TSTP Solution File: SWW610_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW610_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 : Thu Sep 29 20:59:26 EDT 2022
% Result : Theorem 7.62s 5.14s
% Output : Proof 7.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW610_2 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 20:17:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 7.62/5.14 % SZS status Theorem
% 7.62/5.14 % SZS output start Proof
% 7.62/5.14 tff(tptp_fun_N_2_type, type, (
% 7.62/5.14 tptp_fun_N_2: $int)).
% 7.62/5.14 tff(tptp_fun_Nqt_1_type, type, (
% 7.62/5.14 tptp_fun_Nqt_1: $int)).
% 7.62/5.14 tff(matches1_type, type, (
% 7.62/5.14 matches1: ( array_char * $int * array_char * $int * $int ) > $o)).
% 7.62/5.14 tff(tptp_fun_I2_3_type, type, (
% 7.62/5.14 tptp_fun_I2_3: $int)).
% 7.62/5.14 tff(tptp_fun_A2_5_type, type, (
% 7.62/5.14 tptp_fun_A2_5: array_char)).
% 7.62/5.14 tff(tptp_fun_I1_4_type, type, (
% 7.62/5.14 tptp_fun_I1_4: $int)).
% 7.62/5.14 tff(tptp_fun_A1_6_type, type, (
% 7.62/5.14 tptp_fun_A1_6: array_char)).
% 7.62/5.14 tff(tptp_fun_I_0_type, type, (
% 7.62/5.14 tptp_fun_I_0: ( $int * $int * array_char * $int * array_char ) > $int)).
% 7.62/5.14 tff(tb2t2_type, type, (
% 7.62/5.14 tb2t2: uni > char1)).
% 7.62/5.14 tff(get2_type, type, (
% 7.62/5.14 get2: ( ty * uni * $int ) > uni)).
% 7.62/5.14 tff(t2tb1_type, type, (
% 7.62/5.14 t2tb1: array_char > uni)).
% 7.62/5.14 tff(char_type, type, (
% 7.62/5.14 char: ty)).
% 7.62/5.14 tff(length1_type, type, (
% 7.62/5.14 length1: ( ty * uni ) > $int)).
% 7.62/5.14 tff(1,plain,
% 7.62/5.14 ((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | $lesseq($sum(N!2, $product(-1, Nqt!1)), 0) | (~matches1(A1!6, I1!4, A2!5, I2!3, N!2)))) <=> (~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | $greatereq($sum(Nqt!1, $product(-1, N!2)), 0)))),
% 7.62/5.15 inference(rewrite,[status(thm)],[])).
% 7.62/5.15 tff(2,plain,
% 7.62/5.15 ((~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | $lesseq($sum(N, $product(-1, Nqt)), 0) | (~matches1(A1, I1, A2, I2, N)))) <=> (~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | $lesseq($sum(N, $product(-1, Nqt)), 0) | (~matches1(A1, I1, A2, I2, N))))),
% 7.62/5.15 inference(rewrite,[status(thm)],[])).
% 7.62/5.15 tff(3,plain,
% 7.62/5.15 ((~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | (~matches1(A1, I1, A2, I2, N)) | $lesseq(N, Nqt))) <=> (~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | $lesseq($sum(N, $product(-1, Nqt)), 0) | (~matches1(A1, I1, A2, I2, N))))),
% 7.62/5.15 inference(rewrite,[status(thm)],[])).
% 7.62/5.15 tff(4,plain,
% 7.62/5.15 ((~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | (~matches1(A1, I1, A2, I2, N)) | $lesseq(N, Nqt))) <=> (~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | (~matches1(A1, I1, A2, I2, N)) | $lesseq(N, Nqt)))),
% 7.62/5.15 inference(rewrite,[status(thm)],[])).
% 7.62/5.15 tff(5,plain,
% 7.62/5.15 ((~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, N) => ($less(Nqt, N) => matches1(A1, I1, A2, I2, Nqt)))) <=> (~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | (~matches1(A1, I1, A2, I2, N)) | $lesseq(N, Nqt)))),
% 7.62/5.15 inference(rewrite,[status(thm)],[])).
% 7.62/5.15 tff(6,axiom,(~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, N) => ($less(Nqt, N) => matches1(A1, I1, A2, I2, Nqt)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','matches_right_weakening')).
