TSTP Solution File: DAT017_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT017_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 14:36:23 EDT 2022
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT017_1 : TPTP v8.1.0. Released v5.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 01:27:16 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(read_type, type, (
% 0.14/0.41 read: ( array * $int ) > $int)).
% 0.14/0.41 tff(tptp_fun_W_2_type, type, (
% 0.14/0.41 tptp_fun_W_2: $int)).
% 0.14/0.41 tff(tptp_fun_V_3_type, type, (
% 0.14/0.41 tptp_fun_V_3: array)).
% 0.14/0.41 tff(tptp_fun_X_1_type, type, (
% 0.14/0.41 tptp_fun_X_1: $int)).
% 0.14/0.41 tff(write_type, type, (
% 0.14/0.41 write: ( array * $int * $int ) > array)).
% 0.14/0.41 tff(tptp_fun_Y_0_type, type, (
% 0.14/0.41 tptp_fun_Y_0: $int)).
% 0.14/0.41 tff(tptp_fun_U_4_type, type, (
% 0.14/0.41 tptp_fun_U_4: array)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 (^[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))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (![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)),
% 0.14/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (^[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)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (![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)),
% 0.14/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (^[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))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (![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)),
% 0.14/0.41 inference(quant_intro,[status(thm)],[5])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (![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)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(8,axiom,(![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)), file('/export/starexec/sandbox2/benchmark/Axioms/DAT001=0.ax','ax1')).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (![U: array, V: $int, W: $int] : ($sum(read(write(U, V, W), V), $product(-1, W)) = 0)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.14/0.41 tff(12,plain,(
% 0.14/0.41 ![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.14/0.41 inference(skolemize,[status(sab)],[11])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2) = 0))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 (($product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2)) = 0) <=> (read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2) = 0)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 ($sum(0, $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2))) = $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 (($sum(0, $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2))) = 0) <=> ($product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2)) = 0)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[16])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 (($sum(0, $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2))) = 0) <=> (read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2) = 0)),
% 0.14/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(0, $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2) = 0))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(0, $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2) = 0))),
% 0.14/0.41 inference(transitivity,[status(thm)],[19, 14])).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(0, $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2))) = 0)),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2) = 0)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 (read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2) = 0),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[22, 13])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 ((((~($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0)) & (U!4 = write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0))) & ![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0)) <=> ((~($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0)) & (U!4 = write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0)) & ![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 (^[Z: $int] : rewrite((~(~($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0))) <=> ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 (![Z: $int] : (~(~($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0))) <=> ![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0)),
% 0.14/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 ((~(~((~($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0)) & (U!4 = write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0))))) <=> ((~($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0)) & (U!4 = write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 (((~(~((~($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0)) & (U!4 = write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0))))) & ![Z: $int] : (~(~($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0)))) <=> (((~($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0)) & (U!4 = write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0))) & ![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[27, 26])).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 (((~(~((~($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0)) & (U!4 = write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0))))) & ![Z: $int] : (~(~($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0)))) <=> ((~($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0)) & (U!4 = write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0)) & ![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0))),
