TSTP Solution File: SWW667_2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW667_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 20:59:36 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW667_2 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.13 % 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 20:59:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(tb2t_type, type, (
% 0.20/0.42 tb2t: uni > $int)).
% 0.20/0.42 tff(get2_type, type, (
% 0.20/0.42 get2: ( ty * uni * $int ) > uni)).
% 0.20/0.42 tff(t2tb_type, type, (
% 0.20/0.42 t2tb: $int > uni)).
% 0.20/0.42 tff(tptp_fun_I_6_type, type, (
% 0.20/0.42 tptp_fun_I_6: $int)).
% 0.20/0.42 tff(t2tb2_type, type, (
% 0.20/0.42 t2tb2: array_int > uni)).
% 0.20/0.42 tff(tb2t2_type, type, (
% 0.20/0.42 tb2t2: uni > array_int)).
% 0.20/0.42 tff(mk_array1_type, type, (
% 0.20/0.42 mk_array1: ( ty * $int * uni ) > uni)).
% 0.20/0.42 tff(t2tb1_type, type, (
% 0.20/0.42 t2tb1: map_int_int > uni)).
% 0.20/0.42 tff(tptp_fun_A1_4_type, type, (
% 0.20/0.42 tptp_fun_A1_4: map_int_int)).
% 0.20/0.42 tff(tptp_fun_A_5_type, type, (
% 0.20/0.42 tptp_fun_A_5: $int)).
% 0.20/0.42 tff(int_type, type, (
% 0.20/0.42 int: ty)).
% 0.20/0.42 tff(tptp_fun_M1_9_type, type, (
% 0.20/0.42 tptp_fun_M1_9: $int)).
% 0.20/0.42 tff(tptp_fun_M_8_type, type, (
% 0.20/0.42 tptp_fun_M_8: $int)).
% 0.20/0.42 tff(tptp_fun_S_7_type, type, (
% 0.20/0.42 tptp_fun_S_7: $int)).
% 0.20/0.42 tff(is_max1_type, type, (
% 0.20/0.42 is_max1: ( array_int * $int * $int * $int ) > $o)).
% 0.20/0.42 tff(sum2_type, type, (
% 0.20/0.42 sum2: ( map_int_int * $int * $int ) > $int)).
% 0.20/0.42 tff(get_type, type, (
% 0.20/0.42 get: ( ty * ty * uni * uni ) > uni)).
% 0.20/0.42 tff(tptp_fun_S1_10_type, type, (
% 0.20/0.42 tptp_fun_S1_10: $int)).
% 0.20/0.42 tff(tptp_fun_N_3_type, type, (
% 0.20/0.42 tptp_fun_N_3: $int)).
% 0.20/0.42 tff(tptp_fun_K_2_type, type, (
% 0.20/0.42 tptp_fun_K_2: ( $int * $int * $int * array_int ) > $int)).
% 0.20/0.42 tff(elts_type, type, (
% 0.20/0.42 elts: ( ty * uni ) > uni)).
% 0.20/0.42 tff(sort1_type, type, (
% 0.20/0.42 sort1: ( ty * uni ) > $o)).
% 0.20/0.42 tff(map_type, type, (
% 0.20/0.42 map: ( ty * ty ) > ty)).
