int] : ($sum(read(write(U, V, W), V), $product(-1, W)) = 0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.19/0.39 tff(33,plain,(
% 0.19/0.39 ![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.19/0.39 inference(skolemize,[status(sab)],[32])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(V!0, 3, 5), 7, 9), 7) = 9)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(V!0, 3, 5), 7, 9), 7) = 9))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (($sum(9, $product(-1, read(write(write(V!0, 3, 5), 7, 9), 7))) = 0) <=> (read(write(write(V!0, 3, 5), 7, 9), 7) = 9)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(9, $product(-1, read(write(write(V!0, 3, 5), 7, 9), 7))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(V!0, 3, 5), 7, 9), 7) = 9))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(9, $product(-1, read(write(write(V!0, 3, 5), 7, 9), 7))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(V!0, 3, 5), 7, 9), 7) = 9))),
% 0.19/0.39 inference(transitivity,[status(thm)],[37, 35])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(9, $product(-1, read(write(write(V!0, 3, 5), 7, 9), 7))) = 0)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(V!0, 3, 5), 7, 9), 7) = 9)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (read(write(write(V!0, 3, 5), 7, 9), 7) = 9),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 5), 3) = 5)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 5), 3) = 5))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (($sum(5, $product(-1, read(write(V!0, 3, 5), 3))) = 0) <=> (read(write(V!0, 3, 5), 3) = 5)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(5, $product(-1, read(write(V!0, 3, 5), 3))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 5), 3) = 5))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(5, $product(-1, read(write(V!0, 3, 5), 3))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 5), 3) = 5))),
% 0.19/0.39 inference(transitivity,[status(thm)],[44, 42])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(5, $product(-1, read(write(V!0, 3, 5), 3))) = 0)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 5), 3) = 5)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (read(write(V!0, 3, 5), 3) = 5),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[47, 34])).
% 0.19/0.39 tff(49,assumption,($lesseq($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))), 0)), introduced(assumption)).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (^[W: $int] : refl((~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)) <=> (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0)) <=> ![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0))),
% 0.19/0.39 inference(and_elim,[status(thm)],[20])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((~![W: $int] : (~$greatereq($sum(W, $product(-1, read(V!0, W))), 0))) | (~$greatereq($sum(X!2, $product(-1, read(V!0, X!2))), 0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (~$greatereq($sum(X!2, $product(-1, read(V!0, X!2))), 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.39 tff(56,assumption,($greatereq($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))), 0)), introduced(assumption)).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (U!1 = write(write(V!0, 3, 5), 7, 9)),
% 0.19/0.39 inference(and_elim,[status(thm)],[20])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (write(write(V!0, 3, 5), 7, 9) = U!1),
% 0.19/0.39 inference(symmetry,[status(thm)],[57])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (read(write(write(V!0, 3, 5), 7, 9), X!2) = read(U!1, X!2)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (read(U!1, X!2) = read(write(write(V!0, 3, 5), 7, 9), X!2)),
% 0.19/0.39 inference(symmetry,[status(thm)],[59])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 ((~(read(U!1, X!2) = read(write(write(V!0, 3, 5), 7, 9), X!2))) | $greatereq($sum(read(U!1, X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))), 0)),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 ($greatereq($sum(read(U!1, X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))), 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[62, 49, 56, 55, 21])).
% 0.19/0.39 tff(64,plain,((~$greatereq($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))), 0)) | (~$lesseq($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (~$greatereq($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))), 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[64, 49])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 ((~($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))) = 0)) | $greatereq($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))), 0)),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (~($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))) = 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (^[X: array, Y: $int, Z: $int, X1: $int] : refl((($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0)) <=> (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0)) <=> ![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (^[X: array, Y: $int, Z: $int, X1: $int] : rewrite((($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0)) <=> (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0)) <=> ![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (^[X: array, Y: $int, Z: $int, X1: $int] : rewrite(((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z))) <=> (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z))) <=> ![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z))) <=> ![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(75,axiom,(![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/DAT001=0.ax','ax2')).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[76, 73])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[77, 71])).
% 0.19/0.39 tff(79,plain,(
% 0.19/0.39 ![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 0.19/0.39 inference(skolemize,[status(sab)],[78])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[79, 69])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 3) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 3) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))) = 0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 ((($sum(X!2, $product(-1, 3)) = 0) | ($sum(read(V!0, X!2), $product(-1, read(write(V!0, 3, 5), X!2))) = 0)) <=> ((X!2 = 3) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))) = 0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 3)) = 0) | ($sum(read(V!0, X!2), $product(-1, read(write(V!0, 3, 5), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 3) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))) = 0)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 3)) = 0) | ($sum(read(V!0, X!2), $product(-1, read(write(V!0, 3, 5), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 3) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))) = 0))),
% 0.19/0.39 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 3)) = 0) | ($sum(read(V!0, X!2), $product(-1, read(write(V!0, 3, 5), X!2))) = 0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 3) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))) = 0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 ((X!2 = 3) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(V!0, X!2))) = 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[86, 80])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 (X!2 = 3),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[87, 67])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 (read(write(V!0, 3, 5), X!2) = read(write(V!0, 3, 5), 3)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (read(write(V!0, 3, 5), X!2) = 5),
% 0.19/0.39 inference(transitivity,[status(thm)],[89, 48])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 ((~(read(write(V!0, 3, 5), X!2) = 5)) | $greatereq(read(write(V!0, 3, 5), X!2), 5)),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 ($greatereq(read(write(V!0, 3, 5), X!2), 5)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 ((~(X!2 = 3)) | $lesseq(X!2, 3)),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 ($lesseq(X!2, 3)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[93, 88])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (read(U!1, X!2) = read(write(write(V!0, 3, 5), 7, 9), X!2)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[57])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 ($greatereq($sum(read(U!1, X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))), 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[61, 95])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[96, 49, 94, 92, 21])).
% 0.19/0.39 tff(98,plain,(~$lesseq($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 ((~($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0)) | $lesseq($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))), 0)),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (~($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 7) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 7) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 ((($sum(X!2, $product(-1, 7)) = 0) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0)) <=> ((X!2 = 7) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 7)) = 0) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 7) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[102])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 7)) = 0) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 7) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0))),
% 0.19/0.40 inference(transitivity,[status(thm)],[103, 101])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 7)) = 0) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 7) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 ((X!2 = 7) | ($sum(read(write(V!0, 3, 5), X!2), $product(-1, read(write(write(V!0, 3, 5), 7, 9), X!2))) = 0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[106, 80])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (X!2 = 7),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[107, 100])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (read(U!1, X!2) = read(write(write(V!0, 3, 5), 7, 9), 7)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[57, 108])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (read(U!1, X!2) = 9),
% 0.19/0.40 inference(transitivity,[status(thm)],[109, 41])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 ((~(read(U!1, X!2) = 9)) | $greatereq(read(U!1, X!2), 9)),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 ($greatereq(read(U!1, X!2), 9)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 ((~(X!2 = 7)) | $lesseq(X!2, 7)),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 ($lesseq(X!2, 7)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[113, 108])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[114, 112, 21])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------