TSTP Solution File: SWW614_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW614_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 20:59:27 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW614_2 : TPTP v8.1.0. Released v6.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 20:33:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(tptp_fun_L_5_type, type, (
% 0.21/0.44 tptp_fun_L_5: $int)).
% 0.21/0.44 tff(tptp_fun_A_4_type, type, (
% 0.21/0.44 tptp_fun_A_4: $int)).
% 0.21/0.44 tff(tptp_fun_X_2_type, type, (
% 0.21/0.44 tptp_fun_X_2: $int)).
% 0.21/0.44 tff(tb2t_type, type, (
% 0.21/0.44 tb2t: uni > $int)).
% 0.21/0.44 tff(get_type, type, (
% 0.21/0.44 get: ( ty * ty * uni * uni ) > uni)).
% 0.21/0.44 tff(t2tb_type, type, (
% 0.21/0.44 t2tb: $int > uni)).
% 0.21/0.44 tff(t2tb2_type, type, (
% 0.21/0.44 t2tb2: map_int_int > uni)).
% 0.21/0.44 tff(tptp_fun_A1_3_type, type, (
% 0.21/0.44 tptp_fun_A1_3: map_int_int)).
% 0.21/0.44 tff(int_type, type, (
% 0.21/0.44 int: ty)).
% 0.21/0.44 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.44 tptp_fun_Y_1: $int)).
% 0.21/0.44 tff(eqseq_type, type, (
% 0.21/0.44 eqseq: ( array_int * $int * $int * $int ) > $o)).
% 0.21/0.44 tff(tb2t1_type, type, (
% 0.21/0.44 tb2t1: uni > array_int)).
% 0.21/0.44 tff(mk_array_type, type, (
% 0.21/0.44 mk_array: ( ty * $int * uni ) > uni)).
% 0.21/0.44 tff(tptp_fun_L1_6_type, type, (
% 0.21/0.44 tptp_fun_L1_6: $int)).
% 0.21/0.44 tff(length_type, type, (
% 0.21/0.44 length: ( ty * uni ) > $int)).
% 0.21/0.44 tff(t2tb1_type, type, (
% 0.21/0.44 t2tb1: array_int > uni)).
% 0.21/0.44 tff(tptp_fun_I_0_type, type, (
% 0.21/0.44 tptp_fun_I_0: ( $int * $int * $int * array_int ) > $int)).
% 0.21/0.44 tff(get1_type, type, (
% 0.21/0.44 get1: ( ty * uni * $int ) > uni)).
% 0.21/0.44 tff(elts_type, type, (
% 0.21/0.44 elts: ( ty * uni ) > uni)).
% 0.21/0.44 tff(sort_type, type, (
% 0.21/0.44 sort: ( ty * uni ) > $o)).
% 0.21/0.44 tff(map_type, type, (
% 0.21/0.44 map: ( ty * ty ) > ty)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 ((($greatereq(A!4, 0) & $greatereq(X!2, 0) & (~$greatereq($sum(X!2, $product(-1, A!4)), 0)) & $greatereq(Y!1, 0) & (~$greatereq($sum(Y!1, $product(-1, A!4)), 0))) & ((~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & $greatereq($sum(X!2, L!5), 0) & $greatereq($sum(Y!1, L!5), 0) & eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) & ($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0))) <=> ($greatereq(A!4, 0) & $greatereq(X!2, 0) & (~$greatereq($sum(X!2, $product(-1, A!4)), 0)) & $greatereq(Y!1, 0) & (~$greatereq($sum(Y!1, $product(-1, A!4)), 0)) & (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & $greatereq($sum(X!2, L!5), 0) & $greatereq($sum(Y!1, L!5), 0) & eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) & ($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (((~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & ($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0))) & ($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0))) & eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) & ($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0)) <=> ((~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & $greatereq($sum(X!2, L!5), 0) & $greatereq($sum(Y!1, L!5), 0) & eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) & ($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 ((~(~($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0))) <=> ($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 ((~(~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5))) <=> eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 ((~(~($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0))))) <=> ($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 ((~($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0)))) <=> (~($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 ((~(~($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0))))) <=> (~(~($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[6])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 ((~(~($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0))))) <=> ($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[7, 5])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 ((~(~($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0))))) <=> ($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 ((~($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0)))) <=> (~($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 ((~(~($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0))))) <=> (~(~($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[10])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 ((~(~($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0))))) <=> ($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[11, 9])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 ((~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0)) <=> (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 ((~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0)) <=> (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 (((~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0)) & (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & (~(~($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0))))) & (~(~($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0))))) & (~(~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5))) & (~(~($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0)))) <=> ((~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & ($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0))) & ($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0))) & eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) & ($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[14, 13, 12, 8, 4, 3])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.45 (((~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0)) & (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & (~(~($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0))))) & (~(~($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0))))) & (~(~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5))) & (~(~($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0)))) <=> ((~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & $greatereq($sum(X!2, L!5), 0) & $greatereq($sum(Y!1, L!5), 0) & eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) & ($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0))),
% 0.21/0.45 inference(transitivity,[status(thm)],[15, 2])).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 ((~(~($greatereq(A!4, 0) & $greatereq(X!2, 0) & (~$greatereq($sum(X!2, $product(-1, A!4)), 0)) & $greatereq(Y!1, 0) & (~$greatereq($sum(Y!1, $product(-1, A!4)), 0))))) <=> ($greatereq(A!4, 0) & $greatereq(X!2, 0) & (~$greatereq($sum(X!2, $product(-1, A!4)), 0)) & $greatereq(Y!1, 0) & (~$greatereq($sum(Y!1, $product(-1, A!4)), 0)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 (((~(~($greatereq(A!4, 0) & $greatereq(X!2, 0) & (~$greatereq($sum(X!2, $product(-1, A!4)), 0)) & $greatereq(Y!1, 0) & (~$greatereq($sum(Y!1, $product(-1, A!4)), 0))))) & ((~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0)) & (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & (~(~($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0))))) & (~(~($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0))))) & (~(~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5))) & (~(~($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0))))) <=> (($greatereq(A!4, 0) & $greatereq(X!2, 0) & (~$greatereq($sum(X!2, $product(-1, A!4)), 0)) & $greatereq(Y!1, 0) & (~$greatereq($sum(Y!1, $product(-1, A!4)), 0))) & ((~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & $greatereq($sum(X!2, L!5), 0) & $greatereq($sum(Y!1, L!5), 0) & eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) & ($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[17, 16])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (((~(~($greatereq(A!4, 0) & $greatereq(X!2, 0) & (~$greatereq($sum(X!2, $product(-1, A!4)), 0)) & $greatereq(Y!1, 0) & (~$greatereq($sum(Y!1, $product(-1, A!4)), 0))))) & ((~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0)) & (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & (~(~($greatereq($sum(X!2, L!5), 0) & (~$greatereq($sum(X!2, $sum(L!5, $product(-1, A!4))), 0))))) & (~(~($greatereq($sum(Y!1, L!5), 0) & (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, A!4))), 0))))) & (~(~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5))) & (~(~($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0))))) <=> ($greatereq(A!4, 0) & $greatereq(X!2, 0) & (~$greatereq($sum(X!2, $product(-1, A!4)), 0)) & $greatereq(Y!1, 0) & (~$greatereq($sum(Y!1, $product(-1, A!4)), 0)) & (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & $greatereq($sum(X!2, L!5), 0) & $greatereq($sum(Y!1, L!5), 0) & eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) & ($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0))),
% 0.21/0.45 inference(transitivity,[status(thm)],[18, 1])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 ((~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($greatereq(A, 0) & $greatereq(X, 0) & (~$greatereq($sum(X, $product(-1, A)), 0)) & $greatereq(Y, 0) & (~$greatereq($sum(Y, $product(-1, A)), 0)))) | ![L: $int] : ($greatereq($sum(X, $sum(L, $product(-1, A))), 0) | $greatereq($sum(Y, $sum(L, $product(-1, A))), 0) | ![L1: $int] : ((~($sum(L, $product(-1, L1)) = -1)) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($greatereq($sum(X, L), 0) & (~$greatereq($sum(X, $sum(L, $product(-1, A))), 0)))) | (~($greatereq($sum(Y, L), 0) & (~$greatereq($sum(Y, $sum(L, $product(-1, A))), 0)))) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | (~($sum(tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))), $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))))) = 0))))) <=> (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($greatereq(A, 0) & $greatereq(X, 0) & (~$greatereq($sum(X, $product(-1, A)), 0)) & $greatereq(Y, 0) & (~$greatereq($sum(Y, $product(-1, A)), 0)))) | ![L: $int] : ($greatereq($sum(X, $sum(L, $product(-1, A))), 0) | $greatereq($sum(Y, $sum(L, $product(-1, A))), 0) | ![L1: $int] : ((~($sum(L, $product(-1, L1)) = -1)) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($greatereq($sum(X, L), 0) & (~$greatereq($sum(X, $sum(L, $product(-1, A))), 0)))) | (~($greatereq($sum(Y, L), 0) & (~$greatereq($sum(Y, $sum(L, $product(-1, A))), 0)))) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | (~($sum(tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))), $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))))) = 0)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 ((~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($greatereq(A, 0) & $greatereq(X, 0) & (~$lesseq($sum(A, $product(-1, X)), 0)) & $greatereq(Y, 0) & (~$lesseq($sum(A, $product(-1, Y)), 0)))) | ![L: $int] : ((~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | (~($sum(tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))), $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))))) = 0)) | $lesseq($sum(A, $sum($product(-1, X), $product(-1, L))), 0) | $lesseq($sum(A, $sum($product(-1, Y), $product(-1, L))), 0) | ![L1: $int] : ((~($sum(L1, $product(-1, L)) = 1)) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($greatereq($sum(X, L), 0) & (~$lesseq($sum(A, $sum($product(-1, X), $product(-1, L))), 0)))) | (~($greatereq($sum(Y, L), 0) & (~$lesseq($sum(A, $sum($product(-1, Y), $product(-1, L))), 0))))))) <=> (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($greatereq(A, 0) & $greatereq(X, 0) & (~$greatereq($sum(X, $product(-1, A)), 0)) & $greatereq(Y, 0) & (~$greatereq($sum(Y, $product(-1, A)), 0)))) | ![L: $int] : ($greatereq($sum(X, $sum(L, $product(-1, A))), 0) | $greatereq($sum(Y, $sum(L, $product(-1, A))), 0) | ![L1: $int] : ((~($sum(L, $product(-1, L1)) = -1)) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($greatereq($sum(X, L), 0) & (~$greatereq($sum(X, $sum(L, $product(-1, A))), 0)))) | (~($greatereq($sum(Y, L), 0) & (~$greatereq($sum(Y, $sum(L, $product(-1, A))), 0)))) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | (~($sum(tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))), $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))))) = 0)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(22,plain,