% 0.20/0.42 tff(tptp_fun_K_1_type, type, (
% 0.20/0.42 tptp_fun_K_1: ( $int * $int * $int * array_int ) > $int)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 (^[I: $int] : refl(($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (^[I: $int] : rewrite((tb2t(t2tb(I)) = I) <=> ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(8,axiom,(![I: $int] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeL')).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.20/0.42 tff(12,plain,(
% 0.20/0.42 ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.20/0.42 inference(skolemize,[status(sab)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(I!6, $product(-1, tb2t(t2tb(I!6)))) = 0)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ($sum(I!6, $product(-1, tb2t(t2tb(I!6)))) = 0),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 ((~($sum(I!6, $product(-1, tb2t(t2tb(I!6)))) = 0)) | $greatereq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), 0)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 ($greatereq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), 0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 ((~$lesseq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), -1)) | (~$greatereq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), 0))),
% 0.20/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (~$lesseq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), -1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (($greatereq(N!3, 1) & ($greatereq(A!5, 0) & ($sum(N!3, $product(-1, A!5)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!3)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1!4), t2tb(I))), 0))) & ((~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & $greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)) & $greatereq($sum(N!3, $product(-1, I!6)), 1) & (~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0) & ($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0))) <=> ($greatereq(N!3, 1) & $greatereq(A!5, 0) & ($sum(N!3, $product(-1, A!5)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!3)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1!4), t2tb(I))), 0)) & (~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & $greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)) & $greatereq($sum(N!3, $product(-1, I!6)), 1) & (~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0) & ($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (((~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & ($greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0))) & ($greatereq(I!6, 0) & $greatereq($sum(N!3, $product(-1, I!6)), 1)) & ((~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & $greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0)) & (($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0))) <=> ((~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & $greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)) & $greatereq($sum(N!3, $product(-1, I!6)), 1) & (~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0) & ($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 ((~(~(($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0)))) <=> (($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 ((~(($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(M!8, I!6))), 0))) <=> (~(($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 ((~(~(($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(M!8, I!6))), 0)))) <=> (~(~(($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 ((~(~(($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(M!8, I!6))), 0)))) <=> (($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0))),
% 0.20/0.43 inference(transitivity,[status(thm)],[24, 22])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 (((~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & ($greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0))) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0)) <=> ((~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & $greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 ((~(~($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0))) <=> ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 ((~($sum(M1!9, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))) = 0)) <=> (~($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 ((~(~($sum(M1!9, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))) = 0))) <=> (~(~($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 ((~(~($sum(M1!9, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))) = 0))) <=> ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0)),
% 0.20/0.43 inference(transitivity,[status(thm)],[29, 27])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 ((~(~($greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0))))) <=> ($greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 ((~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0)))) <=> (~($greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 ((~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) <=> (~(~($greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 ((~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) <=> ($greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[33, 31])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 ((~((~($sum(S1!10, $sum($product(-1, S!7), $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) <=> (~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (((~((~($sum(S1!10, $sum($product(-1, S!7), $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & (~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) & (~(~($sum(M1!9, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))) = 0)))) <=> ((~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & ($greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0))) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[35, 34, 30])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (((~((~($sum(S1!10, $sum($product(-1, S!7), $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & (~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) & (~(~($sum(M1!9, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))) = 0)))) <=> ((~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & $greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0))),