% 7.62/5.15 tff(7,plain,
% 7.62/5.15 (~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | (~matches1(A1, I1, A2, I2, N)) | $lesseq(N, Nqt))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[6, 5])).
% 7.62/5.15 tff(8,plain,
% 7.62/5.15 (~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | (~matches1(A1, I1, A2, I2, N)) | $lesseq(N, Nqt))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[7, 4])).
% 7.62/5.15 tff(9,plain,
% 7.62/5.15 (~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | (~matches1(A1, I1, A2, I2, N)) | $lesseq(N, Nqt))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[8, 4])).
% 7.62/5.15 tff(10,plain,
% 7.62/5.15 (~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | (~matches1(A1, I1, A2, I2, N)) | $lesseq(N, Nqt))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[9, 4])).
% 7.62/5.15 tff(11,plain,
% 7.62/5.15 (~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | $lesseq($sum(N, $product(-1, Nqt)), 0) | (~matches1(A1, I1, A2, I2, N)))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[10, 3])).
% 7.62/5.15 tff(12,plain,
% 7.62/5.15 (~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | $lesseq($sum(N, $product(-1, Nqt)), 0) | (~matches1(A1, I1, A2, I2, N)))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[11, 2])).
% 7.62/5.15 tff(13,plain,
% 7.62/5.15 (~![A1: array_char, A2: array_char, I1: $int, I2: $int, N: $int, Nqt: $int] : (matches1(A1, I1, A2, I2, Nqt) | $lesseq($sum(N, $product(-1, Nqt)), 0) | (~matches1(A1, I1, A2, I2, N)))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[12, 2])).
% 7.62/5.15 tff(14,plain,(
% 7.62/5.15 ~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | $lesseq($sum(N!2, $product(-1, Nqt!1)), 0) | (~matches1(A1!6, I1!4, A2!5, I2!3, N!2)))),
% 7.62/5.15 inference(skolemize,[status(sab)],[13])).
% 7.62/5.15 tff(15,plain,
% 7.62/5.15 (~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | $greatereq($sum(Nqt!1, $product(-1, N!2)), 0))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[14, 1])).
% 7.62/5.15 tff(16,plain,
% 7.62/5.15 (~$greatereq($sum(Nqt!1, $product(-1, N!2)), 0)),
% 7.62/5.15 inference(or_elim,[status(thm)],[15])).
% 7.62/5.15 tff(17,plain,
% 7.62/5.15 (^[A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : rewrite((~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))))) <=> (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))))))),
% 7.62/5.15 inference(bind,[status(th)],[])).
% 7.62/5.15 tff(18,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))))) <=> ![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))),
% 7.62/5.15 inference(quant_intro,[status(thm)],[17])).
% 7.62/5.15 tff(19,plain,
% 7.62/5.15 (^[A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : refl((~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))))) <=> (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))))))),
% 7.62/5.15 inference(bind,[status(th)],[])).
% 7.62/5.15 tff(20,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))))) <=> ![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))))))),
% 7.62/5.15 inference(quant_intro,[status(thm)],[19])).
% 7.62/5.15 tff(21,plain,
% 7.62/5.15 (^[A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : rewrite((~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))))) <=> (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))))))),
% 7.62/5.15 inference(bind,[status(th)],[])).
% 7.62/5.15 tff(22,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))))) <=> ![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))))))),
% 7.62/5.15 inference(quant_intro,[status(thm)],[21])).
% 7.62/5.15 tff(23,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))))) <=> ![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))))))),
% 7.62/5.15 inference(transitivity,[status(thm)],[22, 20])).
% 7.62/5.15 tff(24,plain,
% 7.62/5.15 (^[A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : trans(monotonicity(rewrite(((~matches1(A1, I1, A2, I2, N)) | ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) <=> ((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))), trans(monotonicity(rewrite((~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))))) <=> (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))), ((matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1)))))))) <=> (matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))))), rewrite((matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))) <=> (matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))), ((matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1)))))))) <=> (matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))))), ((((~matches1(A1, I1, A2, I2, N)) | ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) & (matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))))))) <=> (((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))) & (matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))))), rewrite((((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))) & (matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) <=> (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))))))), ((((~matches1(A1, I1, A2, I2, N)) | ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) & (matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))))))) <=> (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))))))))),
% 7.62/5.15 inference(bind,[status(th)],[])).