% 0.14/0.41 inference(transitivity,[status(thm)],[28, 24])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 ((~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~($sum(read(V, X), $product(-1, read(V, W))) = 0)) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~($sum(read(V, Z), $product(-1, read(U, Z))) = 0)))) <=> (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~($sum(read(V, X), $product(-1, read(V, W))) = 0)) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~($sum(read(V, Z), $product(-1, read(U, Z))) = 0))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 ((~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~($sum(read(V, W), $product(-1, read(V, X))) = 0)) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~($sum(read(U, Z), $product(-1, read(V, Z))) = 0)))) <=> (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~($sum(read(V, X), $product(-1, read(V, W))) = 0)) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~($sum(read(V, Z), $product(-1, read(U, Z))) = 0))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 ((~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~(read(V, W) = read(V, X))) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~(read(U, Z) = read(V, Z))))) <=> (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~($sum(read(V, W), $product(-1, read(V, X))) = 0)) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~($sum(read(U, Z), $product(-1, read(V, Z))) = 0))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 ((~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~(read(V, W) = read(V, X))) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~(read(U, Z) = read(V, Z))))) <=> (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~(read(V, W) = read(V, X))) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~(read(U, Z) = read(V, Z)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(34,plain,
% 0.14/0.41 ((~![U: array, V: array, W: $int, X: $int, Y: $int] : (((~(read(V, W) = read(V, X))) & (U = write(write(write(V, X, 0), Y, $sum(read(V, Y), 1)), W, 0))) => ?[Z: $int] : (~(read(U, Z) = read(V, Z))))) <=> (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~(read(V, W) = read(V, X))) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~(read(U, Z) = read(V, Z)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(35,axiom,(~![U: array, V: array, W: $int, X: $int, Y: $int] : (((~(read(V, W) = read(V, X))) & (U = write(write(write(V, X, 0), Y, $sum(read(V, Y), 1)), W, 0))) => ?[Z: $int] : (~(read(U, Z) = read(V, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~(read(V, W) = read(V, X))) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~(read(U, Z) = read(V, Z))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~(read(V, W) = read(V, X))) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~(read(U, Z) = read(V, Z))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.14/0.41 tff(38,plain,
% 0.14/0.41 (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~(read(V, W) = read(V, X))) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~(read(U, Z) = read(V, Z))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.14/0.41 tff(39,plain,
% 0.14/0.41 (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~(read(V, W) = read(V, X))) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~(read(U, Z) = read(V, Z))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.14/0.41 tff(40,plain,
% 0.14/0.41 (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~($sum(read(V, W), $product(-1, read(V, X))) = 0)) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~($sum(read(U, Z), $product(-1, read(V, Z))) = 0)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.14/0.41 tff(41,plain,
% 0.14/0.41 (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~($sum(read(V, X), $product(-1, read(V, W))) = 0)) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~($sum(read(V, Z), $product(-1, read(U, Z))) = 0)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[40, 31])).
% 0.14/0.41 tff(42,plain,
% 0.14/0.41 (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~($sum(read(V, X), $product(-1, read(V, W))) = 0)) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~($sum(read(V, Z), $product(-1, read(U, Z))) = 0)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[41, 30])).
% 0.14/0.41 tff(43,plain,
% 0.14/0.41 (~![U: array, V: array, W: $int, X: $int, Y: $int] : ((~((~($sum(read(V, X), $product(-1, read(V, W))) = 0)) & (U = write(write(write(V, X, 0), Y, $sum(1, read(V, Y))), W, 0)))) | ?[Z: $int] : (~($sum(read(V, Z), $product(-1, read(U, Z))) = 0)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[42, 30])).
% 0.14/0.41 tff(44,plain,
% 0.14/0.41 ((~($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0)) & (U!4 = write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0)) & ![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[43, 29])).
% 0.14/0.41 tff(45,plain,
% 0.14/0.41 (U!4 = write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0)),
% 0.14/0.41 inference(and_elim,[status(thm)],[44])).
% 0.14/0.41 tff(46,plain,
% 0.14/0.41 (read(U!4, W!2) = read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), W!2)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[45])).
% 0.14/0.41 tff(47,plain,
% 0.14/0.41 (^[Z: $int] : refl(($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0) <=> ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(48,plain,
% 0.14/0.41 (![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0) <=> ![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0)),
% 0.14/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.14/0.41 tff(49,plain,
% 0.14/0.41 (![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0)),
% 0.14/0.41 inference(and_elim,[status(thm)],[44])).
% 0.14/0.41 tff(50,plain,
% 0.14/0.41 (![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.14/0.41 tff(51,plain,
% 0.14/0.41 ((~![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0)) | ($sum(read(V!3, W!2), $product(-1, read(U!4, W!2))) = 0)),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(52,plain,
% 0.14/0.41 ($sum(read(V!3, W!2), $product(-1, read(U!4, W!2))) = 0),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.14/0.41 tff(53,plain,
% 0.14/0.41 ((~($sum(read(V!3, W!2), $product(-1, read(U!4, W!2))) = 0)) | $lesseq($sum(read(V!3, W!2), $product(-1, read(U!4, W!2))), 0)),
% 0.14/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.41 tff(54,plain,
% 0.14/0.41 ($lesseq($sum(read(V!3, W!2), $product(-1, read(U!4, W!2))), 0)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.14/0.41 tff(55,plain,
% 0.14/0.41 ((~($sum(read(V!3, W!2), $product(-1, read(U!4, W!2))) = 0)) | $greatereq($sum(read(V!3, W!2), $product(-1, read(U!4, W!2))), 0)),
% 0.14/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.41 tff(56,plain,
% 0.14/0.41 ($greatereq($sum(read(V!3, W!2), $product(-1, read(U!4, W!2))), 0)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.14/0.41 tff(57,plain,
% 0.14/0.41 (read(V!3, W!2) = read(U!4, W!2)),
% 0.14/0.41 inference(theory_lemma,[status(thm)],[56, 54])).
