TSTP Solution File: DAT011_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT011_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 14:36:22 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT011_1 : TPTP v8.1.0. Released v5.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 01:26:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(read_type, type, (
% 0.20/0.41 read: ( array * $int ) > $int)).
% 0.20/0.41 tff(tptp_fun_Z_4_type, type, (
% 0.20/0.41 tptp_fun_Z_4: $int)).
% 0.20/0.41 tff(tptp_fun_U_3_type, type, (
% 0.20/0.41 tptp_fun_U_3: array)).
% 0.20/0.41 tff(tptp_fun_X_0_type, type, (
% 0.20/0.41 tptp_fun_X_0: $int)).
% 0.20/0.41 tff(tptp_fun_W_1_type, type, (
% 0.20/0.41 tptp_fun_W_1: $int)).
% 0.20/0.41 tff(write_type, type, (
% 0.20/0.41 write: ( array * $int * $int ) > array)).
% 0.20/0.41 tff(tptp_fun_V_2_type, type, (
% 0.20/0.41 tptp_fun_V_2: array)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (((![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0)))) & (U!3 = write(V!2, $sum(1, X!0), 3))) & (~((~$lesseq(read(U!3, Z!4), 0)) | (~($lesseq($sum(W!1, $product(-1, Z!4)), 0) & $greatereq($sum(X!0, $product(-1, Z!4)), -1)))))) <=> (![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0)))) & (U!3 = write(V!2, $sum(1, X!0), 3)) & (~((~$lesseq(read(U!3, Z!4), 0)) | (~($lesseq($sum(W!1, $product(-1, Z!4)), 0) & $greatereq($sum(X!0, $product(-1, Z!4)), -1))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 ((~((~$lesseq(read(U!3, Z!4), 0)) | (~($greatereq($sum(Z!4, $product(-1, W!1)), 0) & $greatereq($sum(X!0, $product(-1, Z!4)), -1))))) <=> (~((~$lesseq(read(U!3, Z!4), 0)) | (~($lesseq($sum(W!1, $product(-1, Z!4)), 0) & $greatereq($sum(X!0, $product(-1, Z!4)), -1)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 ((![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $greatereq($sum(X!0, $product(-1, Y)), 0)))) & (U!3 = write(V!2, $sum(1, X!0), 3))) <=> (![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0)))) & (U!3 = write(V!2, $sum(1, X!0), 3)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (((![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $greatereq($sum(X!0, $product(-1, Y)), 0)))) & (U!3 = write(V!2, $sum(1, X!0), 3))) & (~((~$lesseq(read(U!3, Z!4), 0)) | (~($greatereq($sum(Z!4, $product(-1, W!1)), 0) & $greatereq($sum(X!0, $product(-1, Z!4)), -1)))))) <=> ((![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0)))) & (U!3 = write(V!2, $sum(1, X!0), 3))) & (~((~$lesseq(read(U!3, Z!4), 0)) | (~($lesseq($sum(W!1, $product(-1, Z!4)), 0) & $greatereq($sum(X!0, $product(-1, Z!4)), -1))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[3, 2])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (((![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $greatereq($sum(X!0, $product(-1, Y)), 0)))) & (U!3 = write(V!2, $sum(1, X!0), 3))) & (~((~$lesseq(read(U!3, Z!4), 0)) | (~($greatereq($sum(Z!4, $product(-1, W!1)), 0) & $greatereq($sum(X!0, $product(-1, Z!4)), -1)))))) <=> (![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0)))) & (U!3 = write(V!2, $sum(1, X!0), 3)) & (~((~$lesseq(read(U!3, Z!4), 0)) | (~($lesseq($sum(W!1, $product(-1, Z!4)), 0) & $greatereq($sum(X!0, $product(-1, Z!4)), -1))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[4, 1])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 ((~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Y)), 0)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($greatereq($sum(Z, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Z)), -1)))))) <=> (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Y)), 0)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($greatereq($sum(Z, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Z)), -1))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 ((~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($lesseq($sum(W, $product(-1, Y)), 0) & $lesseq($sum(Y, $product(-1, X)), 0)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($lesseq($sum(W, $product(-1, Z)), 0) & $lesseq($sum(Z, $product(-1, X)), 1)))))) <=> (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Y)), 0)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($greatereq($sum(Z, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Z)), -1))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 ((~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($lesseq(W, Y) & $lesseq(Y, X)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($lesseq(W, Z) & $lesseq(Z, $sum(1, X))))))) <=> (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($lesseq($sum(W, $product(-1, Y)), 0) & $lesseq($sum(Y, $product(-1, X)), 0)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($lesseq($sum(W, $product(-1, Z)), 0) & $lesseq($sum(Z, $product(-1, X)), 1))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 ((~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($lesseq(W, Y) & $lesseq(Y, X)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($lesseq(W, Z) & $lesseq(Z, $sum(1, X))))))) <=> (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($lesseq(W, Y) & $lesseq(Y, X)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($lesseq(W, Z) & $lesseq(Z, $sum(1, X)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ((~![U: array, V: array, W: $int, X: $int] : ((![Y: $int] : (($lesseq(W, Y) & $lesseq(Y, X)) => $greater(read(V, Y), 0)) & (U = write(V, $sum(X, 1), 3))) => ![Z: $int] : (($lesseq(W, Z) & $lesseq(Z, $sum(X, 1))) => $greater(read(U, Z), 0)))) <=> (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($lesseq(W, Y) & $lesseq(Y, X)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($lesseq(W, Z) & $lesseq(Z, $sum(1, X)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(11,axiom,(~![U: array, V: array, W: $int, X: $int] : ((![Y: $int] : (($lesseq(W, Y) & $lesseq(Y, X)) => $greater(read(V, Y), 0)) & (U = write(V, $sum(X, 1), 3))) => ![Z: $int] : (($lesseq(W, Z) & $lesseq(Z, $sum(X, 1))) => $greater(read(U, Z), 0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($lesseq(W, Y) & $lesseq(Y, X)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($lesseq(W, Z) & $lesseq(Z, $sum(1, X))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($lesseq(W, Y) & $lesseq(Y, X)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($lesseq(W, Z) & $lesseq(Z, $sum(1, X))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($lesseq(W, Y) & $lesseq(Y, X)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($lesseq(W, Z) & $lesseq(Z, $sum(1, X))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($lesseq(W, Y) & $lesseq(Y, X)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($lesseq(W, Z) & $lesseq(Z, $sum(1, X))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($lesseq($sum(W, $product(-1, Y)), 0) & $lesseq($sum(Y, $product(-1, X)), 0)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($lesseq($sum(W, $product(-1, Z)), 0) & $lesseq($sum(Z, $product(-1, X)), 1)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Y)), 0)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($greatereq($sum(Z, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Z)), -1)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 7])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Y)), 0)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($greatereq($sum(Z, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Z)), -1)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 6])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (~![U: array, V: array, W: $int, X: $int] : ((~(![Y: $int] : ((~$lesseq(read(V, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Y)), 0)))) & (U = write(V, $sum(1, X), 3)))) | ![Z: $int] : ((~$lesseq(read(U, Z), 0)) | (~($greatereq($sum(Z, $product(-1, W)), 0) & $greatereq($sum(X, $product(-1, Z)), -1)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 6])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0)))) & (U!3 = write(V!2, $sum(1, X!0), 3)) & (~((~$lesseq(read(U!3, Z!4), 0)) | (~($lesseq($sum(W!1, $product(-1, Z!4)), 0) & $greatereq($sum(X!0, $product(-1, Z!4)), -1)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 5])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (~((~$lesseq(read(U!3, Z!4), 0)) | (~($lesseq($sum(W!1, $product(-1, Z!4)), 0) & $greatereq($sum(X!0, $product(-1, Z!4)), -1))))),
% 0.20/0.41 inference(and_elim,[status(thm)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 ($lesseq(read(U!3, Z!4), 0)),
% 0.20/0.41 inference(or_elim,[status(thm)],[21])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 ((~$greatereq(read(U!3, Z!4), 3)) | (~$lesseq(read(U!3, Z!4), 0))),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (~$greatereq(read(U!3, Z!4), 3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (^[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))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (![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)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (^[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)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (![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)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (^[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))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (![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)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![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)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(32,axiom,(![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)), file('/export/starexec/sandbox2/benchmark/Axioms/DAT001=0.ax','ax1')).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![U: array, V: $int, W: $int] : ($sum(read(write(U, V, W), V), $product(-1, W)) = 0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[34, 28])).