% 7.62/5.15 tff(25,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (((~matches1(A1, I1, A2, I2, N)) | ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) & (matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))))))) <=> ![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))))))),
% 7.62/5.15 inference(quant_intro,[status(thm)],[24])).
% 7.62/5.15 tff(26,plain,
% 7.62/5.15 (^[A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : rewrite((((~matches1(A1, I1, A2, I2, N)) | ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) & (matches1(A1, I1, A2, I2, N) | ((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(tptp_fun_I_0(N, I2, A2, I1, A1), I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1)))))))))) <=> (((~matches1(A1, I1, A2, I2, N)) | ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) & (matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))))))))),
% 7.62/5.15 inference(bind,[status(th)],[])).
% 7.62/5.15 tff(27,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (((~matches1(A1, I1, A2, I2, N)) | ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) & (matches1(A1, I1, A2, I2, N) | ((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(tptp_fun_I_0(N, I2, A2, I1, A1), I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1)))))))))) <=> ![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (((~matches1(A1, I1, A2, I2, N)) | ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) & (matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1)))))))))),
% 7.62/5.15 inference(quant_intro,[status(thm)],[26])).
% 7.62/5.15 tff(28,plain,
% 7.62/5.15 (^[A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : rewrite((matches1(A1, I1, A2, I2, N) <=> ($greatereq(I1, 0) & $lesseq($sum(I1, $sum($product(-1, length1(char, t2tb1(A1))), N)), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum($product(-1, length1(char, t2tb1(A2))), N)), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) <=> (matches1(A1, I1, A2, I2, N) <=> ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))),
% 7.62/5.15 inference(bind,[status(th)],[])).
% 7.62/5.15 tff(29,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> ($greatereq(I1, 0) & $lesseq($sum(I1, $sum($product(-1, length1(char, t2tb1(A1))), N)), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum($product(-1, length1(char, t2tb1(A2))), N)), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) <=> ![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))),
% 7.62/5.15 inference(quant_intro,[status(thm)],[28])).
% 7.62/5.15 tff(30,plain,
% 7.62/5.15 (^[A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : rewrite((matches1(A1, I1, A2, I2, N) <=> ($lesseq(0, I1) & $lesseq(I1, $sum(length1(char, t2tb1(A1)), $product(-1, N))) & $lesseq(0, I2) & $lesseq(I2, $sum(length1(char, t2tb1(A2)), $product(-1, N))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) <=> (matches1(A1, I1, A2, I2, N) <=> ($greatereq(I1, 0) & $lesseq($sum(I1, $sum($product(-1, length1(char, t2tb1(A1))), N)), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum($product(-1, length1(char, t2tb1(A2))), N)), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))),
% 7.62/5.15 inference(bind,[status(th)],[])).
% 7.62/5.15 tff(31,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> ($lesseq(0, I1) & $lesseq(I1, $sum(length1(char, t2tb1(A1)), $product(-1, N))) & $lesseq(0, I2) & $lesseq(I2, $sum(length1(char, t2tb1(A2)), $product(-1, N))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) <=> ![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> ($greatereq(I1, 0) & $lesseq($sum(I1, $sum($product(-1, length1(char, t2tb1(A1))), N)), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum($product(-1, length1(char, t2tb1(A2))), N)), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))),
% 7.62/5.15 inference(quant_intro,[status(thm)],[30])).
% 7.62/5.15 tff(32,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> ($lesseq(0, I1) & $lesseq(I1, $sum(length1(char, t2tb1(A1)), $product(-1, N))) & $lesseq(0, I2) & $lesseq(I2, $sum(length1(char, t2tb1(A2)), $product(-1, N))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) <=> ![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> ($lesseq(0, I1) & $lesseq(I1, $sum(length1(char, t2tb1(A1)), $product(-1, N))) & $lesseq(0, I2) & $lesseq(I2, $sum(length1(char, t2tb1(A2)), $product(-1, N))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))),
% 7.62/5.15 inference(rewrite,[status(thm)],[])).