% 0.14/0.41 tff(58,plain,
% 0.14/0.41 ((~![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0)) | ($sum(read(V!3, Y!0), $product(-1, read(U!4, Y!0))) = 0)),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 ($sum(read(V!3, Y!0), $product(-1, read(U!4, Y!0))) = 0),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[58, 50])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 ((~($sum(read(V!3, Y!0), $product(-1, read(U!4, Y!0))) = 0)) | $greatereq($sum(read(V!3, Y!0), $product(-1, read(U!4, Y!0))), 0)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 ($greatereq($sum(read(V!3, Y!0), $product(-1, read(U!4, Y!0))), 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = -1)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = -1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (($sum(1, $sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0)))) = 0) <=> ($sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = -1)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 ($sum($sum(1, read(V!3, Y!0)), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = $sum(1, $sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (($sum($sum(1, read(V!3, Y!0)), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = 0) <=> ($sum(1, $sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0)))) = 0)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[64])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (($sum($sum(1, read(V!3, Y!0)), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = 0) <=> ($sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = -1)),
% 0.21/0.41 inference(transitivity,[status(thm)],[65, 63])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum($sum(1, read(V!3, Y!0)), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = -1))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[66])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum($sum(1, read(V!3, Y!0)), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = -1))),
% 0.21/0.41 inference(transitivity,[status(thm)],[67, 62])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum($sum(1, read(V!3, Y!0)), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = 0)),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = -1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 ($sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = -1),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[70, 13])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 ((~($sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))) = -1)) | $lesseq($sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))), -1)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 ($lesseq($sum(read(V!3, Y!0), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0))), -1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.21/0.42 tff(74,assumption,($lesseq($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))), 0)), introduced(assumption)).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0) = U!4),
% 0.21/0.42 inference(symmetry,[status(thm)],[45])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0) = read(U!4, Y!0)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (read(U!4, Y!0) = read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0)),
% 0.21/0.42 inference(symmetry,[status(thm)],[76])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 ((~(read(U!4, Y!0) = read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))) | $greatereq($sum(read(U!4, Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 ($greatereq($sum(read(U!4, Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[79, 74, 73, 61])).
% 0.21/0.42 tff(81,plain,(~$lesseq($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 ((~($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))) = 0)) | $lesseq($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (~($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))) = 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (^[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)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (^[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)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (^[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)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(91,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')).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[92, 89])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[93, 87])).
% 0.21/0.42 tff(95,plain,(
% 0.21/0.42 ![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))),
% 0.21/0.42 inference(skolemize,[status(sab)],[94])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (((~![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(Y!0, $product(-1, W!2)) = 0) | ($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))) = 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(Y!0, $product(-1, W!2)) = 0) | ($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))) = 0))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 ((~![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(Y!0, $product(-1, W!2)) = 0) | ($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))) = 0))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((~![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(Y!0, $product(-1, W!2)) = 0) | ($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))) = 0)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (($sum(Y!0, $product(-1, W!2)) = 0) | ($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), Y!0), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), Y!0))) = 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 ($sum(Y!0, $product(-1, W!2)) = 0),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[100, 83])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 ((~($sum(Y!0, $product(-1, W!2)) = 0)) | $lesseq($sum(Y!0, $product(-1, W!2)), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 ($lesseq($sum(Y!0, $product(-1, W!2)), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 ((~($sum(Y!0, $product(-1, W!2)) = 0)) | $greatereq($sum(Y!0, $product(-1, W!2)), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 ($greatereq($sum(Y!0, $product(-1, W!2)), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (Y!0 = W!2),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[105, 103])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (read(V!3, Y!0) = read(V!3, W!2)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[106])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (W!2 = Y!0),
% 0.21/0.42 inference(symmetry,[status(thm)],[106])).
