TSTP Solution File: DAT010_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT010_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:36:21 EDT 2022
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT010_1 : TPTP v8.1.0. Released v5.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 01:53:06 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(read_type, type, (
% 0.21/0.40 read: ( array * $int ) > $int)).
% 0.21/0.40 tff(tptp_fun_X_2_type, type, (
% 0.21/0.40 tptp_fun_X_2: $int)).
% 0.21/0.40 tff(tptp_fun_U_1_type, type, (
% 0.21/0.40 tptp_fun_U_1: array)).
% 0.21/0.40 tff(tptp_fun_V_0_type, type, (
% 0.21/0.40 tptp_fun_V_0: array)).
% 0.21/0.40 tff(write_type, type, (
% 0.21/0.40 write: ( array * $int * $int ) > array)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 ((((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V!0, W), 100))) & $greatereq(read(U!1, X!2), 100)) <=> ((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V!0, W), 100)) & $greatereq(read(U!1, X!2), 100))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 ((~(~$greatereq(read(U!1, X!2), 100))) <=> $greatereq(read(U!1, X!2), 100)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V!0, W), 100))) <=> ((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V!0, W), 100)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 ((((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V!0, W), 100))) & (~(~$greatereq(read(U!1, X!2), 100)))) <=> (((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V!0, W), 100))) & $greatereq(read(U!1, X!2), 100))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[3, 2])).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 ((((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V!0, W), 100))) & (~(~$greatereq(read(U!1, X!2), 100)))) <=> ((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V!0, W), 100)) & $greatereq(read(U!1, X!2), 100))),
% 0.21/0.40 inference(transitivity,[status(thm)],[4, 1])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 ((~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V, W), 100)))) | ![X: $int] : (~$greatereq(read(U, X), 100)))) <=> (~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V, W), 100)))) | ![X: $int] : (~$greatereq(read(U, X), 100))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 ((~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$lesseq(100, read(V, W))))) | ![X: $int] : (~$lesseq(100, read(U, X))))) <=> (~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V, W), 100)))) | ![X: $int] : (~$greatereq(read(U, X), 100))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 ((~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$lesseq(100, read(V, W))))) | ![X: $int] : (~$lesseq(100, read(U, X))))) <=> (~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$lesseq(100, read(V, W))))) | ![X: $int] : (~$lesseq(100, read(U, X)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 ((~![U: array, V: array] : (((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : $less(read(V, W), 100)) => ![X: $int] : $less(read(U, X), 100))) <=> (~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$lesseq(100, read(V, W))))) | ![X: $int] : (~$lesseq(100, read(U, X)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(10,axiom,(~![U: array, V: array] : (((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : $less(read(V, W), 100)) => ![X: $int] : $less(read(U, X), 100))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$lesseq(100, read(V, W))))) | ![X: $int] : (~$lesseq(100, read(U, X))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$lesseq(100, read(V, W))))) | ![X: $int] : (~$lesseq(100, read(U, X))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$lesseq(100, read(V, W))))) | ![X: $int] : (~$lesseq(100, read(U, X))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$lesseq(100, read(V, W))))) | ![X: $int] : (~$lesseq(100, read(U, X))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V, W), 100)))) | ![X: $int] : (~$greatereq(read(U, X), 100)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V, W), 100)))) | ![X: $int] : (~$greatereq(read(U, X), 100)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[15, 6])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (~![U: array, V: array] : ((~((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V, W), 100)))) | ![X: $int] : (~$greatereq(read(U, X), 100)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 ((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~$greatereq(read(V!0, W), 100)) & $greatereq(read(U!1, X!2), 100)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[17, 5])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 ($greatereq(read(U!1, X!2), 100)),
% 0.21/0.40 inference(and_elim,[status(thm)],[18])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 ((~$lesseq(read(U!1, X!2), 44)) | (~$greatereq(read(U!1, X!2), 100))),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (~$lesseq(read(U!1, X!2), 44)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (^[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))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 (![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)),
% 0.21/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (^[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)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (![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)),
% 0.21/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (^[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))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (![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)),
% 0.21/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (![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)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(29,axiom,(![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)), file('/export/starexec/sandbox2/benchmark/Axioms/DAT001=0.ax','ax1')).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (![U: array, V: $int, W: $int] : ($sum(read(write(U, V, W), V), $product(-1, W)) = 0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.21/0.40 tff(33,plain,(
% 0.21/0.40 ![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.21/0.40 inference(skolemize,[status(sab)],[32])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4) = 44)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4) = 44))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (($sum(44, $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4))) = 0) <=> (read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4) = 44)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(44, $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4) = 44))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(44, $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4) = 44))),
% 0.21/0.40 inference(transitivity,[status(thm)],[37, 35])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(44, $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4))) = 0)),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4) = 44)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 (read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4) = 44),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5) = 55)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5) = 55))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (($sum(55, $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5))) = 0) <=> (read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5) = 55)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(55, $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5) = 55))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(55, $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5) = 55))),
% 0.21/0.40 inference(transitivity,[status(thm)],[44, 42])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(55, $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5))) = 0)),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5) = 55)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5) = 55),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[47, 34])).