% 7.62/5.15 tff(33,plain,
% 7.62/5.15 (^[A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : rewrite((matches1(A1, I1, A2, I2, N) <=> (((($lesseq(0, I1) & $lesseq(I1, $difference(length1(char, t2tb1(A1)), N))) & $lesseq(0, I2)) & $lesseq(I2, $difference(length1(char, t2tb1(A2)), N))) & ![I: $int] : (($lesseq(0, I) & $less(I, N)) => (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) <=> (matches1(A1, I1, A2, I2, N) <=> ($lesseq(0, I1) & $lesseq(I1, $sum(length1(char, t2tb1(A1)), $product(-1, N))) & $lesseq(0, I2) & $lesseq(I2, $sum(length1(char, t2tb1(A2)), $product(-1, N))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))),
% 7.62/5.15 inference(bind,[status(th)],[])).
% 7.62/5.15 tff(34,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> (((($lesseq(0, I1) & $lesseq(I1, $difference(length1(char, t2tb1(A1)), N))) & $lesseq(0, I2)) & $lesseq(I2, $difference(length1(char, t2tb1(A2)), N))) & ![I: $int] : (($lesseq(0, I) & $less(I, N)) => (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) <=> ![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> ($lesseq(0, I1) & $lesseq(I1, $sum(length1(char, t2tb1(A1)), $product(-1, N))) & $lesseq(0, I2) & $lesseq(I2, $sum(length1(char, t2tb1(A2)), $product(-1, N))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))),
% 7.62/5.15 inference(quant_intro,[status(thm)],[33])).
% 7.62/5.15 tff(35,axiom,(![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> (((($lesseq(0, I1) & $lesseq(I1, $difference(length1(char, t2tb1(A1)), N))) & $lesseq(0, I2)) & $lesseq(I2, $difference(length1(char, t2tb1(A2)), N))) & ![I: $int] : (($lesseq(0, I) & $less(I, N)) => (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','matches_def')).
% 7.62/5.15 tff(36,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> ($lesseq(0, I1) & $lesseq(I1, $sum(length1(char, t2tb1(A1)), $product(-1, N))) & $lesseq(0, I2) & $lesseq(I2, $sum(length1(char, t2tb1(A2)), $product(-1, N))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[35, 34])).
% 7.62/5.15 tff(37,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> ($lesseq(0, I1) & $lesseq(I1, $sum(length1(char, t2tb1(A1)), $product(-1, N))) & $lesseq(0, I2) & $lesseq(I2, $sum(length1(char, t2tb1(A2)), $product(-1, N))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[36, 32])).
% 7.62/5.15 tff(38,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> ($greatereq(I1, 0) & $lesseq($sum(I1, $sum($product(-1, length1(char, t2tb1(A1))), N)), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum($product(-1, length1(char, t2tb1(A2))), N)), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, I))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[37, 31])).
% 7.62/5.15 tff(39,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (matches1(A1, I1, A2, I2, N) <=> ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[38, 29])).
% 7.62/5.15 tff(40,plain,(
% 7.62/5.15 ![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (((~matches1(A1, I1, A2, I2, N)) | ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) & (matches1(A1, I1, A2, I2, N) | ((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(tptp_fun_I_0(N, I2, A2, I1, A1), I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))))))))),
% 7.62/5.15 inference(skolemize,[status(sab)],[39])).
% 7.62/5.15 tff(41,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (((~matches1(A1, I1, A2, I2, N)) | ($greatereq(I1, 0) & $lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0) & $greatereq(I2, 0) & $lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))) & (matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~((~($greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0)))) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1)))))))))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[40, 27])).
% 7.62/5.15 tff(42,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))))))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[41, 25])).
% 7.62/5.15 tff(43,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I)))))))))) | (~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0))))))))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[42, 23])).
% 7.62/5.15 tff(44,plain,
% 7.62/5.15 (![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))),
% 7.62/5.15 inference(modus_ponens,[status(thm)],[43, 18])).
% 7.62/5.15 tff(45,plain,
% 7.62/5.15 (((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Nqt!1)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))))))))) <=> ((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Nqt!1)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))))))))),
% 7.62/5.16 inference(rewrite,[status(thm)],[])).
% 7.62/5.16 tff(46,plain,
% 7.62/5.16 ((~((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(Nqt!1, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(Nqt!1, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Nqt!1, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, I)))))))))))) <=> (~((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Nqt!1)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))))))))),
% 7.62/5.16 inference(rewrite,[status(thm)],[])).
% 7.62/5.16 tff(47,plain,
% 7.62/5.16 (((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(Nqt!1, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(Nqt!1, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Nqt!1, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, I))))))))))))) <=> ((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Nqt!1)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))))))))),
% 7.62/5.16 inference(monotonicity,[status(thm)],[46])).