% 0.21/0.42 tff(109,assumption,($lesseq($sum(Y!0, $product(-1, W!2)), 0)), introduced(assumption)).
% 0.21/0.42 tff(110,assumption,($greatereq($sum(Y!0, $product(-1, W!2)), 0)), introduced(assumption)).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (Y!0 = W!2),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[110, 109])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (read(V!3, Y!0) = read(V!3, W!2)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[111])).
% 0.21/0.42 tff(113,assumption,($sum(Y!0, $product(-1, X!1)) = 0), introduced(assumption)).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 ((~($sum(Y!0, $product(-1, X!1)) = 0)) | $lesseq($sum(Y!0, $product(-1, X!1)), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 ($lesseq($sum(Y!0, $product(-1, X!1)), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 ((~($sum(Y!0, $product(-1, X!1)) = 0)) | $greatereq($sum(Y!0, $product(-1, X!1)), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 ($greatereq($sum(Y!0, $product(-1, X!1)), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (Y!0 = X!1),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[117, 115])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (X!1 = Y!0),
% 0.21/0.42 inference(symmetry,[status(thm)],[118])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (read(V!3, X!1) = read(V!3, Y!0)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[119])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (read(U!4, W!2) = 0),
% 0.21/0.42 inference(transitivity,[status(thm)],[46, 23])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 ((~(read(U!4, W!2) = 0)) | $lesseq(read(U!4, W!2), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 ($lesseq(read(U!4, W!2), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 ((~(read(U!4, W!2) = 0)) | $greatereq(read(U!4, W!2), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 ($greatereq(read(U!4, W!2), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[124, 121])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (read(V!3, X!1) = $sum(read(V!3, X!1), $product(-1, read(V!3, W!2)))),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[125, 123, 56, 54])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 ($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = read(V!3, X!1)),
% 0.21/0.42 inference(symmetry,[status(thm)],[126])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 ($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0),
% 0.21/0.42 inference(transitivity,[status(thm)],[127, 120, 112, 57, 46, 23])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (~($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0)),
% 0.21/0.42 inference(and_elim,[status(thm)],[44])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.21/0.42 tff(131,plain,((~($sum(Y!0, $product(-1, X!1)) = 0)) | (~$greatereq($sum(Y!0, $product(-1, W!2)), 0)) | (~$lesseq($sum(Y!0, $product(-1, W!2)), 0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 (~($sum(Y!0, $product(-1, X!1)) = 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[131, 103, 105])).
% 0.21/0.42 tff(133,assumption,(~($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0)), introduced(assumption)).
% 0.21/0.42 tff(134,assumption,(~($sum(Y!0, $product(-1, X!1)) = 0)), introduced(assumption)).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 (((~![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(Y!0, $product(-1, X!1)) = 0) | ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 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(Y!0, $product(-1, X!1)) = 0) | ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 ((($sum(X!1, $product(-1, Y!0)) = 0) | ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0)) <=> (($sum(Y!0, $product(-1, X!1)) = 0) | ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 (((~![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!1, $product(-1, Y!0)) = 0) | ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 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(Y!0, $product(-1, X!1)) = 0) | ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[136])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 (((~![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!1, $product(-1, Y!0)) = 0) | ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 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(Y!0, $product(-1, X!1)) = 0) | ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0))),
% 0.21/0.42 inference(transitivity,[status(thm)],[137, 135])).
% 0.21/0.42 tff(139,plain,
% 0.21/0.42 ((~![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!1, $product(-1, Y!0)) = 0) | ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(140,plain,
% 0.21/0.42 ((~![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(Y!0, $product(-1, X!1)) = 0) | ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.42 tff(141,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[140, 96, 134, 133])).
% 0.21/0.42 tff(142,plain,(($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0) | ($sum(Y!0, $product(-1, X!1)) = 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(143,plain,
% 0.21/0.42 ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[142, 132])).