% 0.21/0.45 ((~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($lesseq(0, A) & $lesseq(0, X) & (~$lesseq(A, X)) & $lesseq(0, Y) & (~$lesseq(A, Y)))) | ![L: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))) = tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))))) | $lesseq(A, $sum(X, L)) | $lesseq(A, $sum(Y, L)) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | ![L1: $int] : ((~(L1 = $sum(1, L))) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($lesseq(0, $sum(X, L)) & (~$lesseq(A, $sum(X, L))))) | (~($lesseq(0, $sum(Y, L)) & (~$lesseq(A, $sum(Y, L)))))))) <=> (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($greatereq(A, 0) & $greatereq(X, 0) & (~$lesseq($sum(A, $product(-1, X)), 0)) & $greatereq(Y, 0) & (~$lesseq($sum(A, $product(-1, Y)), 0)))) | ![L: $int] : ((~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | (~($sum(tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))), $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))))) = 0)) | $lesseq($sum(A, $sum($product(-1, X), $product(-1, L))), 0) | $lesseq($sum(A, $sum($product(-1, Y), $product(-1, L))), 0) | ![L1: $int] : ((~($sum(L1, $product(-1, L)) = 1)) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($greatereq($sum(X, L), 0) & (~$lesseq($sum(A, $sum($product(-1, X), $product(-1, L))), 0)))) | (~($greatereq($sum(Y, L), 0) & (~$lesseq($sum(A, $sum($product(-1, Y), $product(-1, L))), 0)))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(23,plain,
% 0.21/0.45 ((~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($lesseq(0, A) & $lesseq(0, X) & (~$lesseq(A, X)) & $lesseq(0, Y) & (~$lesseq(A, Y)))) | ![L: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))) = tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))))) | $lesseq(A, $sum(X, L)) | $lesseq(A, $sum(Y, L)) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | ![L1: $int] : ((~(L1 = $sum(1, L))) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($lesseq(0, $sum(X, L)) & (~$lesseq(A, $sum(X, L))))) | (~($lesseq(0, $sum(Y, L)) & (~$lesseq(A, $sum(Y, L)))))))) <=> (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($lesseq(0, A) & $lesseq(0, X) & (~$lesseq(A, X)) & $lesseq(0, Y) & (~$lesseq(A, Y)))) | ![L: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))) = tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))))) | $lesseq(A, $sum(X, L)) | $lesseq(A, $sum(Y, L)) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | ![L1: $int] : ((~(L1 = $sum(1, L))) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($lesseq(0, $sum(X, L)) & (~$lesseq(A, $sum(X, L))))) | (~($lesseq(0, $sum(Y, L)) & (~$lesseq(A, $sum(Y, L))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(24,plain,
% 0.21/0.45 ((~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((((($lesseq(0, A) & $lesseq(0, X)) & $less(X, A)) & $lesseq(0, Y)) & $less(Y, A)) => ![L: $int] : (eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L) => ($less($sum(X, L), A) => ($less($sum(Y, L), A) => (($lesseq(0, $sum(Y, L)) & $less($sum(Y, L), A)) => (($lesseq(0, $sum(X, L)) & $less($sum(X, L), A)) => ((tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))) = tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L))))) => ![L1: $int] : ((L1 = $sum(L, 1)) => eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)))))))))) <=> (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($lesseq(0, A) & $lesseq(0, X) & (~$lesseq(A, X)) & $lesseq(0, Y) & (~$lesseq(A, Y)))) | ![L: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))) = tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))))) | $lesseq(A, $sum(X, L)) | $lesseq(A, $sum(Y, L)) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | ![L1: $int] : ((~(L1 = $sum(1, L))) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($lesseq(0, $sum(X, L)) & (~$lesseq(A, $sum(X, L))))) | (~($lesseq(0, $sum(Y, L)) & (~$lesseq(A, $sum(Y, L))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(25,axiom,(~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((((($lesseq(0, A) & $lesseq(0, X)) & $less(X, A)) & $lesseq(0, Y)) & $less(Y, A)) => ![L: $int] : (eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L) => ($less($sum(X, L), A) => ($less($sum(Y, L), A) => (($lesseq(0, $sum(Y, L)) & $less($sum(Y, L), A)) => (($lesseq(0, $sum(X, L)) & $less($sum(X, L), A)) => ((tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))) = tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L))))) => ![L1: $int] : ((L1 = $sum(L, 1)) => eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_lcp')).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($lesseq(0, A) & $lesseq(0, X) & (~$lesseq(A, X)) & $lesseq(0, Y) & (~$lesseq(A, Y)))) | ![L: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))) = tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))))) | $lesseq(A, $sum(X, L)) | $lesseq(A, $sum(Y, L)) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | ![L1: $int] : ((~(L1 = $sum(1, L))) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($lesseq(0, $sum(X, L)) & (~$lesseq(A, $sum(X, L))))) | (~($lesseq(0, $sum(Y, L)) & (~$lesseq(A, $sum(Y, L)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($lesseq(0, A) & $lesseq(0, X) & (~$lesseq(A, X)) & $lesseq(0, Y) & (~$lesseq(A, Y)))) | ![L: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))) = tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))))) | $lesseq(A, $sum(X, L)) | $lesseq(A, $sum(Y, L)) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | ![L1: $int] : ((~(L1 = $sum(1, L))) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($lesseq(0, $sum(X, L)) & (~$lesseq(A, $sum(X, L))))) | (~($lesseq(0, $sum(Y, L)) & (~$lesseq(A, $sum(Y, L)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($lesseq(0, A) & $lesseq(0, X) & (~$lesseq(A, X)) & $lesseq(0, Y) & (~$lesseq(A, Y)))) | ![L: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))) = tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))))) | $lesseq(A, $sum(X, L)) | $lesseq(A, $sum(Y, L)) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | ![L1: $int] : ((~(L1 = $sum(1, L))) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($lesseq(0, $sum(X, L)) & (~$lesseq(A, $sum(X, L))))) | (~($lesseq(0, $sum(Y, L)) & (~$lesseq(A, $sum(Y, L)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($lesseq(0, A) & $lesseq(0, X) & (~$lesseq(A, X)) & $lesseq(0, Y) & (~$lesseq(A, Y)))) | ![L: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))) = tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))))) | $lesseq(A, $sum(X, L)) | $lesseq(A, $sum(Y, L)) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | ![L1: $int] : ((~(L1 = $sum(1, L))) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($lesseq(0, $sum(X, L)) & (~$lesseq(A, $sum(X, L))))) | (~($lesseq(0, $sum(Y, L)) & (~$lesseq(A, $sum(Y, L)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($greatereq(A, 0) & $greatereq(X, 0) & (~$lesseq($sum(A, $product(-1, X)), 0)) & $greatereq(Y, 0) & (~$lesseq($sum(A, $product(-1, Y)), 0)))) | ![L: $int] : ((~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | (~($sum(tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))), $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))))) = 0)) | $lesseq($sum(A, $sum($product(-1, X), $product(-1, L))), 0) | $lesseq($sum(A, $sum($product(-1, Y), $product(-1, L))), 0) | ![L1: $int] : ((~($sum(L1, $product(-1, L)) = 1)) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($greatereq($sum(X, L), 0) & (~$lesseq($sum(A, $sum($product(-1, X), $product(-1, L))), 0)))) | (~($greatereq($sum(Y, L), 0) & (~$lesseq($sum(A, $sum($product(-1, Y), $product(-1, L))), 0))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($greatereq(A, 0) & $greatereq(X, 0) & (~$greatereq($sum(X, $product(-1, A)), 0)) & $greatereq(Y, 0) & (~$greatereq($sum(Y, $product(-1, A)), 0)))) | ![L: $int] : ($greatereq($sum(X, $sum(L, $product(-1, A))), 0) | $greatereq($sum(Y, $sum(L, $product(-1, A))), 0) | ![L1: $int] : ((~($sum(L, $product(-1, L1)) = -1)) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($greatereq($sum(X, L), 0) & (~$greatereq($sum(X, $sum(L, $product(-1, A))), 0)))) | (~($greatereq($sum(Y, L), 0) & (~$greatereq($sum(Y, $sum(L, $product(-1, A))), 0)))) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | (~($sum(tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))), $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))))) = 0))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[30, 21])).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($greatereq(A, 0) & $greatereq(X, 0) & (~$greatereq($sum(X, $product(-1, A)), 0)) & $greatereq(Y, 0) & (~$greatereq($sum(Y, $product(-1, A)), 0)))) | ![L: $int] : ($greatereq($sum(X, $sum(L, $product(-1, A))), 0) | $greatereq($sum(Y, $sum(L, $product(-1, A))), 0) | ![L1: $int] : ((~($sum(L, $product(-1, L1)) = -1)) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($greatereq($sum(X, L), 0) & (~$greatereq($sum(X, $sum(L, $product(-1, A))), 0)))) | (~($greatereq($sum(Y, L), 0) & (~$greatereq($sum(Y, $sum(L, $product(-1, A))), 0)))) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | (~($sum(tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))), $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))))) = 0))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[31, 20])).