% 7.62/5.16 tff(48,plain,
% 7.62/5.16 (((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(Nqt!1, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(Nqt!1, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Nqt!1, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, I))))))))))))) <=> ((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Nqt!1)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))))))))),
% 7.62/5.16 inference(transitivity,[status(thm)],[47, 45])).
% 7.62/5.16 tff(49,plain,
% 7.62/5.16 ((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(Nqt!1, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(Nqt!1, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Nqt!1, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, I))))))))))))),
% 7.62/5.16 inference(quant_inst,[status(thm)],[])).
% 7.62/5.16 tff(50,plain,
% 7.62/5.16 ((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Nqt!1)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))))))))),
% 7.62/5.16 inference(modus_ponens,[status(thm)],[49, 48])).
% 7.62/5.16 tff(51,plain,
% 7.62/5.16 (~((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Nqt!1)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))))))),
% 7.62/5.16 inference(unit_resolution,[status(thm)],[50, 44])).
% 7.62/5.16 tff(52,plain,
% 7.62/5.16 (((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Nqt!1)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))))))) | (matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))),
% 7.62/5.16 inference(tautology,[status(thm)],[])).
% 7.62/5.16 tff(53,plain,
% 7.62/5.16 (matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0))),
% 7.62/5.16 inference(unit_resolution,[status(thm)],[52, 51])).
% 7.62/5.16 tff(54,plain,
% 7.62/5.16 (((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))))))))) <=> ((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))))))))),
% 7.62/5.16 inference(rewrite,[status(thm)],[])).
% 7.62/5.16 tff(55,plain,
% 7.62/5.16 ((~((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(N!2, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(N!2, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N!2, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, I)))))))))))) <=> (~((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))))))))),
% 7.62/5.17 inference(rewrite,[status(thm)],[])).
% 7.62/5.17 tff(56,plain,
% 7.62/5.17 (((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(N!2, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(N!2, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N!2, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, I))))))))))))) <=> ((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))))))))),
% 7.62/5.17 inference(monotonicity,[status(thm)],[55])).
% 7.62/5.17 tff(57,plain,
% 7.62/5.17 (((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(N!2, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(N!2, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N!2, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, I))))))))))))) <=> ((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))))))))),
% 7.62/5.17 inference(transitivity,[status(thm)],[56, 54])).
% 7.62/5.17 tff(58,plain,
% 7.62/5.17 ((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(N!2, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(I2!3, $sum(N!2, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N!2, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, I))))))))))))),
% 7.62/5.17 inference(quant_inst,[status(thm)],[])).
% 7.62/5.17 tff(59,plain,
% 7.62/5.17 ((~![A1: array_char, I1: $int, A2: array_char, I2: $int, N: $int] : (~((~(matches1(A1, I1, A2, I2, N) | (~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_0(N, I2, A2, I1, A1))), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I1, tptp_fun_I_0(N, I2, A2, I1, A1)))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, tptp_fun_I_0(N, I2, A2, I1, A1))))) | (~$greatereq(tptp_fun_I_0(N, I2, A2, I1, A1), 0)))))) | (~((~matches1(A1, I1, A2, I2, N)) | (~((~$greatereq(I1, 0)) | (~$lesseq($sum(N, $sum(I1, $product(-1, length1(char, t2tb1(A1))))), 0)) | (~$greatereq(I2, 0)) | (~$lesseq($sum(I2, $sum(N, $product(-1, length1(char, t2tb1(A2))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0) | (tb2t2(get2(char, t2tb1(A1), $sum(I, I1))) = tb2t2(get2(char, t2tb1(A2), $sum(I2, I))))))))))))) | (~((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))))))))),
% 7.62/5.17 inference(modus_ponens,[status(thm)],[58, 57])).
% 7.62/5.17 tff(60,plain,
% 7.62/5.17 (~((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))))))),
% 7.62/5.17 inference(unit_resolution,[status(thm)],[59, 44])).
% 7.62/5.17 tff(61,plain,
% 7.62/5.17 (((~(matches1(A1!6, I1!4, A2!5, I2!3, N!2) | (~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(N!2, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))))))) | ((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))))),
% 7.62/5.17 inference(tautology,[status(thm)],[])).