% 0.20/0.44 inference(transitivity,[status(thm)],[36, 26])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 ((~(~($greatereq(I!6, 0) & $greatereq($sum(N!3, $product(-1, I!6)), 1)))) <=> ($greatereq(I!6, 0) & $greatereq($sum(N!3, $product(-1, I!6)), 1))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 ((~($greatereq(I!6, 0) & $lesseq($sum(I!6, $product(-1, N!3)), -1))) <=> (~($greatereq(I!6, 0) & $greatereq($sum(N!3, $product(-1, I!6)), 1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 ((~(~($greatereq(I!6, 0) & $lesseq($sum(I!6, $product(-1, N!3)), -1)))) <=> (~(~($greatereq(I!6, 0) & $greatereq($sum(N!3, $product(-1, I!6)), 1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 ((~(~($greatereq(I!6, 0) & $lesseq($sum(I!6, $product(-1, N!3)), -1)))) <=> ($greatereq(I!6, 0) & $greatereq($sum(N!3, $product(-1, I!6)), 1))),
% 0.20/0.44 inference(transitivity,[status(thm)],[40, 38])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (((~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & (~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) & (~(~($greatereq(I!6, 0) & $lesseq($sum(I!6, $product(-1, N!3)), -1)))) & ((~((~($sum(S1!10, $sum($product(-1, S!7), $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & (~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) & (~(~($sum(M1!9, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))) = 0)))) & (~(~(($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(M!8, I!6))), 0))))) <=> ((~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & ($greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0))) & ($greatereq(I!6, 0) & $greatereq($sum(N!3, $product(-1, I!6)), 1)) & ((~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & $greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0)) & (($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[34, 41, 37, 25])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (((~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & (~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) & (~(~($greatereq(I!6, 0) & $lesseq($sum(I!6, $product(-1, N!3)), -1)))) & ((~((~($sum(S1!10, $sum($product(-1, S!7), $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & (~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) & (~(~($sum(M1!9, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))) = 0)))) & (~(~(($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(M!8, I!6))), 0))))) <=> ((~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & $greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)) & $greatereq($sum(N!3, $product(-1, I!6)), 1) & (~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0) & ($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0))),
% 0.20/0.44 inference(transitivity,[status(thm)],[42, 21])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (($greatereq(A!5, 0) & ($sum(A!5, $product(-1, N!3)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N!3, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1!4), t2tb(I))), 0))) <=> ($greatereq(A!5, 0) & ($sum(N!3, $product(-1, A!5)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!3)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1!4), t2tb(I))), 0)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 ((~(~$greatereq(N!3, 1))) <=> $greatereq(N!3, 1)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (((~(~$greatereq(N!3, 1))) & ($greatereq(A!5, 0) & ($sum(A!5, $product(-1, N!3)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N!3, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1!4), t2tb(I))), 0))) & ((~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & (~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) & (~(~($greatereq(I!6, 0) & $lesseq($sum(I!6, $product(-1, N!3)), -1)))) & ((~((~($sum(S1!10, $sum($product(-1, S!7), $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & (~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) & (~(~($sum(M1!9, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))) = 0)))) & (~(~(($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(M!8, I!6))), 0)))))) <=> ($greatereq(N!3, 1) & ($greatereq(A!5, 0) & ($sum(N!3, $product(-1, A!5)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!3)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1!4), t2tb(I))), 0))) & ((~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & $greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)) & $greatereq($sum(N!3, $product(-1, I!6)), 1) & (~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0) & ($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[45, 44, 43])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (((~(~$greatereq(N!3, 1))) & ($greatereq(A!5, 0) & ($sum(A!5, $product(-1, N!3)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N!3, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1!4), t2tb(I))), 