% 0.21/0.40 tff(49,assumption,(~(X!2 = 4)), introduced(assumption)).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (^[W: $int] : refl((~$greatereq(read(V!0, W), 100)) <=> (~$greatereq(read(V!0, W), 100)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (![W: $int] : (~$greatereq(read(V!0, W), 100)) <=> ![W: $int] : (~$greatereq(read(V!0, W), 100))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (![W: $int] : (~$greatereq(read(V!0, W), 100))),
% 0.21/0.40 inference(and_elim,[status(thm)],[18])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (![W: $int] : (~$greatereq(read(V!0, W), 100))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 ((~![W: $int] : (~$greatereq(read(V!0, W), 100))) | (~$greatereq(read(V!0, X!2), 100))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (~$greatereq(read(V!0, X!2), 100)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)),
% 0.21/0.40 inference(and_elim,[status(thm)],[18])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44) = U!1),
% 0.21/0.40 inference(symmetry,[status(thm)],[56])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2) = read(U!1, X!2)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[57])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (read(U!1, X!2) = read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2)),
% 0.21/0.40 inference(symmetry,[status(thm)],[58])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 ((~(read(U!1, X!2) = read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) | $lesseq($sum(read(U!1, X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))), 0)),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 ($lesseq($sum(read(U!1, X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))), 0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (^[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)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0)) <=> ![X: 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))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (^[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)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0)) <=> ![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))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (^[X: array, Y: $int, Z: $int, X1: $int] : rewrite(((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z))) <=> (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z))) <=> ![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z))) <=> ![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(69,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')).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[71, 65])).
% 0.21/0.40 tff(73,plain,(
% 0.21/0.40 ![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 0.21/0.40 inference(skolemize,[status(sab)],[72])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 4) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 4) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 ((($sum(X!2, $product(-1, 4)) = 0) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0)) <=> ((X!2 = 4) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 4)) = 0) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 4) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[76])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 4)) = 0) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 4) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0))),
% 0.21/0.41 inference(transitivity,[status(thm)],[77, 75])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 4)) = 0) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 4) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 ((X!2 = 4) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[80, 74])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[81, 49])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 ((~($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))) = 0)) | $greatereq($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))), 0)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 ($greatereq($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))), 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.21/0.41 tff(85,assumption,($lesseq($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))), 0)), introduced(assumption)).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 4) | ($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 4) | ($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 ((($sum(X!2, $product(-1, 4)) = 0) | ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0)) <=> ((X!2 = 4) | ($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 4)) = 0) | ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 4) | ($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[87])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 4)) = 0) | ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 4) | ($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0))),
% 0.21/0.41 inference(transitivity,[status(thm)],[88, 86])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 4)) = 0) | ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 4) | ($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 ($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[91, 74, 49])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 ((~($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0)) | $lesseq($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))), 0)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 ($lesseq($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))), 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.21/0.41 tff(95,assumption,($lesseq(read(write(V!0, 3, 33), X!2), 33)), introduced(assumption)).
% 0.21/0.41 tff(96,assumption,($greatereq($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))), 0)), introduced(assumption)).
% 0.21/0.41 tff(97,assumption,($lesseq($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))), 0)), introduced(assumption)).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[97, 85, 96, 19, 61, 95])).
% 0.21/0.41 tff(99,plain,((~$lesseq(read(write(V!0, 3, 33), X!2), 33)) | (~$lesseq($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(V!0, 3, 33), X!2))), 0)) | (~$lesseq($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))), 0)) | (~$greatereq($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), X!2))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 (~$lesseq(read(write(V!0, 3, 33), X!2), 33)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[99, 94, 85, 84])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 ((~(read(write(V!0, 3, 33), X!2) = 33)) | $lesseq(read(write(V!0, 3, 33), X!2), 33)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 (~(read(write(V!0, 3, 33), X!2) = 33)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 33), 3) = 33)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 33), 3) = 33))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 (($sum(33, $product(-1, read(write(V!0, 3, 33), 3))) = 0) <=> (read(write(V!0, 3, 33), 3) = 33)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(33, $product(-1, read(write(V!0, 3, 33), 3))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 33), 3) = 33))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[104])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(33, $product(-1, read(write(V!0, 3, 33), 3))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 33), 3) = 33))),
% 0.21/0.41 inference(transitivity,[status(thm)],[105, 103])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(33, $product(-1, read(write(V!0, 3, 33), 3))) = 0)),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 33), 3) = 33)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (read(write(V!0, 3, 33), 3) = 33),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[108, 34])).