% 0.21/0.45 tff(33,plain,
% 0.21/0.45 (~![A: $int, A1: map_int_int, X: $int, Y: $int] : ((~($greatereq(A, 0) & $greatereq(X, 0) & (~$greatereq($sum(X, $product(-1, A)), 0)) & $greatereq(Y, 0) & (~$greatereq($sum(Y, $product(-1, A)), 0)))) | ![L: $int] : ($greatereq($sum(X, $sum(L, $product(-1, A))), 0) | $greatereq($sum(Y, $sum(L, $product(-1, A))), 0) | ![L1: $int] : ((~($sum(L, $product(-1, L1)) = -1)) | eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L1)) | (~($greatereq($sum(X, L), 0) & (~$greatereq($sum(X, $sum(L, $product(-1, A))), 0)))) | (~($greatereq($sum(Y, L), 0) & (~$greatereq($sum(Y, $sum(L, $product(-1, A))), 0)))) | (~eqseq(tb2t1(mk_array(int, A, t2tb2(A1))), X, Y, L)) | (~($sum(tb2t(get(int, int, t2tb2(A1), t2tb($sum(Y, L)))), $product(-1, tb2t(get(int, int, t2tb2(A1), t2tb($sum(X, L)))))) = 0))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[32, 20])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 ($greatereq(A!4, 0) & $greatereq(X!2, 0) & (~$greatereq($sum(X!2, $product(-1, A!4)), 0)) & $greatereq(Y!1, 0) & (~$greatereq($sum(Y!1, $product(-1, A!4)), 0)) & (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)) & (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)) & (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))) & $greatereq($sum(X!2, L!5), 0) & $greatereq($sum(Y!1, L!5), 0) & eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) & ($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[33, 19])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 (~$greatereq($sum(X!2, $sum($product(-1, A!4), L!5)), 0)),
% 0.21/0.45 inference(and_elim,[status(thm)],[34])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 (~((~($sum(L!5, $product(-1, L1!6)) = -1)) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6))),
% 0.21/0.45 inference(and_elim,[status(thm)],[34])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 ($sum(L!5, $product(-1, L1!6)) = -1),
% 0.21/0.45 inference(or_elim,[status(thm)],[36])).
% 0.21/0.45 tff(38,plain,
% 0.21/0.45 ((~($sum(L!5, $product(-1, L1!6)) = -1)) | $greatereq($sum(L!5, $product(-1, L1!6)), -1)),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 ($greatereq($sum(L!5, $product(-1, L1!6)), -1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.45 tff(40,plain,
% 0.21/0.45 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(41,plain,
% 0.21/0.45 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(42,axiom,(![J: uni] : (t2tb1(tb2t1(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR1')).
% 0.21/0.45 tff(43,plain,
% 0.21/0.46 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.46 tff(44,plain,(
% 0.21/0.46 ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.46 inference(skolemize,[status(sab)],[43])).
% 0.21/0.46 tff(45,plain,
% 0.21/0.46 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.21/0.46 tff(46,plain,
% 0.21/0.46 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))) = mk_array(int, A!4, t2tb2(A1!3)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(47,plain,
% 0.21/0.46 (t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))) = mk_array(int, A!4, t2tb2(A1!3))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.21/0.46 tff(48,plain,
% 0.21/0.46 (length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3))))) = length(int, mk_array(int, A!4, t2tb2(A1!3)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[47])).
% 0.21/0.46 tff(49,plain,
% 0.21/0.46 (length(int, mk_array(int, A!4, t2tb2(A1!3))) = length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))),
% 0.21/0.46 inference(symmetry,[status(thm)],[48])).
% 0.21/0.46 tff(50,plain,
% 0.21/0.46 ((~(length(int, mk_array(int, A!4, t2tb2(A1!3))) = length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))) | $lesseq($sum(length(int, mk_array(int, A!4, t2tb2(A1!3))), $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0)),
% 0.21/0.46 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.46 tff(51,plain,
% 0.21/0.46 ($lesseq($sum(length(int, mk_array(int, A!4, t2tb2(A1!3))), $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.21/0.46 tff(52,plain,
% 0.21/0.46 (~$greatereq($sum(Y!1, $sum($product(-1, A!4), L!5)), 0)),
% 0.21/0.46 inference(and_elim,[status(thm)],[34])).
% 0.21/0.46 tff(53,assumption,(~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)), introduced(assumption)).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 (^[A: ty, U: $int, U1: uni] : refl(($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0) <=> ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)),
% 0.21/0.46 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 (^[A: ty, U: $int, U1: uni] : trans(monotonicity(rewrite($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = $sum($product(-1, U), length(A, mk_array(A, U, U1)))), (($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0) <=> ($sum($product(-1, U), length(A, mk_array(A, U, U1))) = 0))), rewrite(($sum($product(-1, U), length(A, mk_array(A, U, U1))) = 0) <=> ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)), (($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0) <=> ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(57,plain,
% 0.21/0.46 (![A: ty, U: $int, U1: uni] : ($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)),
% 0.21/0.46 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 (^[A: ty, U: $int, U1: uni] : rewrite((length(A, mk_array(A, U, U1)) = U) <=> ($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(59,plain,
% 0.21/0.46 (![A: ty, U: $int, U1: uni] : (length(A, mk_array(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : ($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0)),
% 0.21/0.46 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 (![A: ty, U: $int, U1: uni] : (length(A, mk_array(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : (length(A, mk_array(A, U, U1)) = U)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(61,axiom,(![A: ty, U: $int, U1: uni] : (length(A, mk_array(A, U, U1)) = U)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','length_def')).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (![A: ty, U: $int, U1: uni] : (length(A, mk_array(A, U, U1)) = U)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 (![A: ty, U: $int, U1: uni] : ($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[63, 57])).
% 0.21/0.46 tff(65,plain,(
% 0.21/0.46 ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)),
% 0.21/0.46 inference(skolemize,[status(sab)],[64])).
