TSTP Solution File: DAT009_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT009_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : DAT009_1 : TPTP v8.1.0. Released v5.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 01:52:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(read_type, type, (
% 0.12/0.39 read: ( array * $int ) > $int)).
% 0.12/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.12/0.39 tptp_fun_Y_3: $int)).
% 0.12/0.39 tff(tptp_fun_U_2_type, type, (
% 0.12/0.39 tptp_fun_U_2: array)).
% 0.12/0.39 tff(write_type, type, (
% 0.12/0.39 write: ( array * $int * $int ) > array)).
% 0.12/0.39 tff(tptp_fun_W_0_type, type, (
% 0.12/0.39 tptp_fun_W_0: $int)).
% 0.12/0.39 tff(tptp_fun_V_1_type, type, (
% 0.12/0.39 tptp_fun_V_1: array)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (((![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)) & (U!2 = write(V!1, W!0, $sum(3, W!0)))) & $greatereq($sum(Y!3, $product(-1, read(U!2, Y!3))), 0)) <=> (![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)) & (U!2 = write(V!1, W!0, $sum(3, W!0))) & $greatereq($sum(Y!3, $product(-1, read(U!2, Y!3))), 0))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 ((~(~$greatereq($sum(Y!3, $product(-1, read(U!2, Y!3))), 0))) <=> $greatereq($sum(Y!3, $product(-1, read(U!2, Y!3))), 0)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 ((![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)) & (U!2 = write(V!1, W!0, $sum(3, W!0)))) <=> (![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)) & (U!2 = write(V!1, W!0, $sum(3, W!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (((![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)) & (U!2 = write(V!1, W!0, $sum(3, W!0)))) & (~(~$greatereq($sum(Y!3, $product(-1, read(U!2, Y!3))), 0)))) <=> ((![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)) & (U!2 = write(V!1, W!0, $sum(3, W!0)))) & $greatereq($sum(Y!3, $product(-1, read(U!2, Y!3))), 0))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[3, 2])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (((![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)) & (U!2 = write(V!1, W!0, $sum(3, W!0)))) & (~(~$greatereq($sum(Y!3, $product(-1, read(U!2, Y!3))), 0)))) <=> (![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)) & (U!2 = write(V!1, W!0, $sum(3, W!0))) & $greatereq($sum(Y!3, $product(-1, read(U!2, Y!3))), 0))),
% 0.12/0.39 inference(transitivity,[status(thm)],[4, 1])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 ((~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$greatereq($sum(X, $product(-1, read(V, X))), 0)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$greatereq($sum(Y, $product(-1, read(U, Y))), 0)))) <=> (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$greatereq($sum(X, $product(-1, read(V, X))), 0)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$greatereq($sum(Y, $product(-1, read(U, Y))), 0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 ((~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$lesseq($sum(read(V, X), $product(-1, X)), 0)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$lesseq($sum(read(U, Y), $product(-1, Y)), 0)))) <=> (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$greatereq($sum(X, $product(-1, read(V, X))), 0)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$greatereq($sum(Y, $product(-1, read(U, Y))), 0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$lesseq(read(V, X), X)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$lesseq(read(U, Y), Y)))) <=> (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$lesseq($sum(read(V, X), $product(-1, X)), 0)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$lesseq($sum(read(U, Y), $product(-1, Y)), 0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 ((~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$lesseq(read(V, X), X)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$lesseq(read(U, Y), Y)))) <=> (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$lesseq(read(V, X), X)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$lesseq(read(U, Y), Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ((~![U: array, V: array, W: $int] : ((![X: $int] : $greater(read(V, X), X) & (U = write(V, W, $sum(W, 3)))) => ![Y: $int] : $greater(read(U, Y), Y))) <=> (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$lesseq(read(V, X), X)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$lesseq(read(U, Y), Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(11,axiom,(~![U: array, V: array, W: $int] : ((![X: $int] : $greater(read(V, X), X) & (U = write(V, W, $sum(W, 3)))) => ![Y: $int] : $greater(read(U, Y), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$lesseq(read(V, X), X)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$lesseq(read(U, Y), Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$lesseq(read(V, X), X)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$lesseq(read(U, Y), Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$lesseq(read(V, X), X)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$lesseq(read(U, Y), Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$lesseq(read(V, X), X)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$lesseq(read(U, Y), Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$lesseq($sum(read(V, X), $product(-1, X)), 0)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$lesseq($sum(read(U, Y), $product(-1, Y)), 0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$greatereq($sum(X, $product(-1, read(V, X))), 0)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$greatereq($sum(Y, $product(-1, read(U, Y))), 0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 7])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$greatereq($sum(X, $product(-1, read(V, X))), 0)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$greatereq($sum(Y, $product(-1, read(U, Y))), 0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[17, 6])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (~![U: array, V: array, W: $int] : ((~(![X: $int] : (~$greatereq($sum(X, $product(-1, read(V, X))), 0)) & (U = write(V, W, $sum(3, W))))) | ![Y: $int] : (~$greatereq($sum(Y, $product(-1, read(U, Y))), 0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 6])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)) & (U!2 = write(V!1, W!0, $sum(3, W!0))) & $greatereq($sum(Y!3, $product(-1, read(U!2, Y!3))), 0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 5])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 ($greatereq($sum(Y!3, $product(-1, read(U!2, Y!3))), 0)),
% 0.12/0.39 inference(and_elim,[status(thm)],[20])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (^[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))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![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)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (^[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)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![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)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (^[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))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![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)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![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)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 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')).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![U: array, V: $int, W: $int] : ($sum(read(write(U, V, W), V), $product(-1, W)) = 0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.12/0.39 tff(33,plain,(
