TSTP Solution File: DAT013_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT013_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:36:22 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : DAT013_1 : TPTP v8.1.0. Released v5.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 01:38:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.13/0.39 tptp_fun_Y_3: $int)).
% 0.13/0.39 tff(tptp_fun_V_1_type, type, (
% 0.13/0.39 tptp_fun_V_1: $int)).
% 0.13/0.39 tff(tptp_fun_W_0_type, type, (
% 0.13/0.39 tptp_fun_W_0: $int)).
% 0.13/0.39 tff(read_type, type, (
% 0.13/0.39 read: ( array * $int ) > $int)).
% 0.13/0.39 tff(tptp_fun_U_2_type, type, (
% 0.13/0.39 tptp_fun_U_2: array)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~($greatereq($sum(X, $product(-1, V!1)), 0) & $greatereq($sum(W!0, $product(-1, X)), 0)))) & (~((~$lesseq(read(U!2, Y!3), 0)) | (~($greatereq($sum(Y!3, $product(-1, V!1)), 3) & $greatereq($sum(W!0, $product(-1, Y!3)), 0)))))) <=> (![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~($greatereq($sum(X, $product(-1, V!1)), 0) & $lesseq($sum(X, $product(-1, W!0)), 0)))) & (~((~$lesseq(read(U!2, Y!3), 0)) | (~($lesseq($sum(V!1, $product(-1, Y!3)), -3) & $greatereq($sum(W!0, $product(-1, Y!3)), 0))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($greatereq($sum(X, $product(-1, V)), 0) & $greatereq($sum(W, $product(-1, X)), 0))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($greatereq($sum(Y, $product(-1, V)), 3) & $greatereq($sum(W, $product(-1, Y)), 0)))))) <=> (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($greatereq($sum(X, $product(-1, V)), 0) & $greatereq($sum(W, $product(-1, X)), 0))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($greatereq($sum(Y, $product(-1, V)), 3) & $greatereq($sum(W, $product(-1, Y)), 0))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($lesseq($sum(V, $product(-1, X)), 0) & $lesseq($sum(X, $product(-1, W)), 0))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($lesseq($sum(V, $product(-1, Y)), -3) & $lesseq($sum(Y, $product(-1, W)), 0)))))) <=> (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($greatereq($sum(X, $product(-1, V)), 0) & $greatereq($sum(W, $product(-1, X)), 0))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($greatereq($sum(Y, $product(-1, V)), 3) & $greatereq($sum(W, $product(-1, Y)), 0))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 ((~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($lesseq(V, X) & $lesseq(X, W))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($lesseq(V, $sum(-3, Y)) & $lesseq(Y, W)))))) <=> (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($lesseq($sum(V, $product(-1, X)), 0) & $lesseq($sum(X, $product(-1, W)), 0))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($lesseq($sum(V, $product(-1, Y)), -3) & $lesseq($sum(Y, $product(-1, W)), 0))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 ((~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($lesseq(V, X) & $lesseq(X, W))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($lesseq(V, $sum(-3, Y)) & $lesseq(Y, W)))))) <=> (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($lesseq(V, X) & $lesseq(X, W))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($lesseq(V, $sum(-3, Y)) & $lesseq(Y, W))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 ((~![U: array, V: $int, W: $int] : (![X: $int] : (($lesseq(V, X) & $lesseq(X, W)) => $greater(read(U, X), 0)) => ![Y: $int] : (($lesseq($sum(V, 3), Y) & $lesseq(Y, W)) => $greater(read(U, Y), 0)))) <=> (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($lesseq(V, X) & $lesseq(X, W))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($lesseq(V, $sum(-3, Y)) & $lesseq(Y, W))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(7,axiom,(~![U: array, V: $int, W: $int] : (![X: $int] : (($lesseq(V, X) & $lesseq(X, W)) => $greater(read(U, X), 0)) => ![Y: $int] : (($lesseq($sum(V, 3), Y) & $lesseq(Y, W)) => $greater(read(U, Y), 0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($lesseq(V, X) & $lesseq(X, W))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($lesseq(V, $sum(-3, Y)) & $lesseq(Y, W)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($lesseq(V, X) & $lesseq(X, W))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($lesseq(V, $sum(-3, Y)) & $lesseq(Y, W)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($lesseq(V, X) & $lesseq(X, W))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($lesseq(V, $sum(-3, Y)) & $lesseq(Y, W)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($lesseq(V, X) & $lesseq(X, W))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($lesseq(V, $sum(-3, Y)) & $lesseq(Y, W)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($lesseq($sum(V, $product(-1, X)), 0) & $lesseq($sum(X, $product(-1, W)), 0))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($lesseq($sum(V, $product(-1, Y)), -3) & $lesseq($sum(Y, $product(-1, W)), 0)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($greatereq($sum(X, $product(-1, V)), 0) & $greatereq($sum(W, $product(-1, X)), 0))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($greatereq($sum(Y, $product(-1, V)), 3) & $greatereq($sum(W, $product(-1, Y)), 0)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($greatereq($sum(X, $product(-1, V)), 0) & $greatereq($sum(W, $product(-1, X)), 0))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($greatereq($sum(Y, $product(-1, V)), 3) & $greatereq($sum(W, $product(-1, Y)), 0)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (~![U: array, V: $int, W: $int] : ((~![X: $int] : ((~$lesseq(read(U, X), 0)) | (~($greatereq($sum(X, $product(-1, V)), 0) & $greatereq($sum(W, $product(-1, X)), 0))))) | ![Y: $int] : ((~$lesseq(read(U, Y), 0)) | (~($greatereq($sum(Y, $product(-1, V)), 3) & $greatereq($sum(W, $product(-1, Y)), 0)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~($greatereq($sum(X, $product(-1, V!1)), 0) & $lesseq($sum(X, $product(-1, W!0)), 0)))) & (~((~$lesseq(read(U!2, Y!3), 0)) | (~($lesseq($sum(V!1, $product(-1, Y!3)), -3) & $greatereq($sum(W!0, $product(-1, Y!3)), 0)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 1])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (~((~$lesseq(read(U!2, Y!3), 0)) | (~($lesseq($sum(V!1, $product(-1, Y!3)), -3) & $greatereq($sum(W!0, $product(-1, Y!3)), 0))))),