% 0.21/0.46 tff(66,plain,
% 0.21/0.46 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.21/0.46 tff(67,plain,
% 0.21/0.46 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)) | ($sum(A!4, $product(-1, length(int, mk_array(int, A!4, t2tb2(A1!3))))) = 0)),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(68,plain,
% 0.21/0.46 ($sum(A!4, $product(-1, length(int, mk_array(int, A!4, t2tb2(A1!3))))) = 0),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.21/0.46 tff(69,plain,
% 0.21/0.46 ((~($sum(A!4, $product(-1, length(int, mk_array(int, A!4, t2tb2(A1!3))))) = 0)) | $lesseq($sum(A!4, $product(-1, length(int, mk_array(int, A!4, t2tb2(A1!3))))), 0)),
% 0.21/0.46 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.46 tff(70,plain,
% 0.21/0.46 ($lesseq($sum(A!4, $product(-1, length(int, mk_array(int, A!4, t2tb2(A1!3))))), 0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.46 tff(71,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(theory_lemma,[status(thm)],[70, 53, 51, 39, 52])).
% 0.21/0.46 tff(72,plain,($lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(73,assumption,(~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))), introduced(assumption)).
% 0.21/0.46 tff(74,plain,
% 0.21/0.46 (($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0))) | (~($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(75,plain,
% 0.21/0.46 (~($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.46 tff(76,plain,
% 0.21/0.46 (($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0))) | $greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(77,plain,
% 0.21/0.46 ($greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.21/0.46 tff(78,plain,
% 0.21/0.46 (^[A: array_int, X: $int, Y: $int, I: $int] : refl(((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0))) <=> ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(79,plain,
% 0.21/0.46 (![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0))) <=> ![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.46 tff(80,plain,
% 0.21/0.46 (^[A: array_int, X: $int, Y: $int, I: $int] : rewrite(((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0))) <=> ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(81,plain,
% 0.21/0.46 (![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0))) <=> ![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.46 tff(82,plain,
% 0.21/0.46 (![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0))) <=> ![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[81, 79])).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 (^[A: array_int, X: $int, Y: $int, I: $int] : rewrite(((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq($sum(Len, $product(-1, I)), 0))) <=> ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 (![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq($sum(Len, $product(-1, I)), 0))) <=> ![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.47 tff(85,plain,
% 0.21/0.47 (^[A: array_int, X: $int, Y: $int, I: $int] : trans(monotonicity(rewrite((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) <=> ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0)), rewrite((~$lesseq(0, I)) <=> (~$greatereq(I, 0))), quant_intro(proof_bind(^[Len: $int] : rewrite(((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)) <=> ((~eqseq(A, X, Y, Len)) | $lesseq($sum(Len, $product(-1, I)), 0)))), (![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)) <=> ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq($sum(Len, $product(-1, I)), 0)))), (((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | (~$lesseq(0, I)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I))) <=> (($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0) | (~$greatereq(I, 0)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq($sum(Len, $product(-1, I)), 0))))), rewrite((($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0) | (~$greatereq(I, 0)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq($sum(Len, $product(-1, I)), 0))) <=> ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq($sum(Len, $product(-1, I)), 0)))), (((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | (~$lesseq(0, I)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I))) <=> ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq($sum(Len, $product(-1, I)), 0)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(86,plain,
% 0.21/0.47 (![A: array_int, X: $int, Y: $int, I: $int] : ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | (~$lesseq(0, I)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I))) <=> ![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq($sum(Len, $product(-1, I)), 0)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 (![A: array_int, X: $int, Y: $int, I: $int] : ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | (~$lesseq(0, I)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I))) <=> ![A: array_int, X: $int, Y: $int, I: $int] : ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | (~$lesseq(0, I)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(88,plain,
% 0.21/0.47 (^[A: array_int, X: $int, Y: $int, I: $int] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Len: $int] : trans(monotonicity(rewrite($less(I, Len) <=> (~$lesseq(Len, I))), (($less(I, Len) => (~eqseq(A, X, Y, Len))) <=> ((~$lesseq(Len, I)) => (~eqseq(A, X, Y, Len))))), rewrite(((~$lesseq(Len, I)) => (~eqseq(A, X, Y, Len))) <=> ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I))), (($less(I, Len) => (~eqseq(A, X, Y, Len))) <=> ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I))))), (![Len: $int] : ($less(I, Len) => (~eqseq(A, X, Y, Len))) <=> ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)))), (((~(tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))) => ![Len: $int] : ($less(I, Len) => (~eqseq(A, X, Y, Len)))) <=> ((~(tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))) => ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I))))), rewrite(((~(tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))) => ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I))) <=> ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)))), (((~(tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))) => ![Len: $int] : ($less(I, Len) => (~eqseq(A, X, Y, Len)))) <=> ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I))))), (($lesseq(0, I) => ((~(tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))) => ![Len: $int] : ($less(I, Len) => (~eqseq(A, X, Y, Len))))) <=> ($lesseq(0, I) => ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)))))), rewrite(($lesseq(0, I) => ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)))) <=> ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | (~$lesseq(0, I)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)))), (($lesseq(0, I) => ((~(tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))) => ![Len: $int] : ($less(I, Len) => (~eqseq(A, X, Y, Len))))) <=> ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | (~$lesseq(0, I)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(89,plain,
% 0.21/0.47 (![A: array_int, X: $int, Y: $int, I: $int] : ($lesseq(0, I) => ((~(tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))) => ![Len: $int] : ($less(I, Len) => (~eqseq(A, X, Y, Len))))) <=> ![A: array_int, X: $int, Y: $int, I: $int] : ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | (~$lesseq(0, I)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.47 tff(90,axiom,(![A: array_int, X: $int, Y: $int, I: $int] : ($lesseq(0, I) => ((~(tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))) => ![Len: $int] : ($less(I, Len) => (~eqseq(A, X, Y, Len)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_eqseq')).
% 0.21/0.47 tff(91,plain,
% 0.21/0.47 (![A: array_int, X: $int, Y: $int, I: $int] : ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | (~$lesseq(0, I)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.47 tff(92,plain,
% 0.21/0.47 (![A: array_int, X: $int, Y: $int, I: $int] : ((tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))) | (~$lesseq(0, I)) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq(Len, I)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.21/0.47 tff(93,plain,
% 0.21/0.47 (![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $lesseq($sum(Len, $product(-1, I)), 0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[92, 86])).
% 0.21/0.47 tff(94,plain,
% 0.21/0.47 (![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[93, 84])).
% 0.21/0.47 tff(95,plain,(
% 0.21/0.47 ![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[94])).
% 0.21/0.47 tff(96,plain,
% 0.21/0.47 (![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[95, 82])).
% 0.21/0.47 tff(97,plain,
% 0.21/0.47 (((~![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))) | ((~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | ![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $lesseq($sum(Len, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0)))) <=> ((~![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | ![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $lesseq($sum(Len, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(98,plain,
% 0.21/0.47 (((~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | ![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $greatereq($sum(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $product(-1, Len)), 0))) <=> ((~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | ![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $lesseq($sum(Len, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(99,plain,
% 0.21/0.47 (((~![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))) | ((~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | ![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $greatereq($sum(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $product(-1, Len)), 0)))) <=> ((~![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))) | ((~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | ![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $lesseq($sum(Len, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[98])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 (((~![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))) | ((~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | ![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $greatereq($sum(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $product(-1, Len)), 0)))) <=> ((~![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | ![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $lesseq($sum(Len, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[99, 97])).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 ((~![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))) | ((~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | ![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $greatereq($sum(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $product(-1, Len)), 0)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 ((~![A: array_int, X: $int, Y: $int, I: $int] : ((~$greatereq(I, 0)) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, I))))) = 0) | ![Len: $int] : ((~eqseq(A, X, Y, Len)) | $greatereq($sum(I, $product(-1, Len)), 0)))) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | ![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $lesseq($sum(Len, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.48 tff(103,plain,
% 0.21/0.48 (![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $lesseq($sum(Len, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[102, 96, 75, 77])).
% 0.21/0.48 tff(104,plain,
% 0.21/0.48 (eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)),
% 0.21/0.48 inference(and_elim,[status(thm)],[34])).
% 0.21/0.48 tff(105,plain,
% 0.21/0.48 (((~![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $lesseq($sum(Len, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))) | ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | $lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))) <=> ((~![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $lesseq($sum(Len, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))) | (~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | $lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(106,plain,
% 0.21/0.48 ((~![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $lesseq($sum(Len, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))) | ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | $lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 ((~![Len: $int] : ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, Len)) | $lesseq($sum(Len, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))) | (~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | $lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 ($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[107, 104, 103])).
% 0.21/0.48 tff(109,assumption,($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0)), introduced(assumption)).
% 0.21/0.48 tff(110,assumption,(~$lesseq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0)), introduced(assumption)).
% 0.21/0.48 tff(111,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[110, 109])).