% 0.20/0.42 tff(36,plain,(
% 0.20/0.42 ![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.20/0.42 inference(skolemize,[status(sab)],[35])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0)) = 3)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0)) = 3))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (($sum(3, $product(-1, read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0)))) = 0) <=> (read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0)) = 3)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(3, $product(-1, read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0)))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0)) = 3))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(3, $product(-1, read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0)))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0)) = 3))),
% 0.20/0.42 inference(transitivity,[status(thm)],[40, 38])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(3, $product(-1, read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0)))) = 0)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0)) = 3)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0)) = 3),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (U!3 = write(V!2, $sum(1, X!0), 3)),
% 0.20/0.42 inference(and_elim,[status(thm)],[20])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (write(V!2, $sum(1, X!0), 3) = U!3),
% 0.20/0.42 inference(symmetry,[status(thm)],[45])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (read(write(V!2, $sum(1, X!0), 3), Z!4) = read(U!3, Z!4)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (read(U!3, Z!4) = read(write(V!2, $sum(1, X!0), 3), Z!4)),
% 0.20/0.42 inference(symmetry,[status(thm)],[47])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 ((~(read(U!3, Z!4) = read(write(V!2, $sum(1, X!0), 3), Z!4))) | $greatereq($sum(read(U!3, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))), 0)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 ($greatereq($sum(read(U!3, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.42 tff(51,assumption,(~($sum(X!0, $product(-1, Z!4)) = -1)), introduced(assumption)).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(59,axiom,(![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT001=0.ax','ax2')).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[60, 57])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[61, 55])).
% 0.20/0.42 tff(63,plain,(
% 0.20/0.42 ![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))),
% 0.20/0.42 inference(skolemize,[status(sab)],[62])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (((~![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!0, $product(-1, Z!4)) = -1) | ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 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(X!0, $product(-1, Z!4)) = -1) | ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 ((($sum(Z!4, $product(-1, $sum(1, X!0))) = 0) | ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 0)) <=> (($sum(X!0, $product(-1, Z!4)) = -1) | ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (((~![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(Z!4, $product(-1, $sum(1, X!0))) = 0) | ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 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(X!0, $product(-1, Z!4)) = -1) | ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 0)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (((~![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(Z!4, $product(-1, $sum(1, X!0))) = 0) | ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 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(X!0, $product(-1, Z!4)) = -1) | ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 0))),
% 0.20/0.42 inference(transitivity,[status(thm)],[67, 65])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 ((~![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(Z!4, $product(-1, $sum(1, X!0))) = 0) | ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 0))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 ((~![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!0, $product(-1, Z!4)) = -1) | ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (($sum(X!0, $product(-1, Z!4)) = -1) | ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[70, 64])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 ($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 0),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[71, 51])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((~($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))) = 0)) | $lesseq($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))), 0)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 ($lesseq($sum(read(V!2, Z!4), $product(-1, read(write(V!2, $sum(1, X!0), 3), Z!4))), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ($lesseq($sum(W!1, $product(-1, Z!4)), 0) & $greatereq($sum(X!0, $product(-1, Z!4)), -1)),
% 0.20/0.42 inference(or_elim,[status(thm)],[21])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 ($greatereq($sum(X!0, $product(-1, Z!4)), -1)),
% 0.20/0.42 inference(and_elim,[status(thm)],[75])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (($sum(X!0, $product(-1, Z!4)) = -1) | (~$lesseq($sum(X!0, $product(-1, Z!4)), -1)) | (~$greatereq($sum(X!0, $product(-1, Z!4)), -1))),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (($sum(X!0, $product(-1, Z!4)) = -1) | (~$lesseq($sum(X!0, $product(-1, Z!4)), -1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (~$lesseq($sum(X!0, $product(-1, Z!4)), -1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[78, 51])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ($greatereq($sum(X!0, $product(-1, Z!4)), 0) | $lesseq($sum(X!0, $product(-1, Z!4)), -1)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 ($greatereq($sum(X!0, $product(-1, Z!4)), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 ($lesseq($sum(W!1, $product(-1, Z!4)), 0)),