% 0.21/0.42 tff(144,plain,
% 0.21/0.42 ((~($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0)) | $greatereq($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(145,plain,
% 0.21/0.42 ($greatereq($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.21/0.42 tff(146,assumption,($sum(Y!0, $product(-1, W!2)) = 0), introduced(assumption)).
% 0.21/0.42 tff(147,plain,
% 0.21/0.42 ($lesseq($sum(Y!0, $product(-1, W!2)), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[102, 146])).
% 0.21/0.42 tff(148,plain,
% 0.21/0.42 ($greatereq($sum(Y!0, $product(-1, W!2)), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[104, 146])).
% 0.21/0.42 tff(149,plain,
% 0.21/0.42 (Y!0 = W!2),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[148, 147])).
% 0.21/0.42 tff(150,plain,
% 0.21/0.42 (read(V!3, Y!0) = read(V!3, W!2)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[149])).
% 0.21/0.42 tff(151,plain,
% 0.21/0.42 (W!2 = Y!0),
% 0.21/0.42 inference(symmetry,[status(thm)],[149])).
% 0.21/0.42 tff(152,assumption,(~$greatereq($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))), 0)), introduced(assumption)).
% 0.21/0.42 tff(153,plain,
% 0.21/0.42 ((~![Z: $int] : ($sum(read(V!3, Z), $product(-1, read(U!4, Z))) = 0)) | ($sum(read(V!3, X!1), $product(-1, read(U!4, X!1))) = 0)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(154,plain,
% 0.21/0.42 ($sum(read(V!3, X!1), $product(-1, read(U!4, X!1))) = 0),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[153, 50])).
% 0.21/0.42 tff(155,plain,
% 0.21/0.42 ((~($sum(read(V!3, X!1), $product(-1, read(U!4, X!1))) = 0)) | $greatereq($sum(read(V!3, X!1), $product(-1, read(U!4, X!1))), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(156,plain,
% 0.21/0.42 ($greatereq($sum(read(V!3, X!1), $product(-1, read(U!4, X!1))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.21/0.42 tff(157,plain,
% 0.21/0.42 (read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1) = read(U!4, X!1)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.42 tff(158,plain,
% 0.21/0.42 (read(U!4, X!1) = read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1)),
% 0.21/0.42 inference(symmetry,[status(thm)],[157])).
% 0.21/0.42 tff(159,plain,
% 0.21/0.42 ((~(read(U!4, X!1) = read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))) | $greatereq($sum(read(U!4, X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(160,plain,
% 0.21/0.42 ($greatereq($sum(read(U!4, X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.21/0.42 tff(161,plain,
% 0.21/0.42 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!3, X!1, 0), X!1) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!3, X!1, 0), X!1) = 0))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(162,plain,
% 0.21/0.42 (($product(-1, read(write(V!3, X!1, 0), X!1)) = 0) <=> (read(write(V!3, X!1, 0), X!1) = 0)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(163,plain,
% 0.21/0.42 ($sum(0, $product(-1, read(write(V!3, X!1, 0), X!1))) = $product(-1, read(write(V!3, X!1, 0), X!1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(164,plain,
% 0.21/0.42 (($sum(0, $product(-1, read(write(V!3, X!1, 0), X!1))) = 0) <=> ($product(-1, read(write(V!3, X!1, 0), X!1)) = 0)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[163])).
% 0.21/0.42 tff(165,plain,
% 0.21/0.42 (($sum(0, $product(-1, read(write(V!3, X!1, 0), X!1))) = 0) <=> (read(write(V!3, X!1, 0), X!1) = 0)),
% 0.21/0.42 inference(transitivity,[status(thm)],[164, 162])).
% 0.21/0.42 tff(166,plain,
% 0.21/0.42 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(0, $product(-1, read(write(V!3, X!1, 0), X!1))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!3, X!1, 0), X!1) = 0))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[165])).
% 0.21/0.42 tff(167,plain,
% 0.21/0.42 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(0, $product(-1, read(write(V!3, X!1, 0), X!1))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!3, X!1, 0), X!1) = 0))),
% 0.21/0.42 inference(transitivity,[status(thm)],[166, 161])).