% 7.62/5.17 tff(62,plain,
% 7.62/5.17 ((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))))),
% 7.62/5.17 inference(unit_resolution,[status(thm)],[61, 60])).
% 7.62/5.17 tff(63,plain,
% 7.62/5.17 (matches1(A1!6, I1!4, A2!5, I2!3, N!2)),
% 7.62/5.17 inference(or_elim,[status(thm)],[15])).
% 7.62/5.17 tff(64,plain,
% 7.62/5.17 ((~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))))) | (~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))))),
% 7.62/5.17 inference(tautology,[status(thm)],[])).
% 7.62/5.17 tff(65,plain,
% 7.62/5.17 ((~((~matches1(A1!6, I1!4, A2!5, I2!3, N!2)) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))))) | (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))))),
% 7.62/5.17 inference(unit_resolution,[status(thm)],[64, 63])).
% 7.62/5.17 tff(66,plain,
% 7.62/5.17 (~((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))))),
% 7.62/5.17 inference(unit_resolution,[status(thm)],[65, 62])).
% 7.62/5.17 tff(67,plain,
% 7.62/5.17 (((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))) | $lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)),
% 7.62/5.17 inference(tautology,[status(thm)],[])).
% 7.62/5.17 tff(68,plain,
% 7.62/5.17 ($lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)),
% 7.62/5.17 inference(unit_resolution,[status(thm)],[67, 66])).
% 7.62/5.17 tff(69,plain,
% 7.62/5.17 ($lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | $greatereq($sum(Nqt!1, $product(-1, N!2)), 0)),
% 7.62/5.17 inference(theory_lemma,[status(thm)],[])).
% 7.62/5.17 tff(70,plain,
% 7.62/5.17 ($lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)),
% 7.62/5.17 inference(unit_resolution,[status(thm)],[69, 16, 68])).
% 7.62/5.17 tff(71,plain,
% 7.62/5.17 (((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))) | $greatereq(I1!4, 0)),
% 7.62/5.17 inference(tautology,[status(thm)],[])).
% 7.62/5.17 tff(72,plain,
% 7.62/5.17 ($greatereq(I1!4, 0)),
% 7.62/5.17 inference(unit_resolution,[status(thm)],[71, 66])).
% 7.62/5.17 tff(73,plain,
% 7.62/5.17 (((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))) | $greatereq(I2!3, 0)),
% 7.62/5.17 inference(tautology,[status(thm)],[])).
% 7.62/5.17 tff(74,plain,
% 7.62/5.17 ($greatereq(I2!3, 0)),
% 7.62/5.17 inference(unit_resolution,[status(thm)],[73, 66])).
% 7.62/5.17 tff(75,plain,
% 7.62/5.17 (((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))) | $lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)),
% 7.62/5.17 inference(tautology,[status(thm)],[])).
% 7.62/5.17 tff(76,plain,
% 7.62/5.17 ($lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)),
% 7.62/5.17 inference(unit_resolution,[status(thm)],[75, 66])).
% 7.62/5.17 tff(77,plain,
% 7.62/5.17 ($lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | $greatereq($sum(Nqt!1, $product(-1, N!2)), 0)),
% 7.62/5.17 inference(theory_lemma,[status(thm)],[])).
% 7.62/5.17 tff(78,plain,
% 7.62/5.17 ($lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)),
% 7.62/5.17 inference(unit_resolution,[status(thm)],[77, 16, 76])).
% 7.62/5.17 tff(79,plain,
% 7.62/5.17 (~matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1)),
% 7.62/5.17 inference(or_elim,[status(thm)],[15])).
% 7.62/5.17 tff(80,plain,
% 7.62/5.17 ((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0))),
% 7.62/5.17 inference(tautology,[status(thm)],[])).
% 7.62/5.17 tff(81,plain,
% 7.62/5.17 ((~(matches1(A1!6, I1!4, A2!5, I2!3, Nqt!1) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)))) | (~$greatereq(I1!4, 0)) | (~$lesseq($sum(Nqt!1, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$greatereq(I2!3, 0)) | (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))) | (~$lesseq($sum(Nqt!1, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0))),
% 7.62/5.17 inference(unit_resolution,[status(thm)],[80, 79])).
