TSTP Solution File: DAT014_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT014_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 0.23s 0.41s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : DAT014_1 : TPTP v8.1.0. Released v5.0.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 31 01:45:57 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 0.23/0.41 % SZS status Theorem
% 0.23/0.41 % SZS output start Proof
% 0.23/0.41 tff(tptp_fun_X_1_type, type, (
% 0.23/0.41 tptp_fun_X_1: $int)).
% 0.23/0.41 tff(read_type, type, (
% 0.23/0.41 read: ( array * $int ) > $int)).
% 0.23/0.41 tff(tptp_fun_U_0_type, type, (
% 0.23/0.41 tptp_fun_U_0: array)).
% 0.23/0.41 tff(1,plain,
% 0.23/0.41 (((![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20)))) & (~((~$lesseq(read(U!0, X!1), 5)) | (~($greatereq(X!1, 6) & $lesseq(X!1, 15)))))) <=> (![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20))) & (~((~$lesseq(read(U!0, X!1), 5)) | (~($greatereq(X!1, 6) & $lesseq(X!1, 15))))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(2,plain,
% 0.23/0.41 ((![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20)))) <=> (![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(3,plain,
% 0.23/0.41 (((![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20)))) & (~((~$lesseq(read(U!0, X!1), 5)) | (~($greatereq(X!1, 6) & $lesseq(X!1, 15)))))) <=> ((![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20)))) & (~((~$lesseq(read(U!0, X!1), 5)) | (~($greatereq(X!1, 6) & $lesseq(X!1, 15))))))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[2])).
% 0.23/0.41 tff(4,plain,
% 0.23/0.41 (((![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20)))) & (~((~$lesseq(read(U!0, X!1), 5)) | (~($greatereq(X!1, 6) & $lesseq(X!1, 15)))))) <=> (![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20))) & (~((~$lesseq(read(U!0, X!1), 5)) | (~($greatereq(X!1, 6) & $lesseq(X!1, 15))))))),
% 0.23/0.41 inference(transitivity,[status(thm)],[3, 1])).
% 0.23/0.41 tff(5,plain,
% 0.23/0.41 ((~![U: array] : ((~(![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U, W)), 20))))) | ![X: $int] : ((~$lesseq(read(U, X), 5)) | (~($greatereq(X, 6) & $lesseq(X, 15)))))) <=> (~![U: array] : ((~(![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U, W)), 20))))) | ![X: $int] : ((~$lesseq(read(U, X), 5)) | (~($greatereq(X, 6) & $lesseq(X, 15))))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(6,plain,
% 0.23/0.41 ((~![U: array] : ((~(![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$lesseq($sum(read(U, V), $product(-1, V)), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(read(U, W), W), 20))))) | ![X: $int] : ((~$lesseq(read(U, X), 5)) | (~($greatereq(X, 6) & $lesseq(X, 15)))))) <=> (~![U: array] : ((~(![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U, W)), 20))))) | ![X: $int] : ((~$lesseq(read(U, X), 5)) | (~($greatereq(X, 6) & $lesseq(X, 15))))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(7,plain,
% 0.23/0.41 ((~![U: array] : ((~(![V: $int] : ((~$lesseq(read(U, V), V)) | (~($lesseq(1, V) & $lesseq(V, 10)))) & ![W: $int] : ((~($lesseq(11, W) & $lesseq(W, 20))) | (~$lesseq(read(U, W), $sum(20, $product(-1, W))))))) | ![X: $int] : ((~($lesseq(6, X) & $lesseq(X, 15))) | (~$lesseq(read(U, X), 5))))) <=> (~![U: array] : ((~(![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$lesseq($sum(read(U, V), $product(-1, V)), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(read(U, W), W), 20))))) | ![X: $int] : ((~$lesseq(read(U, X), 5)) | (~($greatereq(X, 6) & $lesseq(X, 15))))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(8,plain,
% 0.23/0.41 ((~![U: array] : ((~(![V: $int] : ((~$lesseq(read(U, V), V)) | (~($lesseq(1, V) & $lesseq(V, 10)))) & ![W: $int] : ((~($lesseq(11, W) & $lesseq(W, 20))) | (~$lesseq(read(U, W), $sum(20, $product(-1, W))))))) | ![X: $int] : ((~($lesseq(6, X) & $lesseq(X, 15))) | (~$lesseq(read(U, X), 5))))) <=> (~![U: array] : ((~(![V: $int] : ((~$lesseq(read(U, V), V)) | (~($lesseq(1, V) & $lesseq(V, 10)))) & ![W: $int] : ((~($lesseq(11, W) & $lesseq(W, 20))) | (~$lesseq(read(U, W), $sum(20, $product(-1, W))))))) | ![X: $int] : ((~($lesseq(6, X) & $lesseq(X, 15))) | (~$lesseq(read(U, X), 5)))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(9,plain,