% 0.21/0.42 tff(168,plain,
% 0.21/0.42 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(0, $product(-1, read(write(V!3, X!1, 0), X!1))) = 0)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(169,plain,
% 0.21/0.42 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!3, X!1, 0), X!1) = 0)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.21/0.42 tff(170,plain,
% 0.21/0.42 (read(write(V!3, X!1, 0), X!1) = 0),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[169, 13])).
% 0.21/0.42 tff(171,plain,
% 0.21/0.42 ((~(read(write(V!3, X!1, 0), X!1) = 0)) | $greatereq(read(write(V!3, X!1, 0), X!1), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(172,plain,
% 0.21/0.42 ($greatereq(read(write(V!3, X!1, 0), X!1), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.21/0.42 tff(173,plain,
% 0.21/0.42 (~($sum(Y!0, $product(-1, X!1)) = 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[131, 148, 147])).
% 0.21/0.42 tff(174,plain,
% 0.21/0.42 ($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[142, 173])).
% 0.21/0.42 tff(175,plain,
% 0.21/0.42 ((~($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))) = 0)) | $lesseq($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(176,plain,
% 0.21/0.42 ($lesseq($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.21/0.42 tff(177,plain,
% 0.21/0.42 ((~$lesseq($sum(read(write(V!3, X!1, 0), X!1), $product(-1, read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1))), 0)) | (~$greatereq(read(write(V!3, X!1, 0), X!1), 0)) | (~$lesseq($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))), 0)) | (~$greatereq($sum(read(U!4, X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))), 0)) | (~$greatereq($sum(read(V!3, X!1), $product(-1, read(U!4, X!1))), 0)) | (~$lesseq(read(U!4, W!2), 0)) | (~$lesseq($sum(read(V!3, W!2), $product(-1, read(U!4, W!2))), 0)) | $greatereq($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(178,plain,
% 0.21/0.42 (~$lesseq($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[177, 176, 54, 123, 172, 160, 156, 152])).
% 0.21/0.42 tff(179,plain,
% 0.21/0.42 ((~($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))) = 0)) | $lesseq($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(180,plain,
% 0.21/0.42 (~($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))) = 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.21/0.42 tff(181,plain,
% 0.21/0.42 (((~![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!1, $product(-1, W!2)) = 0) | ($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))) = 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!1, $product(-1, W!2)) = 0) | ($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))) = 0))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(182,plain,
% 0.21/0.42 ((~![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!1, $product(-1, W!2)) = 0) | ($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))) = 0))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(183,plain,
% 0.21/0.43 ((~![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!1, $product(-1, W!2)) = 0) | ($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))) = 0)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.21/0.43 tff(184,plain,
% 0.21/0.43 (($sum(X!1, $product(-1, W!2)) = 0) | ($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))) = 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[183, 96])).
% 0.21/0.43 tff(185,plain,
% 0.21/0.43 ($sum(X!1, $product(-1, W!2)) = 0),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[184, 180])).
% 0.21/0.43 tff(186,plain,
% 0.21/0.43 ((~($sum(X!1, $product(-1, W!2)) = 0)) | $lesseq($sum(X!1, $product(-1, W!2)), 0)),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.43 tff(187,plain,
% 0.21/0.43 ($lesseq($sum(X!1, $product(-1, W!2)), 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.21/0.43 tff(188,plain,
% 0.21/0.43 ((~($sum(X!1, $product(-1, W!2)) = 0)) | $greatereq($sum(X!1, $product(-1, W!2)), 0)),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.43 tff(189,plain,
% 0.21/0.43 ($greatereq($sum(X!1, $product(-1, W!2)), 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[188, 185])).
% 0.21/0.43 tff(190,plain,
% 0.21/0.43 (X!1 = W!2),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[189, 187])).
% 0.21/0.43 tff(191,plain,
% 0.21/0.43 (X!1 = Y!0),
% 0.21/0.43 inference(transitivity,[status(thm)],[190, 151])).
% 0.21/0.43 tff(192,plain,
% 0.21/0.43 (read(V!3, X!1) = read(V!3, Y!0)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[191])).
% 0.21/0.43 tff(193,plain,
% 0.21/0.43 ($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0),
% 0.21/0.43 inference(transitivity,[status(thm)],[127, 192, 150, 57, 46, 23])).
% 0.21/0.43 tff(194,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[129, 193])).