% 0.21/0.48 tff(112,plain,($lesseq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0) | (~$lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(113,plain,
% 0.21/0.48 ($lesseq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[112, 108])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 (($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0))) | (~$lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(115,plain,
% 0.21/0.48 (~$lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[114, 73])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 ($greatereq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0) | $lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | (~$greatereq($sum(L!5, $product(-1, L1!6)), -1))),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 ($greatereq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[116, 115, 39])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 (($sum(Y!1, L!5) = $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))) | (~$lesseq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0)) | (~$greatereq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0))),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 (($sum(Y!1, L!5) = $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))) | (~$lesseq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.21/0.48 tff(120,plain,
% 0.21/0.48 ($sum(Y!1, L!5) = $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[119, 113])).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(122,plain,
% 0.21/0.48 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(123,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR')).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.21/0.48 tff(125,plain,(
% 0.21/0.48 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.48 inference(skolemize,[status(sab)],[124])).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5))))) = get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (t2tb(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5))))) = get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 ($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0),
% 0.21/0.48 inference(and_elim,[status(thm)],[34])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 ((~($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))), 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 ($lesseq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 ((~($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))) = 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))), 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(133,plain,
% 0.21/0.48 ($greatereq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))), $product(-1, tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[132, 129])).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 (tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))) = tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5))))),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[133, 131])).
% 0.21/0.48 tff(135,plain,
% 0.21/0.48 (t2tb(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5))))) = t2tb(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[134])).
% 0.21/0.48 tff(136,plain,
% 0.21/0.48 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5))))) = get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(137,plain,
% 0.21/0.48 (t2tb(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5))))) = get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[136, 126])).
% 0.21/0.48 tff(138,plain,
% 0.21/0.48 (get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5))) = t2tb(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))))),
% 0.21/0.48 inference(symmetry,[status(thm)],[137])).
% 0.21/0.48 tff(139,plain,
% 0.21/0.48 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(t2tb($sum(Y!1, L!5)))) = t2tb($sum(Y!1, L!5)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(140,plain,
% 0.21/0.48 (t2tb(tb2t(t2tb($sum(Y!1, L!5)))) = t2tb($sum(Y!1, L!5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[139, 126])).
% 0.21/0.48 tff(141,plain,
% 0.21/0.48 (^[X: map_int_int] : refl(sort(map(int, int), t2tb2(X)) <=> sort(map(int, int), t2tb2(X)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(142,plain,
% 0.21/0.48 (![X: map_int_int] : sort(map(int, int), t2tb2(X)) <=> ![X: map_int_int] : sort(map(int, int), t2tb2(X))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[141])).
% 0.21/0.48 tff(143,plain,
% 0.21/0.48 (![X: map_int_int] : sort(map(int, int), t2tb2(X)) <=> ![X: map_int_int] : sort(map(int, int), t2tb2(X))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(144,axiom,(![X: map_int_int] : sort(map(int, int), t2tb2(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2tb_sort2')).
% 0.21/0.48 tff(145,plain,
% 0.21/0.48 (![X: map_int_int] : sort(map(int, int), t2tb2(X))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.48 tff(146,plain,(
% 0.21/0.48 ![X: map_int_int] : sort(map(int, int), t2tb2(X))),
% 0.21/0.48 inference(skolemize,[status(sab)],[145])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 (![X: map_int_int] : sort(map(int, int), t2tb2(X))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 ((~![X: map_int_int] : sort(map(int, int), t2tb2(X))) | sort(map(int, int), t2tb2(A1!3))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 (sort(map(int, int), t2tb2(A1!3))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 (^[A: ty, U: $int, U1: uni] : refl(((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(151,plain,
% 0.21/0.48 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[150])).
% 0.21/0.48 tff(152,plain,
% 0.21/0.48 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 (^[A: ty, U: $int, U1: uni] : rewrite((sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1)) <=> ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 (![A: ty, U: $int, U1: uni] : (sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[153])).
% 0.21/0.48 tff(155,axiom,(![A: ty, U: $int, U1: uni] : (sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','elts_def')).
% 0.21/0.49 tff(156,plain,
% 0.21/0.49 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.49 tff(157,plain,
% 0.21/0.49 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.21/0.49 tff(158,plain,(
% 0.21/0.49 ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.49 inference(skolemize,[status(sab)],[157])).
% 0.21/0.49 tff(159,plain,
% 0.21/0.49 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.21/0.49 tff(160,plain,
% 0.21/0.49 (((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | ((~sort(map(int, int), t2tb2(A1!3))) | (elts(int, mk_array(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | (~sort(map(int, int), t2tb2(A1!3))) | (elts(int, mk_array(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(161,plain,
% 0.21/0.49 ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | ((~sort(map(int, int), t2tb2(A1!3))) | (elts(int, mk_array(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(162,plain,
% 0.21/0.49 ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | (~sort(map(int, int), t2tb2(A1!3))) | (elts(int, mk_array(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.49 tff(163,plain,
% 0.21/0.49 ((~sort(map(int, int), t2tb2(A1!3))) | (elts(int, mk_array(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[162, 159])).
% 0.21/0.49 tff(164,plain,
% 0.21/0.49 (elts(int, mk_array(int, A!4, t2tb2(A1!3))) = t2tb2(A1!3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[163, 149])).
% 0.21/0.49 tff(165,plain,
% 0.21/0.49 (get(int, int, elts(int, mk_array(int, A!4, t2tb2(A1!3))), t2tb(tb2t(t2tb($sum(Y!1, L!5))))) = get(int, int, t2tb2(A1!3), t2tb($sum(Y!1, L!5)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[164, 140])).
% 0.21/0.49 tff(166,plain,
% 0.21/0.49 (^[A: ty, A1: uni, I: $int] : refl((get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(167,plain,
% 0.21/0.49 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[166])).
% 0.21/0.49 tff(168,plain,
% 0.21/0.49 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(169,axiom,(![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','get_def')).
% 0.21/0.49 tff(170,plain,
% 0.21/0.49 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.21/0.49 tff(171,plain,(
% 0.21/0.49 ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[170])).
% 0.21/0.49 tff(172,plain,
% 0.21/0.49 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.21/0.49 tff(173,plain,
% 0.21/0.49 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(int, mk_array(int, A!4, t2tb2(A1!3)), tb2t(t2tb($sum(Y!1, L!5)))) = get(int, int, elts(int, mk_array(int, A!4, t2tb2(A1!3))), t2tb(tb2t(t2tb($sum(Y!1, L!5))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(174,plain,
% 0.21/0.49 (get1(int, mk_array(int, A!4, t2tb2(A1!3)), tb2t(t2tb($sum(Y!1, L!5)))) = get(int, int, elts(int, mk_array(int, A!4, t2tb2(A1!3))), t2tb(tb2t(t2tb($sum(Y!1, L!5)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.21/0.49 tff(175,plain,
% 0.21/0.49 (^[I: $int] : refl(($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(176,plain,
% 0.21/0.49 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.49 inference(quant_intro,[status(thm)],[175])).
% 0.21/0.49 tff(177,plain,
% 0.21/0.49 (^[I: $int] : trans(monotonicity(rewrite($sum(tb2t(t2tb(I)), $product(-1, I)) = $sum($product(-1, I), tb2t(t2tb(I)))), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum($product(-1, I), tb2t(t2tb(I))) = 0))), rewrite(($sum($product(-1, I), tb2t(t2tb(I))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(178,plain,
% 0.21/0.49 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.49 inference(quant_intro,[status(thm)],[177])).
% 0.21/0.49 tff(179,plain,
% 0.21/0.49 (^[I: $int] : rewrite((tb2t(t2tb(I)) = I) <=> ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(180,plain,
% 0.21/0.49 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.21/0.49 inference(quant_intro,[status(thm)],[179])).
% 0.21/0.49 tff(181,plain,
% 0.21/0.49 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(182,axiom,(![I: $int] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeL')).
% 0.21/0.49 tff(183,plain,
% 0.21/0.49 (![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.21/0.49 tff(184,plain,
% 0.21/0.49 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[183, 180])).
% 0.21/0.49 tff(185,plain,
% 0.21/0.49 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[184, 178])).
% 0.21/0.49 tff(186,plain,(
% 0.21/0.49 ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.49 inference(skolemize,[status(sab)],[185])).
% 0.21/0.49 tff(187,plain,
% 0.21/0.49 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[186, 176])).
% 0.21/0.49 tff(188,plain,
% 0.21/0.49 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))) = 0))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(189,plain,
% 0.21/0.49 (($sum($sum(Y!1, L!5), $product(-1, tb2t(t2tb($sum(Y!1, L!5))))) = 0) <=> ($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))) = 0)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(190,plain,
% 0.21/0.49 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(Y!1, L!5), $product(-1, tb2t(t2tb($sum(Y!1, L!5))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))) = 0))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[189])).