% 0.23/0.41 ((~![U: array] : ((![V: $int] : (($lesseq(1, V) & $lesseq(V, 10)) => $greater(read(U, V), V)) & ![W: $int] : (($lesseq(11, W) & $lesseq(W, 20)) => $greater(read(U, W), $difference(20, W)))) => ![X: $int] : (($lesseq(6, X) & $lesseq(X, 15)) => $greater(read(U, X), 5)))) <=> (~![U: array] : ((~(![V: $int] : ((~$lesseq(read(U, V), V)) | (~($lesseq(1, V) & $lesseq(V, 10)))) & ![W: $int] : ((~($lesseq(11, W) & $lesseq(W, 20))) | (~$lesseq(read(U, W), $sum(20, $product(-1, W))))))) | ![X: $int] : ((~($lesseq(6, X) & $lesseq(X, 15))) | (~$lesseq(read(U, X), 5)))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(10,axiom,(~![U: array] : ((![V: $int] : (($lesseq(1, V) & $lesseq(V, 10)) => $greater(read(U, V), V)) & ![W: $int] : (($lesseq(11, W) & $lesseq(W, 20)) => $greater(read(U, W), $difference(20, W)))) => ![X: $int] : (($lesseq(6, X) & $lesseq(X, 15)) => $greater(read(U, X), 5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.23/0.41 tff(11,plain,
% 0.23/0.41 (~![U: array] : ((~(![V: $int] : ((~$lesseq(read(U, V), V)) | (~($lesseq(1, V) & $lesseq(V, 10)))) & ![W: $int] : ((~($lesseq(11, W) & $lesseq(W, 20))) | (~$lesseq(read(U, W), $sum(20, $product(-1, W))))))) | ![X: $int] : ((~($lesseq(6, X) & $lesseq(X, 15))) | (~$lesseq(read(U, X), 5))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.23/0.41 tff(12,plain,
% 0.23/0.41 (~![U: array] : ((~(![V: $int] : ((~$lesseq(read(U, V), V)) | (~($lesseq(1, V) & $lesseq(V, 10)))) & ![W: $int] : ((~($lesseq(11, W) & $lesseq(W, 20))) | (~$lesseq(read(U, W), $sum(20, $product(-1, W))))))) | ![X: $int] : ((~($lesseq(6, X) & $lesseq(X, 15))) | (~$lesseq(read(U, X), 5))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.23/0.41 tff(13,plain,
% 0.23/0.41 (~![U: array] : ((~(![V: $int] : ((~$lesseq(read(U, V), V)) | (~($lesseq(1, V) & $lesseq(V, 10)))) & ![W: $int] : ((~($lesseq(11, W) & $lesseq(W, 20))) | (~$lesseq(read(U, W), $sum(20, $product(-1, W))))))) | ![X: $int] : ((~($lesseq(6, X) & $lesseq(X, 15))) | (~$lesseq(read(U, X), 5))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.23/0.41 tff(14,plain,
% 0.23/0.41 (~![U: array] : ((~(![V: $int] : ((~$lesseq(read(U, V), V)) | (~($lesseq(1, V) & $lesseq(V, 10)))) & ![W: $int] : ((~($lesseq(11, W) & $lesseq(W, 20))) | (~$lesseq(read(U, W), $sum(20, $product(-1, W))))))) | ![X: $int] : ((~($lesseq(6, X) & $lesseq(X, 15))) | (~$lesseq(read(U, X), 5))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.23/0.41 tff(15,plain,
% 0.23/0.41 (~![U: array] : ((~(![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$lesseq($sum(read(U, V), $product(-1, V)), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(read(U, W), W), 20))))) | ![X: $int] : ((~$lesseq(read(U, X), 5)) | (~($greatereq(X, 6) & $lesseq(X, 15)))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.23/0.41 tff(16,plain,
% 0.23/0.41 (~![U: array] : ((~(![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U, W)), 20))))) | ![X: $int] : ((~$lesseq(read(U, X), 5)) | (~($greatereq(X, 6) & $lesseq(X, 15)))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[15, 6])).
% 0.23/0.41 tff(17,plain,
% 0.23/0.41 (~![U: array] : ((~(![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U, W)), 20))))) | ![X: $int] : ((~$lesseq(read(U, X), 5)) | (~($greatereq(X, 6) & $lesseq(X, 15)))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[16, 5])).
% 0.23/0.41 tff(18,plain,
% 0.23/0.41 (~![U: array] : ((~(![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U, W)), 20))))) | ![X: $int] : ((~$lesseq(read(U, X), 5)) | (~($greatereq(X, 6) & $lesseq(X, 15)))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[17, 5])).