% 0.12/0.39 ![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.12/0.39 inference(skolemize,[status(sab)],[32])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = -3)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = -3))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (($sum(3, $sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0)))) = 0) <=> ($sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = -3)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ($sum($sum(3, W!0), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = $sum(3, $sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (($sum($sum(3, W!0), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = 0) <=> ($sum(3, $sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0)))) = 0)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[37])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (($sum($sum(3, W!0), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = 0) <=> ($sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = -3)),
% 0.12/0.39 inference(transitivity,[status(thm)],[38, 36])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum($sum(3, W!0), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = -3))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[39])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum($sum(3, W!0), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = -3))),
% 0.12/0.39 inference(transitivity,[status(thm)],[40, 35])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum($sum(3, W!0), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = 0)),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = -3)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 ($sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = -3),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[43, 34])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 ((~($sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))) = -3)) | $lesseq($sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))), -3)),
% 0.12/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 ($lesseq($sum(W!0, $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))), -3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (^[X: $int] : refl((~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)) <=> (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0)) <=> ![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0))),
% 0.12/0.39 inference(and_elim,[status(thm)],[20])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 ((~![X: $int] : (~$greatereq($sum(X, $product(-1, read(V!1, X))), 0))) | (~$greatereq($sum(Y!3, $product(-1, read(V!1, Y!3))), 0))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (~$greatereq($sum(Y!3, $product(-1, read(V!1, Y!3))), 0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.12/0.39 tff(53,assumption,($lesseq($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))), 0)), introduced(assumption)).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (U!2 = write(V!1, W!0, $sum(3, W!0))),
% 0.12/0.39 inference(and_elim,[status(thm)],[20])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (write(V!1, W!0, $sum(3, W!0)) = U!2),
% 0.12/0.39 inference(symmetry,[status(thm)],[54])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (read(write(V!1, W!0, $sum(3, W!0)), Y!3) = read(U!2, Y!3)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[55])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (read(U!2, Y!3) = read(write(V!1, W!0, $sum(3, W!0)), Y!3)),
% 0.12/0.39 inference(symmetry,[status(thm)],[56])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 ((~(read(U!2, Y!3) = read(write(V!1, W!0, $sum(3, W!0)), Y!3))) | $greatereq($sum(read(U!2, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))), 0)),
% 0.12/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 ($greatereq($sum(read(U!2, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))), 0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(theory_lemma,[status(thm)],[59, 53, 52, 21])).
% 0.12/0.39 tff(61,plain,(~$lesseq($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 ((~($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0)) | $lesseq($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))), 0)),
% 0.12/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (~($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (^[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)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[64])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (^[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)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (![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))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (^[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)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(71,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')).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[72, 69])).
% 0.19/0.40 tff(74,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))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[73, 67])).
% 0.19/0.40 tff(75,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))),
% 0.19/0.40 inference(skolemize,[status(sab)],[74])).
% 0.19/0.40 tff(76,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))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.19/0.40 tff(77,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(W!0, $product(-1, Y!3)) = 0) | ($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(W!0, $product(-1, Y!3)) = 0) | ($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ((($sum(Y!3, $product(-1, W!0)) = 0) | ($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0)) <=> (($sum(W!0, $product(-1, Y!3)) = 0) | ($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(79,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(Y!3, $product(-1, W!0)) = 0) | ($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(W!0, $product(-1, Y!3)) = 0) | ($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.40 tff(80,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(Y!3, $product(-1, W!0)) = 0) | ($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(W!0, $product(-1, Y!3)) = 0) | ($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0))),
% 0.19/0.40 inference(transitivity,[status(thm)],[79, 77])).
% 0.19/0.40 tff(81,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(Y!3, $product(-1, W!0)) = 0) | ($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(82,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(W!0, $product(-1, Y!3)) = 0) | ($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (($sum(W!0, $product(-1, Y!3)) = 0) | ($sum(read(V!1, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), Y!3))) = 0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[82, 76])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ($sum(W!0, $product(-1, Y!3)) = 0),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[83, 63])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 ((~($sum(W!0, $product(-1, Y!3)) = 0)) | $lesseq($sum(W!0, $product(-1, Y!3)), 0)),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 ($lesseq($sum(W!0, $product(-1, Y!3)), 0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ((~($sum(W!0, $product(-1, Y!3)) = 0)) | $greatereq($sum(W!0, $product(-1, Y!3)), 0)),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ($greatereq($sum(W!0, $product(-1, Y!3)), 0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (W!0 = Y!3),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[88, 86])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (read(write(V!1, W!0, $sum(3, W!0)), W!0) = read(U!2, Y!3)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[55, 89])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (read(U!2, Y!3) = read(write(V!1, W!0, $sum(3, W!0)), W!0)),
% 0.19/0.40 inference(symmetry,[status(thm)],[90])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~(read(U!2, Y!3) = read(write(V!1, W!0, $sum(3, W!0)), W!0))) | $greatereq($sum(read(U!2, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))), 0)),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 ($greatereq($sum(read(U!2, Y!3), $product(-1, read(write(V!1, W!0, $sum(3, W!0)), W!0))), 0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[88, 93, 46, 21])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------