% 0.21/0.49 tff(191,plain,
% 0.21/0.49 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(Y!1, L!5), $product(-1, tb2t(t2tb($sum(Y!1, L!5))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))) = 0))),
% 0.21/0.49 inference(transitivity,[status(thm)],[190, 188])).
% 0.21/0.49 tff(192,plain,
% 0.21/0.49 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(Y!1, L!5), $product(-1, tb2t(t2tb($sum(Y!1, L!5))))) = 0)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(193,plain,
% 0.21/0.49 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))) = 0)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.21/0.49 tff(194,plain,
% 0.21/0.49 ($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))) = 0),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[193, 187])).
% 0.21/0.49 tff(195,plain,
% 0.21/0.49 ((~($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))) = 0)) | $lesseq($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))), 0)),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.49 tff(196,plain,
% 0.21/0.49 ($lesseq($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))), 0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.21/0.49 tff(197,plain,
% 0.21/0.49 ($lesseq($sum($sum(Y!1, L!5), $product(-1, tb2t(t2tb($sum(Y!1, L!5))))), 0) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))), 0))),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.49 tff(198,plain,
% 0.21/0.49 ($lesseq($sum($sum(Y!1, L!5), $product(-1, tb2t(t2tb($sum(Y!1, L!5))))), 0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.21/0.49 tff(199,plain,
% 0.21/0.49 ((~($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))) = 0)) | $greatereq($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))), 0)),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.49 tff(200,plain,
% 0.21/0.49 ($greatereq($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))), 0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[199, 194])).
% 0.21/0.49 tff(201,plain,
% 0.21/0.49 ($greatereq($sum($sum(Y!1, L!5), $product(-1, tb2t(t2tb($sum(Y!1, L!5))))), 0) | (~$greatereq($sum(Y!1, $sum(L!5, $product(-1, tb2t(t2tb($sum(Y!1, L!5)))))), 0))),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.49 tff(202,plain,
% 0.21/0.49 ($greatereq($sum($sum(Y!1, L!5), $product(-1, tb2t(t2tb($sum(Y!1, L!5))))), 0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.21/0.49 tff(203,plain,
% 0.21/0.49 (($sum(Y!1, L!5) = tb2t(t2tb($sum(Y!1, L!5)))) | (~$lesseq($sum($sum(Y!1, L!5), $product(-1, tb2t(t2tb($sum(Y!1, L!5))))), 0)) | (~$greatereq($sum($sum(Y!1, L!5), $product(-1, tb2t(t2tb($sum(Y!1, L!5))))), 0))),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.49 tff(204,plain,
% 0.21/0.49 ($sum(Y!1, L!5) = tb2t(t2tb($sum(Y!1, L!5)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[203, 202, 198])).
% 0.21/0.49 tff(205,assumption,($sum(Y!1, L!5) = $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), introduced(assumption)).
% 0.21/0.49 tff(206,plain,
% 0.21/0.49 ($sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))) = $sum(Y!1, L!5)),
% 0.21/0.49 inference(symmetry,[status(thm)],[205])).
% 0.21/0.49 tff(207,plain,
% 0.21/0.49 ($sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))) = tb2t(t2tb($sum(Y!1, L!5)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[206, 204])).
% 0.21/0.49 tff(208,plain,
% 0.21/0.49 (get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))) = get1(int, mk_array(int, A!4, t2tb2(A1!3)), tb2t(t2tb($sum(Y!1, L!5))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[47, 207])).
% 0.21/0.49 tff(209,plain,
% 0.21/0.49 (get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))) = get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[208, 174, 165, 138, 135, 128])).
% 0.21/0.49 tff(210,plain,
% 0.21/0.49 (tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))) = tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[209])).
% 0.21/0.49 tff(211,plain,
% 0.21/0.49 (tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))),
% 0.21/0.49 inference(symmetry,[status(thm)],[210])).
% 0.21/0.49 tff(212,assumption,(~(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), introduced(assumption)).
% 0.21/0.49 tff(213,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.21/0.49 tff(214,plain,((~($sum(Y!1, L!5) = $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))) | (tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(215,plain,
% 0.21/0.49 (tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[214, 120])).
% 0.21/0.49 tff(216,plain,
% 0.21/0.49 ((~(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) | $lesseq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.49 tff(217,plain,
% 0.21/0.49 ($lesseq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.21/0.49 tff(218,plain,
% 0.21/0.49 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(t2tb($sum(X!2, L!5)))) = t2tb($sum(X!2, L!5)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(219,plain,
% 0.21/0.49 (t2tb(tb2t(t2tb($sum(X!2, L!5)))) = t2tb($sum(X!2, L!5))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[218, 126])).
% 0.21/0.49 tff(220,plain,
% 0.21/0.49 (get(int, int, elts(int, mk_array(int, A!4, t2tb2(A1!3))), t2tb(tb2t(t2tb($sum(X!2, L!5))))) = get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[164, 219])).
% 0.21/0.49 tff(221,plain,
% 0.21/0.49 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(int, mk_array(int, A!4, t2tb2(A1!3)), tb2t(t2tb($sum(X!2, L!5)))) = get(int, int, elts(int, mk_array(int, A!4, t2tb2(A1!3))), t2tb(tb2t(t2tb($sum(X!2, L!5))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(222,plain,
% 0.21/0.49 (get1(int, mk_array(int, A!4, t2tb2(A1!3)), tb2t(t2tb($sum(X!2, L!5)))) = get(int, int, elts(int, mk_array(int, A!4, t2tb2(A1!3))), t2tb(tb2t(t2tb($sum(X!2, L!5)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[221, 172])).
% 0.21/0.49 tff(223,plain,
% 0.21/0.49 (tb2t(t2tb(tb2t(t2tb($sum(X!2, L!5))))) = tb2t(t2tb($sum(X!2, L!5)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[219])).
% 0.21/0.49 tff(224,assumption,($lesseq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0)), introduced(assumption)).
% 0.21/0.49 tff(225,assumption,($greatereq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0)), introduced(assumption)).
% 0.21/0.49 tff(226,plain,
% 0.21/0.49 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(tb2t(t2tb($sum(X!2, L!5))), $product(-1, tb2t(t2tb(tb2t(t2tb($sum(X!2, L!5))))))) = 0)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(227,plain,
% 0.21/0.49 ($sum(tb2t(t2tb($sum(X!2, L!5))), $product(-1, tb2t(t2tb(tb2t(t2tb($sum(X!2, L!5))))))) = 0),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[226, 187])).
% 0.21/0.49 tff(228,plain,
% 0.21/0.49 ((~($sum(tb2t(t2tb($sum(X!2, L!5))), $product(-1, tb2t(t2tb(tb2t(t2tb($sum(X!2, L!5))))))) = 0)) | $lesseq($sum(tb2t(t2tb($sum(X!2, L!5))), $product(-1, tb2t(t2tb(tb2t(t2tb($sum(X!2, L!5))))))), 0)),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.49 tff(229,plain,
% 0.21/0.49 ($lesseq($sum(tb2t(t2tb($sum(X!2, L!5))), $product(-1, tb2t(t2tb(tb2t(t2tb($sum(X!2, L!5))))))), 0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.21/0.49 tff(230,plain,
% 0.21/0.49 ((~($sum(tb2t(t2tb($sum(X!2, L!5))), $product(-1, tb2t(t2tb(tb2t(t2tb($sum(X!2, L!5))))))) = 0)) | $greatereq($sum(tb2t(t2tb($sum(X!2, L!5))), $product(-1, tb2t(t2tb(tb2t(t2tb($sum(X!2, L!5))))))), 0)),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.49 tff(231,plain,
% 0.21/0.49 ($greatereq($sum(tb2t(t2tb($sum(X!2, L!5))), $product(-1, tb2t(t2tb(tb2t(t2tb($sum(X!2, L!5))))))), 0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.21/0.49 tff(232,plain,
% 0.21/0.49 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))) = 0))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(233,plain,
% 0.21/0.49 (($sum($sum(X!2, L!5), $product(-1, tb2t(t2tb($sum(X!2, L!5))))) = 0) <=> ($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))) = 0)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(234,plain,
% 0.21/0.49 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(X!2, L!5), $product(-1, tb2t(t2tb($sum(X!2, L!5))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))) = 0))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[233])).
% 0.21/0.49 tff(235,plain,
% 0.21/0.49 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(X!2, L!5), $product(-1, tb2t(t2tb($sum(X!2, L!5))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))) = 0))),
% 0.21/0.49 inference(transitivity,[status(thm)],[234, 232])).
% 0.21/0.49 tff(236,plain,
% 0.21/0.49 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(X!2, L!5), $product(-1, tb2t(t2tb($sum(X!2, L!5))))) = 0)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(237,plain,
% 0.21/0.49 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))) = 0)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.21/0.49 tff(238,plain,
% 0.21/0.49 ($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))) = 0),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[237, 187])).