% 0.23/0.41 tff(19,plain,
% 0.23/0.41 (![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) & ![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20))) & (~((~$lesseq(read(U!0, X!1), 5)) | (~($greatereq(X!1, 6) & $lesseq(X!1, 15)))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[18, 4])).
% 0.23/0.41 tff(20,plain,
% 0.23/0.41 (~((~$lesseq(read(U!0, X!1), 5)) | (~($greatereq(X!1, 6) & $lesseq(X!1, 15))))),
% 0.23/0.41 inference(and_elim,[status(thm)],[19])).
% 0.23/0.41 tff(21,plain,
% 0.23/0.41 ($lesseq(read(U!0, X!1), 5)),
% 0.23/0.41 inference(or_elim,[status(thm)],[20])).
% 0.23/0.41 tff(22,plain,
% 0.23/0.41 ($greatereq(X!1, 6) & $lesseq(X!1, 15)),
% 0.23/0.41 inference(or_elim,[status(thm)],[20])).
% 0.23/0.41 tff(23,plain,
% 0.23/0.41 ($greatereq(X!1, 6)),
% 0.23/0.41 inference(and_elim,[status(thm)],[22])).
% 0.23/0.41 tff(24,plain,
% 0.23/0.41 ($greatereq($sum(X!1, $product(-1, read(U!0, X!1))), 0) | (~$greatereq(X!1, 6)) | (~$lesseq(read(U!0, X!1), 5))),
% 0.23/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.41 tff(25,plain,
% 0.23/0.41 ($greatereq($sum(X!1, $product(-1, read(U!0, X!1))), 0)),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[24, 23, 21])).
% 0.23/0.41 tff(26,plain,
% 0.23/0.41 ($greatereq(X!1, 1) | (~$greatereq(X!1, 6))),
% 0.23/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.41 tff(27,plain,
% 0.23/0.41 ($greatereq(X!1, 1)),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[26, 23])).
% 0.23/0.41 tff(28,plain,
% 0.23/0.41 (^[V: $int] : refl(((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10))) <=> ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(29,plain,
% 0.23/0.41 (![V: $int] : ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10))) <=> ![V: $int] : ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.23/0.41 tff(30,plain,
% 0.23/0.41 (^[V: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq(V, 1) & $lesseq(V, 10)) <=> (~((~$greatereq(V, 1)) | (~$lesseq(V, 10))))), ((~($greatereq(V, 1) & $lesseq(V, 10))) <=> (~(~((~$greatereq(V, 1)) | (~$lesseq(V, 10))))))), rewrite((~(~((~$greatereq(V, 1)) | (~$lesseq(V, 10))))) <=> ((~$greatereq(V, 1)) | (~$lesseq(V, 10)))), ((~($greatereq(V, 1) & $lesseq(V, 10))) <=> ((~$greatereq(V, 1)) | (~$lesseq(V, 10))))), (((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) <=> (((~$greatereq(V, 1)) | (~$lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))))), rewrite((((~$greatereq(V, 1)) | (~$lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) <=> ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10)))), (((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) <=> ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10)))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(31,plain,
% 0.23/0.42 (![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0))) <=> ![V: $int] : ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[30])).
% 0.23/0.42 tff(32,plain,
% 0.23/0.42 (![V: $int] : ((~($greatereq(V, 1) & $lesseq(V, 10))) | (~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)))),
% 0.23/0.42 inference(and_elim,[status(thm)],[19])).
% 0.23/0.42 tff(33,plain,
% 0.23/0.42 (![V: $int] : ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.23/0.42 tff(34,plain,
% 0.23/0.42 (![V: $int] : ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.23/0.42 tff(35,plain,
% 0.23/0.42 (((~![V: $int] : ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10)))) | ((~$greatereq($sum(X!1, $product(-1, read(U!0, X!1))), 0)) | (~$greatereq(X!1, 1)) | (~$lesseq(X!1, 10)))) <=> ((~![V: $int] : ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10)))) | (~$greatereq($sum(X!1, $product(-1, read(U!0, X!1))), 0)) | (~$greatereq(X!1, 1)) | (~$lesseq(X!1, 10)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(36,plain,
% 0.23/0.42 ((~![V: $int] : ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10)))) | ((~$greatereq($sum(X!1, $product(-1, read(U!0, X!1))), 0)) | (~$greatereq(X!1, 1)) | (~$lesseq(X!1, 10)))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(37,plain,
% 0.23/0.42 ((~![V: $int] : ((~$greatereq($sum(V, $product(-1, read(U!0, V))), 0)) | (~$greatereq(V, 1)) | (~$lesseq(V, 10)))) | (~$greatereq($sum(X!1, $product(-1, read(U!0, X!1))), 0)) | (~$greatereq(X!1, 1)) | (~$lesseq(X!1, 10))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.23/0.42 tff(38,plain,
% 0.23/0.42 ((~$greatereq($sum(X!1, $product(-1, read(U!0, X!1))), 0)) | (~$lesseq(X!1, 10))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[37, 34, 27])).