% 0.13/0.39 inference(and_elim,[status(thm)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 ($lesseq($sum(V!1, $product(-1, Y!3)), -3) & $greatereq($sum(W!0, $product(-1, Y!3)), 0)),
% 0.13/0.39 inference(or_elim,[status(thm)],[17])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 ($lesseq($sum(V!1, $product(-1, Y!3)), -3)),
% 0.13/0.39 inference(and_elim,[status(thm)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ($lesseq($sum(V!1, $product(-1, Y!3)), 0) | (~$lesseq($sum(V!1, $product(-1, Y!3)), -3))),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ($lesseq($sum(V!1, $product(-1, Y!3)), 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ($greatereq($sum(W!0, $product(-1, Y!3)), 0)),
% 0.13/0.39 inference(and_elim,[status(thm)],[18])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 ($lesseq(read(U!2, Y!3), 0)),
% 0.13/0.39 inference(or_elim,[status(thm)],[17])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (^[X: $int] : refl(((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0))) <=> ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0))) <=> ![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (^[X: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq($sum(X, $product(-1, V!1)), 0) & $lesseq($sum(X, $product(-1, W!0)), 0)) <=> (~((~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0))))), ((~($greatereq($sum(X, $product(-1, V!1)), 0) & $lesseq($sum(X, $product(-1, W!0)), 0))) <=> (~(~((~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0))))))), rewrite((~(~((~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0))))) <=> ((~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))), ((~($greatereq($sum(X, $product(-1, V!1)), 0) & $lesseq($sum(X, $product(-1, W!0)), 0))) <=> ((~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0))))), (((~$lesseq(read(U!2, X), 0)) | (~($greatereq($sum(X, $product(-1, V!1)), 0) & $lesseq($sum(X, $product(-1, W!0)), 0)))) <=> ((~$lesseq(read(U!2, X), 0)) | ((~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))))), rewrite(((~$lesseq(read(U!2, X), 0)) | ((~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))) <=> ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))), (((~$lesseq(read(U!2, X), 0)) | (~($greatereq($sum(X, $product(-1, V!1)), 0) & $lesseq($sum(X, $product(-1, W!0)), 0)))) <=> ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~($greatereq($sum(X, $product(-1, V!1)), 0) & $lesseq($sum(X, $product(-1, W!0)), 0)))) <=> ![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~($greatereq($sum(X, $product(-1, V!1)), 0) & $lesseq($sum(X, $product(-1, W!0)), 0))))),
% 0.13/0.39 inference(and_elim,[status(thm)],[16])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (((~![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))) | ((~$lesseq(read(U!2, Y!3), 0)) | (~$lesseq($sum(V!1, $product(-1, Y!3)), 0)) | (~$greatereq($sum(W!0, $product(-1, Y!3)), 0)))) <=> ((~![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))) | (~$lesseq(read(U!2, Y!3), 0)) | (~$lesseq($sum(V!1, $product(-1, Y!3)), 0)) | (~$greatereq($sum(W!0, $product(-1, Y!3)), 0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (((~$lesseq(read(U!2, Y!3), 0)) | (~$greatereq($sum(Y!3, $product(-1, V!1)), 0)) | (~$lesseq($sum(Y!3, $product(-1, W!0)), 0))) <=> ((~$lesseq(read(U!2, Y!3), 0)) | (~$lesseq($sum(V!1, $product(-1, Y!3)), 0)) | (~$greatereq($sum(W!0, $product(-1, Y!3)), 0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (((~![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))) | ((~$lesseq(read(U!2, Y!3), 0)) | (~$greatereq($sum(Y!3, $product(-1, V!1)), 0)) | (~$lesseq($sum(Y!3, $product(-1, W!0)), 0)))) <=> ((~![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))) | ((~$lesseq(read(U!2, Y!3), 0)) | (~$lesseq($sum(V!1, $product(-1, Y!3)), 0)) | (~$greatereq($sum(W!0, $product(-1, Y!3)), 0))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (((~![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))) | ((~$lesseq(read(U!2, Y!3), 0)) | (~$greatereq($sum(Y!3, $product(-1, V!1)), 0)) | (~$lesseq($sum(Y!3, $product(-1, W!0)), 0)))) <=> ((~![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))) | (~$lesseq(read(U!2, Y!3), 0)) | (~$lesseq($sum(V!1, $product(-1, Y!3)), 0)) | (~$greatereq($sum(W!0, $product(-1, Y!3)), 0)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[33, 31])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 ((~![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))) | ((~$lesseq(read(U!2, Y!3), 0)) | (~$greatereq($sum(Y!3, $product(-1, V!1)), 0)) | (~$lesseq($sum(Y!3, $product(-1, W!0)), 0)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 ((~![X: $int] : ((~$lesseq(read(U!2, X), 0)) | (~$greatereq($sum(X, $product(-1, V!1)), 0)) | (~$lesseq($sum(X, $product(-1, W!0)), 0)))) | (~$lesseq(read(U!2, Y!3), 0)) | (~$lesseq($sum(V!1, $product(-1, Y!3)), 0)) | (~$greatereq($sum(W!0, $product(-1, Y!3)), 0))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[36, 30, 23, 22, 21])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------