% 0.21/0.49 tff(239,plain,
% 0.21/0.49 ((~($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))) = 0)) | $lesseq($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))), 0)),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.49 tff(240,plain,
% 0.21/0.49 ($lesseq($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))), 0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.21/0.49 tff(241,plain,
% 0.21/0.49 ((~($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))) = 0)) | $greatereq($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))), 0)),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.49 tff(242,plain,
% 0.21/0.49 ($greatereq($sum(X!2, $sum(L!5, $product(-1, tb2t(t2tb($sum(X!2, L!5)))))), 0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[241, 238])).
% 0.21/0.49 tff(243,plain,
% 0.21/0.49 ($sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))) = tb2t(t2tb(tb2t(t2tb($sum(X!2, L!5)))))),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[242, 240, 231, 229, 225, 224])).
% 0.21/0.49 tff(244,plain,
% 0.21/0.49 ($sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))) = tb2t(t2tb($sum(X!2, L!5)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[243, 223])).
% 0.21/0.49 tff(245,plain,
% 0.21/0.49 (get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))) = get1(int, mk_array(int, A!4, t2tb2(A1!3)), tb2t(t2tb($sum(X!2, L!5))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[47, 244])).
% 0.21/0.49 tff(246,plain,
% 0.21/0.49 (get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))) = get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[245, 222, 220])).
% 0.21/0.49 tff(247,plain,
% 0.21/0.49 (tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))) = tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[246])).
% 0.21/0.49 tff(248,plain,
% 0.21/0.49 (tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))),
% 0.21/0.49 inference(symmetry,[status(thm)],[247])).
% 0.21/0.49 tff(249,assumption,(~(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), introduced(assumption)).
% 0.21/0.50 tff(250,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.21/0.50 tff(251,plain,((tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))) | (~$greatereq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0)) | (~$lesseq($sum($sum(Y!1, L!5), $product(-1, $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(252,plain,
% 0.21/0.50 (tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[251, 117, 113])).
% 0.21/0.50 tff(253,plain,
% 0.21/0.50 ((~(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) | $greatereq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.50 tff(254,plain,
% 0.21/0.50 ($greatereq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.21/0.50 tff(255,assumption,(~$greatereq($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)), introduced(assumption)).
% 0.21/0.50 tff(256,assumption,($lesseq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)), introduced(assumption)).
% 0.21/0.50 tff(257,assumption,($greatereq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)), introduced(assumption)).
% 0.21/0.50 tff(258,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[257, 256, 255])).
% 0.21/0.50 tff(259,plain,((~$greatereq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)) | (~$lesseq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)) | $greatereq($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(260,plain,
% 0.21/0.50 ($greatereq($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[259, 254, 217])).
% 0.21/0.50 tff(261,plain,
% 0.21/0.50 (($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$lesseq($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)) | (~$greatereq($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0))),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.50 tff(262,plain,
% 0.21/0.50 (~$lesseq($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[261, 260, 75])).
% 0.21/0.50 tff(263,plain,
% 0.21/0.50 ((~(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) | $lesseq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.50 tff(264,plain,
% 0.21/0.50 ($lesseq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[263, 252])).
% 0.21/0.50 tff(265,plain,
% 0.21/0.50 ((~(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) | $greatereq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.50 tff(266,plain,
% 0.21/0.50 ($greatereq($sum(tb2t(get(int, int, t2tb2(A1!3), t2tb($sum(X!2, L!5)))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[265, 215])).
% 0.21/0.50 tff(267,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[266, 264, 262])).
% 0.21/0.50 tff(268,plain,($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(269,plain,
% 0.21/0.50 (^[A: array_int, X: $int, Y: $int, Len: $int] : rewrite((~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))))) <=> (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(270,plain,
% 0.21/0.50 (![A: array_int, X: $int, Y: $int, Len: $int] : (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))))) <=> ![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[269])).
% 0.21/0.50 tff(271,plain,
% 0.21/0.50 (^[A: array_int, X: $int, Y: $int, Len: $int] : refl((~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))))) <=> (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(272,plain,
% 0.21/0.50 (![A: array_int, X: $int, Y: $int, Len: $int] : (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))))) <=> ![A: array_int, X: $int, Y: $int, Len: $int] : (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[271])).
% 0.21/0.50 tff(273,plain,
% 0.21/0.50 (^[A: array_int, X: $int, Y: $int, Len: $int] : rewrite((~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))))) <=> (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(274,plain,
% 0.21/0.50 (![A: array_int, X: $int, Y: $int, Len: $int] : (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))))) <=> ![A: array_int, X: $int, Y: $int, Len: $int] : (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[273])).
% 0.21/0.50 tff(275,plain,
% 0.21/0.50 (![A: array_int, X: $int, Y: $int, Len: $int] : (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))))) <=> ![A: array_int, X: $int, Y: $int, Len: $int] : (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[274, 272])).
% 0.21/0.50 tff(276,plain,
% 0.21/0.50 (^[A: array_int, X: $int, Y: $int, Len: $int] : trans(monotonicity(rewrite(((~eqseq(A, X, Y, Len)) | ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))) <=> ((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))), trans(monotonicity(rewrite((~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0))) <=> (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))), ((eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0)))) <=> (eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))))), rewrite((eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))) <=> (eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))), ((eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0)))) <=> (eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))))), ((((~eqseq(A, X, Y, Len)) | ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))) & (eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0))))) <=> (((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))) & (eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))))), rewrite((((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))) & (eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) <=> (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))))))), ((((~eqseq(A, X, Y, Len)) | ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))) & (eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0))))) <=> (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(277,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (((~eqseq(A, X, Y, Len)) | ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))) & (eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0))))) <=> ![A: array_int, X: $int, Y: $int, Len: $int] : (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[276])).
% 0.21/0.51 tff(278,plain,
% 0.21/0.51 (^[A: array_int, X: $int, Y: $int, Len: $int] : rewrite((((~eqseq(A, X, Y, Len)) | ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))) & (eqseq(A, X, Y, Len) | ((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(tptp_fun_I_0(Len, Y, X, A), X))))) = 0)))))) <=> (((~eqseq(A, X, Y, Len)) | ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))) & (eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(279,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (((~eqseq(A, X, Y, Len)) | ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))) & (eqseq(A, X, Y, Len) | ((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(tptp_fun_I_0(Len, Y, X, A), X))))) = 0)))))) <=> ![A: array_int, X: $int, Y: $int, Len: $int] : (((~eqseq(A, X, Y, Len)) | ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))) & (eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[278])).
% 0.21/0.51 tff(280,plain,
% 0.21/0.51 (^[A: array_int, X: $int, Y: $int, Len: $int] : rewrite((eqseq(A, X, Y, Len) <=> ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0)))) <=> (eqseq(A, X, Y, Len) <=> ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(281,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0)))) <=> ![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[280])).
% 0.21/0.51 tff(282,plain,
% 0.21/0.51 (^[A: array_int, X: $int, Y: $int, Len: $int] : rewrite((eqseq(A, X, Y, Len) <=> ($lesseq(0, Len) & $lesseq($sum(X, Len), length(int, t2tb1(A))) & $lesseq($sum(Y, Len), length(int, t2tb1(A))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Len, I)))) | (tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))))) <=> (eqseq(A, X, Y, Len) <=> ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(283,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ($lesseq(0, Len) & $lesseq($sum(X, Len), length(int, t2tb1(A))) & $lesseq($sum(Y, Len), length(int, t2tb1(A))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Len, I)))) | (tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))))) <=> ![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[282])).
% 0.21/0.51 tff(284,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ($lesseq(0, Len) & $lesseq($sum(X, Len), length(int, t2tb1(A))) & $lesseq($sum(Y, Len), length(int, t2tb1(A))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Len, I)))) | (tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))))) <=> ![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ($lesseq(0, Len) & $lesseq($sum(X, Len), length(int, t2tb1(A))) & $lesseq($sum(Y, Len), length(int, t2tb1(A))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Len, I)))) | (tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(285,plain,
% 0.21/0.51 (^[A: array_int, X: $int, Y: $int, Len: $int] : rewrite((eqseq(A, X, Y, Len) <=> ((($lesseq(0, Len) & $lesseq($sum(X, Len), length(int, t2tb1(A)))) & $lesseq($sum(Y, Len), length(int, t2tb1(A)))) & ![I: $int] : (($lesseq(0, I) & $less(I, Len)) => (tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))))) <=> (eqseq(A, X, Y, Len) <=> ($lesseq(0, Len) & $lesseq($sum(X, Len), length(int, t2tb1(A))) & $lesseq($sum(Y, Len), length(int, t2tb1(A))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Len, I)))) | (tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(286,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ((($lesseq(0, Len) & $lesseq($sum(X, Len), length(int, t2tb1(A)))) & $lesseq($sum(Y, Len), length(int, t2tb1(A)))) & ![I: $int] : (($lesseq(0, I) & $less(I, Len)) => (tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I))))))) <=> ![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ($lesseq(0, Len) & $lesseq($sum(X, Len), length(int, t2tb1(A))) & $lesseq($sum(Y, Len), length(int, t2tb1(A))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Len, I)))) | (tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[285])).