% 7.62/5.17 tff(82,plain,
% 7.62/5.17 (~($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)))),
% 7.62/5.18 inference(unit_resolution,[status(thm)],[81, 78, 74, 72, 70, 53])).
% 7.62/5.18 tff(83,plain,
% 7.62/5.18 (($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0))) | (~$lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0))),
% 7.62/5.18 inference(tautology,[status(thm)],[])).
% 7.62/5.18 tff(84,plain,
% 7.62/5.18 (~$lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0)),
% 7.62/5.18 inference(unit_resolution,[status(thm)],[83, 82])).
% 7.62/5.18 tff(85,plain,
% 7.62/5.18 (((~$greatereq(I1!4, 0)) | (~$greatereq(I2!3, 0)) | (~$lesseq($sum(N!2, $sum(I1!4, $product(-1, length1(char, t2tb1(A1!6))))), 0)) | (~$lesseq($sum(N!2, $sum(I2!3, $product(-1, length1(char, t2tb1(A2!5))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3))))))) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))),
% 7.62/5.18 inference(tautology,[status(thm)],[])).
% 7.62/5.18 tff(86,plain,
% 7.62/5.18 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))),
% 7.62/5.18 inference(unit_resolution,[status(thm)],[85, 66])).
% 7.62/5.18 tff(87,plain,
% 7.62/5.18 (($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0))) | $greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)),
% 7.62/5.18 inference(tautology,[status(thm)],[])).
% 7.62/5.18 tff(88,plain,
% 7.62/5.18 ($greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)),
% 7.62/5.18 inference(unit_resolution,[status(thm)],[87, 82])).
% 7.62/5.18 tff(89,plain,
% 7.62/5.18 (($lesseq($sum(Nqt!1, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0))) | (~(tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))))),
% 7.62/5.18 inference(tautology,[status(thm)],[])).
% 7.62/5.18 tff(90,plain,
% 7.62/5.18 (~(tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))))),
% 7.62/5.18 inference(unit_resolution,[status(thm)],[89, 82])).
% 7.62/5.18 tff(91,plain,
% 7.62/5.18 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))) | ((~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))))),
% 7.62/5.18 inference(rewrite,[status(thm)],[])).
% 7.62/5.18 tff(92,plain,
% 7.62/5.18 (((~$greatereq($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), 0)) | $greatereq($sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), I2!3))))) <=> ((~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))))),
% 7.62/5.18 inference(rewrite,[status(thm)],[])).
% 7.62/5.18 tff(93,plain,
% 7.62/5.18 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))) | ((~$greatereq($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), 0)) | $greatereq($sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), I2!3)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))) | ((~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))))))),
% 7.62/5.18 inference(monotonicity,[status(thm)],[92])).
% 7.62/5.18 tff(94,plain,
% 7.62/5.18 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))) | ((~$greatereq($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), 0)) | $greatereq($sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), I2!3)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))))))),
% 7.62/5.18 inference(transitivity,[status(thm)],[93, 91])).
% 7.62/5.18 tff(95,plain,
% 7.62/5.18 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))) | ((~$greatereq($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), 0)) | $greatereq($sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum($sum($sum($sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)), $sum($product(-1, I1!4), I2!3)), $product(-1, I2!3)), I2!3)))))),
% 7.62/5.18 inference(quant_inst,[status(thm)],[])).
% 7.62/5.18 tff(96,plain,
% 7.62/5.18 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!2)), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I, I1!4))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I, I2!3)))))) | (~$greatereq(tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6), 0)) | $lesseq($sum(N!2, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0) | (tb2t2(get2(char, t2tb1(A1!6), $sum(I1!4, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))) = tb2t2(get2(char, t2tb1(A2!5), $sum(I2!3, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6)))))),
% 7.62/5.18 inference(modus_ponens,[status(thm)],[95, 94])).
% 7.62/5.18 tff(97,plain,
% 7.62/5.18 ($lesseq($sum(N!2, $product(-1, tptp_fun_I_0(Nqt!1, I2!3, A2!5, I1!4, A1!6))), 0)),
% 7.62/5.18 inference(unit_resolution,[status(thm)],[96, 90, 88, 86])).
% 7.62/5.18 tff(98,plain,
% 7.62/5.18 ($false),
% 7.62/5.18 inference(theory_lemma,[status(thm)],[97, 84, 16])).
% 7.62/5.18 % SZS output end Proof
%------------------------------------------------------------------------------