% 0.20/0.42 inference(and_elim,[status(thm)],[75])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (^[Y: $int] : refl(((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0))) <=> ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0))) <=> ![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (^[Y: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0)) <=> (~((~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0))))), ((~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0))) <=> (~(~((~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0))))))), rewrite((~(~((~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0))))) <=> ((~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))), ((~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0))) <=> ((~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0))))), (((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0)))) <=> ((~$lesseq(read(V!2, Y), 0)) | ((~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))))), rewrite(((~$lesseq(read(V!2, Y), 0)) | ((~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))) <=> ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))), (((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0)))) <=> ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0)))) <=> ![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~($greatereq($sum(Y, $product(-1, W!1)), 0) & $lesseq($sum(Y, $product(-1, X!0)), 0))))),
% 0.20/0.42 inference(and_elim,[status(thm)],[20])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (((~![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))) | ((~$lesseq(read(V!2, Z!4), 0)) | (~$greatereq($sum(X!0, $product(-1, Z!4)), 0)) | (~$lesseq($sum(W!1, $product(-1, Z!4)), 0)))) <=> ((~![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))) | (~$lesseq(read(V!2, Z!4), 0)) | (~$greatereq($sum(X!0, $product(-1, Z!4)), 0)) | (~$lesseq($sum(W!1, $product(-1, Z!4)), 0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (((~$lesseq(read(V!2, Z!4), 0)) | (~$greatereq($sum(X!0, $product(-1, Z!4)), 0)) | (~$lesseq($sum(W!1, $product(-1, Z!4)), 0))) <=> ((~$lesseq(read(V!2, Z!4), 0)) | (~$greatereq($sum(X!0, $product(-1, Z!4)), 0)) | (~$lesseq($sum(W!1, $product(-1, Z!4)), 0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 ((~$greatereq($sum(Z!4, $product(-1, W!1)), 0)) <=> (~$lesseq($sum(W!1, $product(-1, Z!4)), 0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 ((~$lesseq($sum(Z!4, $product(-1, X!0)), 0)) <=> (~$greatereq($sum(X!0, $product(-1, Z!4)), 0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (((~$lesseq(read(V!2, Z!4), 0)) | (~$lesseq($sum(Z!4, $product(-1, X!0)), 0)) | (~$greatereq($sum(Z!4, $product(-1, W!1)), 0))) <=> ((~$lesseq(read(V!2, Z!4), 0)) | (~$greatereq($sum(X!0, $product(-1, Z!4)), 0)) | (~$lesseq($sum(W!1, $product(-1, Z!4)), 0)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[93, 92])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (((~$lesseq(read(V!2, Z!4), 0)) | (~$lesseq($sum(Z!4, $product(-1, X!0)), 0)) | (~$greatereq($sum(Z!4, $product(-1, W!1)), 0))) <=> ((~$lesseq(read(V!2, Z!4), 0)) | (~$greatereq($sum(X!0, $product(-1, Z!4)), 0)) | (~$lesseq($sum(W!1, $product(-1, Z!4)), 0)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[94, 91])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (((~![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))) | ((~$lesseq(read(V!2, Z!4), 0)) | (~$lesseq($sum(Z!4, $product(-1, X!0)), 0)) | (~$greatereq($sum(Z!4, $product(-1, W!1)), 0)))) <=> ((~![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))) | ((~$lesseq(read(V!2, Z!4), 0)) | (~$greatereq($sum(X!0, $product(-1, Z!4)), 0)) | (~$lesseq($sum(W!1, $product(-1, Z!4)), 0))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (((~![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))) | ((~$lesseq(read(V!2, Z!4), 0)) | (~$lesseq($sum(Z!4, $product(-1, X!0)), 0)) | (~$greatereq($sum(Z!4, $product(-1, W!1)), 0)))) <=> ((~![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))) | (~$lesseq(read(V!2, Z!4), 0)) | (~$greatereq($sum(X!0, $product(-1, Z!4)), 0)) | (~$lesseq($sum(W!1, $product(-1, Z!4)), 0)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[96, 90])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 ((~![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))) | ((~$lesseq(read(V!2, Z!4), 0)) | (~$lesseq($sum(Z!4, $product(-1, X!0)), 0)) | (~$greatereq($sum(Z!4, $product(-1, W!1)), 0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 ((~![Y: $int] : ((~$lesseq(read(V!2, Y), 0)) | (~$lesseq($sum(Y, $product(-1, X!0)), 0)) | (~$greatereq($sum(Y, $product(-1, W!1)), 0)))) | (~$lesseq(read(V!2, Z!4), 0)) | (~$greatereq($sum(X!0, $product(-1, Z!4)), 0)) | (~$lesseq($sum(W!1, $product(-1, Z!4)), 0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (~$lesseq(read(V!2, Z!4), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[99, 89, 82, 81])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[22, 100, 74, 50])).
% 0.20/0.42 tff(102,plain,($sum(X!0, $product(-1, Z!4)) = -1), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((~($sum(X!0, $product(-1, Z!4)) = -1)) | $lesseq($sum(X!0, $product(-1, Z!4)), -1)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 ($lesseq($sum(X!0, $product(-1, Z!4)), -1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 ($sum(1, X!0) = Z!4),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[76, 104])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (Z!4 = $sum(1, X!0)),
% 0.20/0.42 inference(symmetry,[status(thm)],[105])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (read(U!3, Z!4) = read(write(V!2, $sum(1, X!0), 3), $sum(1, X!0))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[45, 106])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (read(U!3, Z!4) = 3),
% 0.20/0.42 inference(transitivity,[status(thm)],[107, 44])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 ((~(read(U!3, Z!4) = 3)) | $greatereq(read(U!3, Z!4), 3)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[109, 108, 24])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------