% 0.21/0.51 tff(287,axiom,(![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ((($lesseq(0, Len) & $lesseq($sum(X, Len), length(int, t2tb1(A)))) & $lesseq($sum(Y, Len), length(int, t2tb1(A)))) & ![I: $int] : (($lesseq(0, I) & $less(I, Len)) => (tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eqseq_def')).
% 0.21/0.51 tff(288,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ($lesseq(0, Len) & $lesseq($sum(X, Len), length(int, t2tb1(A))) & $lesseq($sum(Y, Len), length(int, t2tb1(A))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Len, I)))) | (tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.21/0.51 tff(289,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ($lesseq(0, Len) & $lesseq($sum(X, Len), length(int, t2tb1(A))) & $lesseq($sum(Y, Len), length(int, t2tb1(A))) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Len, I)))) | (tb2t(get1(int, t2tb1(A), $sum(X, I))) = tb2t(get1(int, t2tb1(A), $sum(Y, I)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[288, 284])).
% 0.21/0.51 tff(290,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(X, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(Y, I))))) = 0))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[289, 283])).
% 0.21/0.51 tff(291,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (eqseq(A, X, Y, Len) <=> ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[290, 281])).
% 0.21/0.51 tff(292,plain,(
% 0.21/0.51 ![A: array_int, X: $int, Y: $int, Len: $int] : (((~eqseq(A, X, Y, Len)) | ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))) & (eqseq(A, X, Y, Len) | ((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(tptp_fun_I_0(Len, Y, X, A), X))))) = 0))))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[291])).
% 0.21/0.51 tff(293,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (((~eqseq(A, X, Y, Len)) | ($greatereq(Len, 0) & $lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & $lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Len, $product(-1, I)), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))) & (eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~((~($greatereq(tptp_fun_I_0(Len, Y, X, A), 0) & (~$lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0)))) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[292, 279])).
% 0.21/0.51 tff(294,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[293, 277])).
% 0.21/0.51 tff(295,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (~((~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0))))))) | (~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[294, 275])).
% 0.21/0.51 tff(296,plain,
% 0.21/0.51 (![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[295, 270])).
% 0.21/0.51 tff(297,plain,
% 0.21/0.51 (((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L1!6)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))))))))) <=> ((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L1!6)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(298,plain,
% 0.21/0.51 ((~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(L1!6, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, I))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))))) = 0))))))))) <=> (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L1!6)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(299,plain,
% 0.21/0.51 (((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(L1!6, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, I))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))))) = 0)))))))))) <=> ((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L1!6)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[298])).
% 0.21/0.52 tff(300,plain,
% 0.21/0.52 (((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(L1!6, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, I))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))))) = 0)))))))))) <=> ((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L1!6)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[299, 297])).
% 0.21/0.52 tff(301,plain,
% 0.21/0.52 ((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(L1!6, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, I))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))))) = 0)))))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(302,plain,
% 0.21/0.52 ((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L1!6)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.21/0.52 tff(303,plain,
% 0.21/0.52 (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L1!6)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[302, 296])).
% 0.21/0.52 tff(304,plain,
% 0.21/0.52 (((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)) | (~((~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L1!6)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))))))) | (eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(305,plain,
% 0.21/0.53 (eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.21/0.53 tff(306,plain,
% 0.21/0.53 (((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))))))))) <=> ((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))))))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(307,plain,
% 0.21/0.53 ((~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(L!5, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, I))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))))) = 0))))))))) <=> (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))))))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(308,plain,
% 0.21/0.53 (((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(L!5, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, I))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))))) = 0)))))))))) <=> ((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))))))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[307])).
% 0.21/0.53 tff(309,plain,
% 0.21/0.53 (((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(L!5, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, I))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))))) = 0)))))))))) <=> ((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))))))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[308, 306])).
% 0.21/0.53 tff(310,plain,
% 0.21/0.53 ((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(L!5, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, I))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))))) = 0)))))))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(311,plain,
% 0.21/0.54 ((~![A: array_int, X: $int, Y: $int, Len: $int] : (~((~(eqseq(A, X, Y, Len) | (~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~($lesseq($sum(Len, $product(-1, tptp_fun_I_0(Len, Y, X, A))), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, tptp_fun_I_0(Len, Y, X, A)))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(X, tptp_fun_I_0(Len, Y, X, A)))))) = 0) | (~$greatereq(tptp_fun_I_0(Len, Y, X, A), 0)))))) | (~((~eqseq(A, X, Y, Len)) | (~((~$greatereq(Len, 0)) | (~$lesseq($sum(X, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~$lesseq($sum(Y, $sum(Len, $product(-1, length(int, t2tb1(A))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $lesseq($sum(Len, $product(-1, I)), 0) | ($sum(tb2t(get1(int, t2tb1(A), $sum(Y, I))), $product(-1, tb2t(get1(int, t2tb1(A), $sum(I, X))))) = 0)))))))))) | (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.21/0.54 tff(312,plain,
% 0.21/0.54 (~((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[311, 296])).
% 0.21/0.54 tff(313,plain,
% 0.21/0.54 (((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L!5, $product(-1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L!5, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))))))) | ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))))),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(314,plain,
% 0.21/0.54 ((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[313, 312])).
% 0.21/0.54 tff(315,plain,
% 0.21/0.54 ((~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))))) | (~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))))),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(316,plain,
% 0.21/0.54 ((~((~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L!5)) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))))) | (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[315, 104])).
% 0.21/0.54 tff(317,plain,
% 0.21/0.54 (~((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[316, 314])).
% 0.21/0.54 tff(318,plain,
% 0.21/0.54 (((~$greatereq(L!5, 0)) | (~$lesseq($sum(X!2, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L!5, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!5)), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, X!2))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(I, Y!1))))) = 0)))) | $greatereq(L!5, 0)),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(319,plain,
% 0.21/0.54 ($greatereq(L!5, 0)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[318, 317])).
% 0.21/0.54 tff(320,plain,
% 0.21/0.54 ((~($sum(L!5, $product(-1, L1!6)) = -1)) | $lesseq($sum(L!5, $product(-1, L1!6)), -1)),
% 0.21/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.54 tff(321,plain,
% 0.21/0.54 ($lesseq($sum(L!5, $product(-1, L1!6)), -1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[320, 37])).
% 0.21/0.54 tff(322,plain,
% 0.21/0.54 ($greatereq(L1!6, 0) | (~$greatereq(L!5, 0)) | (~$lesseq($sum(L!5, $product(-1, L1!6)), -1))),
% 0.21/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.54 tff(323,plain,
% 0.21/0.54 ($greatereq(L1!6, 0)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[322, 321, 319])).
% 0.21/0.54 tff(324,plain,
% 0.21/0.54 (~eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6)),
% 0.21/0.54 inference(or_elim,[status(thm)],[36])).
% 0.21/0.54 tff(325,plain,
% 0.21/0.54 ((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0))))),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(326,plain,
% 0.21/0.54 ((~(eqseq(tb2t1(mk_array(int, A!4, t2tb2(A1!3))), X!2, Y!1, L1!6) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0)))))) | (~$greatereq(L1!6, 0)) | (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[325, 324])).
% 0.21/0.54 tff(327,plain,
% 0.21/0.54 ((~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~($lesseq($sum(L1!6, $product(-1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))), 0) | ($sum(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(Y!1, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), $sum(X!2, tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3))))))))) = 0) | (~$greatereq(tptp_fun_I_0(L1!6, Y!1, X!2, tb2t1(mk_array(int, A!4, t2tb2(A1!3)))), 0))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[326, 323, 305])).
% 0.21/0.54 tff(328,plain,
% 0.21/0.54 ((~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)) | (~$lesseq($sum(Y!1, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[327, 268])).
% 0.21/0.55 tff(329,plain,
% 0.21/0.55 (~$lesseq($sum(X!2, $sum(L1!6, $product(-1, length(int, t2tb1(tb2t1(mk_array(int, A!4, t2tb2(A1!3)))))))), 0)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[328, 72])).
% 0.21/0.55 tff(330,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(theory_lemma,[status(thm)],[70, 329, 51, 39, 35])).
% 0.21/0.55 % SZS output end Proof
%------------------------------------------------------------------------------