% 0.21/0.41 tff(110,assumption,(X!2 = 3), introduced(assumption)).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 (read(write(V!0, 3, 33), X!2) = read(write(V!0, 3, 33), 3)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[110])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 (read(write(V!0, 3, 33), X!2) = 33),
% 0.21/0.41 inference(transitivity,[status(thm)],[111, 109])).
% 0.21/0.41 tff(113,assumption,(~(read(write(V!0, 3, 33), X!2) = 33)), introduced(assumption)).
% 0.21/0.41 tff(114,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.21/0.41 tff(115,plain,((~(X!2 = 3)) | (read(write(V!0, 3, 33), X!2) = 33)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(116,plain,
% 0.21/0.41 (~(X!2 = 3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[115, 102])).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 3) | ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(V!0, X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 3) | ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(V!0, X!2))) = 0))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 ((($sum(X!2, $product(-1, 3)) = 0) | ($sum(read(V!0, X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0)) <=> ((X!2 = 3) | ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(V!0, X!2))) = 0))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 3)) = 0) | ($sum(read(V!0, X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 3) | ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(V!0, X!2))) = 0)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 3)) = 0) | ($sum(read(V!0, X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 3) | ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(V!0, X!2))) = 0))),
% 0.21/0.41 inference(transitivity,[status(thm)],[119, 117])).
% 0.21/0.41 tff(121,plain,
% 0.21/0.41 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(X!2, $product(-1, 3)) = 0) | ($sum(read(V!0, X!2), $product(-1, read(write(V!0, 3, 33), X!2))) = 0))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 3) | ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(V!0, X!2))) = 0)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 ((X!2 = 3) | ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(V!0, X!2))) = 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[122, 74])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 ($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(V!0, X!2))) = 0),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[123, 116])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 ((~($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(V!0, X!2))) = 0)) | $lesseq($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(V!0, X!2))), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 ($lesseq($sum(read(write(V!0, 3, 33), X!2), $product(-1, read(V!0, X!2))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[126, 94, 85, 84, 19, 61, 55])).
% 0.21/0.42 tff(128,plain,((~$lesseq($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))), 0)) | (X!2 = 4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (~$lesseq($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[128, 49])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 ((~($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0)) | $lesseq($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))), 0)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (~($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 5) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 5) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 ((($sum(X!2, $product(-1, 5)) = 0) | ($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2))) = 0)) <=> ((X!2 = 5) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(134,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!2, $product(-1, 5)) = 0) | ($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ((X!2 = 5) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[133])).
% 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(X!2, $product(-1, 5)) = 0) | ($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 5) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0))),
% 0.21/0.42 inference(transitivity,[status(thm)],[134, 132])).
% 0.21/0.42 tff(136,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!2, $product(-1, 5)) = 0) | ($sum(read(write(write(V!0, 3, 33), 4, 444), X!2), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2))) = 0))),
% 0.21/0.42 inference(quant_inst,[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), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (X!2 = 5) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 ((X!2 = 5) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), $product(-1, read(write(write(V!0, 3, 33), 4, 444), X!2))) = 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[137, 74])).
% 0.21/0.42 tff(139,plain,
% 0.21/0.42 (X!2 = 5),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[138, 131])).
% 0.21/0.42 tff(140,plain,
% 0.21/0.42 (read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2) = read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 5)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[139])).
% 0.21/0.42 tff(141,plain,
% 0.21/0.42 (read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2) = 55),
% 0.21/0.42 inference(transitivity,[status(thm)],[140, 48])).
% 0.21/0.42 tff(142,plain,
% 0.21/0.42 ((~(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2) = 55)) | $lesseq(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), 55)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(143,plain,
% 0.21/0.42 ($lesseq(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), X!2), 55)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.21/0.42 tff(144,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[84, 19, 61, 143])).
% 0.21/0.42 tff(145,plain,(X!2 = 4), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(146,plain,
% 0.21/0.42 (read(U!1, X!2) = read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 4)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[56, 145])).
% 0.21/0.42 tff(147,plain,
% 0.21/0.42 (read(U!1, X!2) = 44),
% 0.21/0.42 inference(transitivity,[status(thm)],[146, 41])).
% 0.21/0.42 tff(148,plain,
% 0.21/0.42 ((~(read(U!1, X!2) = 44)) | $lesseq(read(U!1, X!2), 44)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(149,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[148, 147, 21])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------