% 0.23/0.42 tff(39,plain,
% 0.23/0.42 (~$lesseq(X!1, 10)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[38, 25])).
% 0.23/0.42 tff(40,plain,
% 0.23/0.42 ($lesseq(X!1, 15)),
% 0.23/0.42 inference(and_elim,[status(thm)],[22])).
% 0.23/0.42 tff(41,plain,
% 0.23/0.42 ($lesseq($sum(X!1, read(U!0, X!1)), 20) | (~$lesseq(X!1, 15)) | (~$lesseq(read(U!0, X!1), 5))),
% 0.23/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.42 tff(42,plain,
% 0.23/0.42 ($lesseq($sum(X!1, read(U!0, X!1)), 20)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[41, 40, 21])).
% 0.23/0.42 tff(43,plain,
% 0.23/0.42 ($lesseq(X!1, 20) | (~$lesseq(X!1, 15))),
% 0.23/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.42 tff(44,plain,
% 0.23/0.42 ($lesseq(X!1, 20)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.23/0.42 tff(45,plain,
% 0.23/0.42 (^[W: $int] : refl(((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20))) <=> ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(46,plain,
% 0.23/0.42 (![W: $int] : ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20))) <=> ![W: $int] : ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.23/0.42 tff(47,plain,
% 0.23/0.42 (^[W: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq(W, 11) & $lesseq(W, 20)) <=> (~((~$greatereq(W, 11)) | (~$lesseq(W, 20))))), ((~($greatereq(W, 11) & $lesseq(W, 20))) <=> (~(~((~$greatereq(W, 11)) | (~$lesseq(W, 20))))))), rewrite((~(~((~$greatereq(W, 11)) | (~$lesseq(W, 20))))) <=> ((~$greatereq(W, 11)) | (~$lesseq(W, 20)))), ((~($greatereq(W, 11) & $lesseq(W, 20))) <=> ((~$greatereq(W, 11)) | (~$lesseq(W, 20))))), (((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20))) <=> (((~$greatereq(W, 11)) | (~$lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20))))), rewrite((((~$greatereq(W, 11)) | (~$lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20))) <=> ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20)))), (((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20))) <=> ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20)))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(48,plain,
% 0.23/0.42 (![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20))) <=> ![W: $int] : ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.23/0.42 tff(49,plain,
% 0.23/0.42 (![W: $int] : ((~($greatereq(W, 11) & $lesseq(W, 20))) | (~$lesseq($sum(W, read(U!0, W)), 20)))),
% 0.23/0.42 inference(and_elim,[status(thm)],[19])).
% 0.23/0.42 tff(50,plain,
% 0.23/0.42 (![W: $int] : ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.23/0.42 tff(51,plain,
% 0.23/0.42 (![W: $int] : ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.23/0.42 tff(52,plain,
% 0.23/0.42 (((~![W: $int] : ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20)))) | ((~$lesseq($sum(X!1, read(U!0, X!1)), 20)) | (~$greatereq(X!1, 11)) | (~$lesseq(X!1, 20)))) <=> ((~![W: $int] : ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20)))) | (~$lesseq($sum(X!1, read(U!0, X!1)), 20)) | (~$greatereq(X!1, 11)) | (~$lesseq(X!1, 20)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(53,plain,
% 0.23/0.42 ((~![W: $int] : ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20)))) | ((~$lesseq($sum(X!1, read(U!0, X!1)), 20)) | (~$greatereq(X!1, 11)) | (~$lesseq(X!1, 20)))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(54,plain,
% 0.23/0.42 ((~![W: $int] : ((~$lesseq($sum(W, read(U!0, W)), 20)) | (~$greatereq(W, 11)) | (~$lesseq(W, 20)))) | (~$lesseq($sum(X!1, read(U!0, X!1)), 20)) | (~$greatereq(X!1, 11)) | (~$lesseq(X!1, 20))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.23/0.42 tff(55,plain,
% 0.23/0.42 ((~$lesseq($sum(X!1, read(U!0, X!1)), 20)) | (~$greatereq(X!1, 11))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[54, 51, 44])).
% 0.23/0.42 tff(56,plain,
% 0.23/0.42 (~$greatereq(X!1, 11)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[55, 42])).
% 0.23/0.42 tff(57,plain,
% 0.23/0.42 ($greatereq(X!1, 11) | $lesseq(X!1, 10)),
% 0.23/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.42 tff(58,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[57, 56, 39])).
% 0.23/0.42 % SZS output end Proof
%------------------------------------------------------------------------------