% 0.21/0.43 tff(195,plain,((~($sum(Y!0, $product(-1, W!2)) = 0)) | $greatereq($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(196,plain,
% 0.21/0.43 ($greatereq($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))), 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[195, 101])).
% 0.21/0.43 tff(197,plain,
% 0.21/0.43 (($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0) | (~$lesseq($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))), 0)) | (~$greatereq($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))), 0))),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.43 tff(198,plain,
% 0.21/0.43 ((~$lesseq($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))), 0)) | (~$greatereq($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))), 0))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[197, 129])).
% 0.21/0.43 tff(199,plain,
% 0.21/0.43 (~$lesseq($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))), 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[198, 196])).
% 0.21/0.43 tff(200,plain,
% 0.21/0.43 ((~($sum(read(V!3, X!1), $product(-1, read(U!4, X!1))) = 0)) | $lesseq($sum(read(V!3, X!1), $product(-1, read(U!4, X!1))), 0)),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.43 tff(201,plain,
% 0.21/0.43 ($lesseq($sum(read(V!3, X!1), $product(-1, read(U!4, X!1))), 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[200, 154])).
% 0.21/0.43 tff(202,plain,
% 0.21/0.43 ((~(read(U!4, X!1) = read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))) | $lesseq($sum(read(U!4, X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))), 0)),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.43 tff(203,plain,
% 0.21/0.43 ($lesseq($sum(read(U!4, X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))), 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[202, 158])).
% 0.21/0.43 tff(204,assumption,($greatereq($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))), 0)), introduced(assumption)).
% 0.21/0.43 tff(205,plain,
% 0.21/0.43 ((~(read(write(V!3, X!1, 0), X!1) = 0)) | $lesseq(read(write(V!3, X!1, 0), X!1), 0)),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.43 tff(206,plain,
% 0.21/0.43 ($lesseq(read(write(V!3, X!1, 0), X!1), 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[205, 170])).
% 0.21/0.43 tff(207,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[206, 204, 203, 201, 125, 56, 199, 145])).
% 0.21/0.43 tff(208,plain,(~$greatereq($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(209,plain,
% 0.21/0.43 ((~($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))) = 0)) | $greatereq($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))), 0)),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.43 tff(210,plain,
% 0.21/0.43 (~($sum(read(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), X!1), $product(-1, read(write(write(write(V!3, X!1, 0), Y!0, $sum(1, read(V!3, Y!0))), W!2, 0), X!1))) = 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.21/0.43 tff(211,plain,
% 0.21/0.43 ($sum(X!1, $product(-1, W!2)) = 0),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[184, 210])).
% 0.21/0.43 tff(212,plain,
% 0.21/0.43 ($lesseq($sum(X!1, $product(-1, W!2)), 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[186, 211])).
% 0.21/0.43 tff(213,plain,
% 0.21/0.43 ($greatereq($sum(X!1, $product(-1, W!2)), 0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[188, 211])).
% 0.21/0.43 tff(214,plain,
% 0.21/0.43 (X!1 = W!2),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[213, 212])).
% 0.21/0.43 tff(215,plain,
% 0.21/0.43 (X!1 = Y!0),
% 0.21/0.43 inference(transitivity,[status(thm)],[214, 108])).
% 0.21/0.43 tff(216,plain,
% 0.21/0.43 (read(V!3, X!1) = read(V!3, Y!0)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[215])).
% 0.21/0.43 tff(217,plain,
% 0.21/0.43 (read(V!3, X!1) = read(U!4, X!1)),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[156, 201])).
% 0.21/0.43 tff(218,plain,
% 0.21/0.43 (read(U!4, X!1) = read(V!3, X!1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[217])).
% 0.21/0.43 tff(219,plain,
% 0.21/0.43 ($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = read(U!4, X!1)),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[156, 201, 125, 123, 56, 54])).
% 0.21/0.43 tff(220,plain,
% 0.21/0.43 ($sum(read(V!3, X!1), $product(-1, read(V!3, W!2))) = 0),
% 0.21/0.43 inference(transitivity,[status(thm)],[219, 218, 216, 107, 57, 46, 23])).
% 0.21/0.43 tff(221,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[129, 220])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------