0))) & ((~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & (~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) & (~(~($greatereq(I!6, 0) & $lesseq($sum(I!6, $product(-1, N!3)), -1)))) & ((~((~($sum(S1!10, $sum($product(-1, S!7), $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & (~(~($greatereq(I!6, 0) & (~$greatereq($sum(I!6, $product(-1, A!5)), 0))))) & (~(~($sum(M1!9, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))) = 0)))) & (~(~(($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(M!8, I!6))), 0)))))) <=> ($greatereq(N!3, 1) & $greatereq(A!5, 0) & ($sum(N!3, $product(-1, A!5)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!3)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1!4), t2tb(I))), 0)) & (~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & $greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)) & $greatereq($sum(N!3, $product(-1, I!6)), 1) & (~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0) & ($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0))),
% 0.20/0.44 inference(transitivity,[status(thm)],[46, 20])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 ((~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), 0)))) | ![M: $int, S: $int, I: $int] : ($greatereq($sum(M, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))), 0) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | ![M1: $int] : (![S1: $int] : ((~($sum(S1, $sum($product(-1, S), $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($sum(M1, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))) = 0))) | (~(($sum(S, $product(-1, sum2(A1, 0, I))) = 0) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq($sum(S, $product(-1, $product(M, I))), 0)))))) <=> (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), 0)))) | ![M: $int, S: $int, I: $int] : ($greatereq($sum(M, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))), 0) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | ![M1: $int] : (![S1: $int] : ((~($sum(S1, $sum($product(-1, S), $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($sum(M1, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))) = 0))) | (~(($sum(S, $product(-1, sum2(A1, 0, I))) = 0) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq($sum(S, $product(-1, $product(M, I))), 0))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 ((~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 1)) | ![M: $int, S: $int, I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | $lesseq($sum(tb2t(get(int, int, t2tb1(A1), t2tb(I))), $product(-1, M)), 0) | ![M1: $int] : (![S1: $int] : ((~($sum(S1, $sum($product(-1, S), $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($sum(M1, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))) = 0)) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0))))) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(($sum(S, $product(-1, sum2(A1, 0, I))) = 0) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq($sum(S, $product(-1, $product(I, M))), 0)))) | (~($greatereq(A, 0) & ($sum(N, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), 0)))))) <=> (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), 0)))) | ![M: $int, S: $int, I: $int] : ($greatereq($sum(M, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))), 0) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | ![M1: $int] : (![S1: $int] : ((~($sum(S1, $sum($product(-1, S), $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($sum(M1, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))) = 0))) | (~(($sum(S, $product(-1, sum2(A1, 0, I))) = 0) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq($sum(S, $product(-1, $product(M, I))), 0))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 ((~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(1, N)) | ![M: $int, S: $int, I: $int] : ($lesseq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), M) | ![M1: $int] : ((~(M1 = tb2t(get(int, int, t2tb1(A1), t2tb(I))))) | ![S1: $int] : ((~(S1 = $sum(S, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($lesseq(0, I) & (~$lesseq(A, I))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~((S = sum2(A1, 0, I)) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq(S, $product(I, M)))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N))))) | (~($lesseq(0, A) & (N = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | $lesseq(0, tb2t(get(int, int, t2tb1(A1), t2tb(I))))))))) <=> (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 1)) | ![M: $int, S: $int, I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | $lesseq($sum(tb2t(get(int, int, t2tb1(A1), t2tb(I))), $product(-1, M)), 0) | ![M1: $int] : (![S1: $int] : ((~($sum(S1, $sum($product(-1, S), $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($sum(M1, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))) = 0)) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0))))) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(($sum(S, $product(-1, sum2(A1, 0, I))) = 0) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq($sum(S, $product(-1, $product(I, M))), 0)))) | (~($greatereq(A, 0) & ($sum(N, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), 0))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 ((~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(1, N)) | ![M: $int, S: $int, I: $int] : ($lesseq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), M) | ![M1: $int] : ((~(M1 = tb2t(get(int, int, t2tb1(A1), t2tb(I))))) | ![S1: $int] : ((~(S1 = $sum(S, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($lesseq(0, I) & (~$lesseq(A, I))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~((S = sum2(A1, 0, I)) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq(S, $product(I, M)))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N))))) | (~($lesseq(0, A) & (N = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | $lesseq(0, tb2t(get(int, int, t2tb1(A1), t2tb(I))))))))) <=> (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(1, N)) | ![M: $int, S: $int, I: $int] : ($lesseq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), M) | ![M1: $int] : ((~(M1 = tb2t(get(int, int, t2tb1(A1), t2tb(I))))) | ![S1: $int] : ((~(S1 = $sum(S, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($lesseq(0, I) & (~$lesseq(A, I))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~((S = sum2(A1, 0, I)) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq(S, $product(I, M)))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N))))) | (~($lesseq(0, A) & (N = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | $lesseq(0, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 ((~![A: $int, A1: map_int_int, N: $int] : ((($lesseq(0, A) & (N = A)) & ![I: $int] : (($lesseq(0, I) & $less(I, N)) => $lesseq(0, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) => ($lesseq(0, $difference(N, 1)) => ![M: $int, S: $int, I: $int] : (($lesseq(0, I) & $lesseq(I, $difference(N, 1))) => ((((S = sum2(A1, 0, I)) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M)) & $lesseq(S, $product(I, M))) => (($lesseq(0, I) & $less(I, A)) => ($less(M, tb2t(get(int, int, t2tb1(A1), t2tb(I)))) => (($lesseq(0, I) & $less(I, A)) => ![M1: $int] : ((M1 = tb2t(get(int, int, t2tb1(A1), t2tb(I)))) => (($lesseq(0, I) & $less(I, A)) => ![S1: $int] : ((S1 = $sum(S, tb2t(get(int, int, t2tb1(A1), t2tb(I))))) => is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(I, 1), M1)))))))))))) <=> (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(1, N)) | ![M: $int, S: $int, I: $int] : ($lesseq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), M) | ![M1: $int] : ((~(M1 = tb2t(get(int, int, t2tb1(A1), t2tb(I))))) | ![S1: $int] : ((~(S1 = $sum(S, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($lesseq(0, I) & (~$lesseq(A, I))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~((S = sum2(A1, 0, I)) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq(S, $product(I, M)))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N))))) | (~($lesseq(0, A) & (N = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | $lesseq(0, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(53,axiom,(~![A: $int, A1: map_int_int, N: $int] : ((($lesseq(0, A) & (N = A)) & ![I: $int] : (($lesseq(0, I) & $less(I, N)) => $lesseq(0, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) => ($lesseq(0, $difference(N, 1)) => ![M: $int, S: $int, I: $int] : (($lesseq(0, I) & $lesseq(I, $difference(N, 1))) => ((((S = sum2(A1, 0, I)) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M)) & $lesseq(S, $product(I, M))) => (($lesseq(0, I) & $less(I, A)) => ($less(M, tb2t(get(int, int, t2tb1(A1), t2tb(I)))) => (($lesseq(0, I) & $less(I, A)) => ![M1: $int] : ((M1 = tb2t(get(int, int, t2tb1(A1), t2tb(I)))) => (($lesseq(0, I) & $less(I, A)) => ![S1: $int] : ((S1 = $sum(S, tb2t(get(int, int, t2tb1(A1), t2tb(I))))) => is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(I, 1), M1)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_max_sum1')).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(1, N)) | ![M: $int, S: $int, I: $int] : ($lesseq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), M) | ![M1: $int] : ((~(M1 = tb2t(get(int, int, t2tb1(A1), t2tb(I))))) | ![S1: $int] : ((~(S1 = $sum(S, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($lesseq(0, I) & (~$lesseq(A, I))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~((S = sum2(A1, 0, I)) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq(S, $product(I, M)))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N))))) | (~($lesseq(0, A) & (N = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | $lesseq(0, tb2t(get(int, int, t2tb1(A1), t2tb(I))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(1, N)) | ![M: $int, S: $int, I: $int] : ($lesseq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), M) | ![M1: $int] : ((~(M1 = tb2t(get(int, int, t2tb1(A1), t2tb(I))))) | ![S1: $int] : ((~(S1 = $sum(S, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($lesseq(0, I) & (~$lesseq(A, I))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~((S = sum2(A1, 0, I)) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq(S, $product(I, M)))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N))))) | (~($lesseq(0, A) & (N = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | $lesseq(0, tb2t(get(int, int, t2tb1(A1), t2tb(I))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(1, N)) | ![M: $int, S: $int, I: $int] : ($lesseq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), M) | ![M1: $int] : ((~(M1 = tb2t(get(int, int, t2tb1(A1), t2tb(I))))) | ![S1: $int] : ((~(S1 = $sum(S, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($lesseq(0, I) & (~$lesseq(A, I))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~((S = sum2(A1, 0, I)) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq(S, $product(I, M)))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N))))) | (~($lesseq(0, A) & (N = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | $lesseq(0, tb2t(get(int, int, t2tb1(A1), t2tb(I))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (~![A: $int, A1: map_int_int, N: $int] : ((~$lesseq(1, N)) | ![M: $int, S: $int, I: $int] : ($lesseq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), M) | ![M1: $int] : ((~(M1 = tb2t(get(int, int, t2tb1(A1), t2tb(I))))) | ![S1: $int] : ((~(S1 = $sum(S, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($lesseq(0, I) & (~$lesseq(A, I))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~((S = sum2(A1, 0, I)) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq(S, $product(I, M)))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, N))))) | (~($lesseq(0, A) & (N = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(N, I)))) | $lesseq(0, tb2t(get(int, int, t2tb1(A1), t2tb(I))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 1)) | ![M: $int, S: $int, I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | $lesseq($sum(tb2t(get(int, int, t2tb1(A1), t2tb(I))), $product(-1, M)), 0) | ![M1: $int] : (![S1: $int] : ((~($sum(S1, $sum($product(-1, S), $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($sum(M1, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))) = 0)) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0))))) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(($sum(S, $product(-1, sum2(A1, 0, I))) = 0) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq($sum(S, $product(-1, $product(I, M))), 0)))) | (~($greatereq(A, 0) & ($sum(N, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), 0)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), 0)))) | ![M: $int, S: $int, I: $int] : ($greatereq($sum(M, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))), 0) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | ![M1: $int] : (![S1: $int] : ((~($sum(S1, $sum($product(-1, S), $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($sum(M1, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))) = 0))) | (~(($sum(S, $product(-1, sum2(A1, 0, I))) = 0) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq($sum(S, $product(-1, $product(M, I))), 0)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[58, 49])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), 0)))) | ![M: $int, S: $int, I: $int] : ($greatereq($sum(M, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))), 0) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | ![M1: $int] : (![S1: $int] : ((~($sum(S1, $sum($product(-1, S), $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($sum(M1, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))) = 0))) | (~(($sum(S, $product(-1, sum2(A1, 0, I))) = 0) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq($sum(S, $product(-1, $product(M, I))), 0)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[59, 48])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (~![A: $int, A1: map_int_int, N: $int] : ((~$greatereq(N, 1)) | (~($greatereq(A, 0) & ($sum(A, $product(-1, N)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1), t2tb(I))), 0)))) | ![M: $int, S: $int, I: $int] : ($greatereq($sum(M, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))), 0) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), -1))) | ![M1: $int] : (![S1: $int] : ((~($sum(S1, $sum($product(-1, S), $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I)))))) = 0)) | is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, $sum(1, I), M1)) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($sum(M1, $product(-1, tb2t(get(int, int, t2tb1(A1), t2tb(I))))) = 0))) | (~(($sum(S, $product(-1, sum2(A1, 0, I))) = 0) & is_max1(tb2t2(mk_array1(int, A, t2tb1(A1))), 0, I, M) & $lesseq($sum(S, $product(-1, $product(M, I))), 0)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[60, 48])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 ($greatereq(N!3, 1) & $greatereq(A!5, 0) & ($sum(N!3, $product(-1, A!5)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!3)), 0)))) | $greatereq(tb2t(get(int, int, t2tb1(A1!4), t2tb(I))), 0)) & (~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)) & $greatereq(I!6, 0) & (~$lesseq($sum(A!5, $product(-1, I!6)), 0)) & $greatereq($sum(N!3, $product(-1, I!6)), 1) & (~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))) & ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0) & ($sum(S!7, $product(-1, sum2(A1!4, 0, I!6))) = 0) & is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) & $lesseq($sum(S!7, $product(-1, $product(I!6, M!8))), 0)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[61, 47])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 ($greatereq(I!6, 0)),
% 0.20/0.45 inference(and_elim,[status(thm)],[62])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 ((~($sum(I!6, $product(-1, tb2t(t2tb(I!6)))) = 0)) | $lesseq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), 0)),
% 0.20/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 ($lesseq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), 0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[64, 15])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 ($greatereq(tb2t(t2tb(I!6)), 0) | (~$greatereq(I!6, 0)) | (~$lesseq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), 0))),
% 0.20/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 ($greatereq(tb2t(t2tb(I!6)), 0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[66, 65, 63])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (^[X: map_int_int] : refl(sort1(map(int, int), t2tb1(X)) <=> sort1(map(int, int), t2tb1(X)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (![X: map_int_int] : sort1(map(int, int), t2tb1(X)) <=> ![X: map_int_int] : sort1(map(int, int), t2tb1(X))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (![X: map_int_int] : sort1(map(int, int), t2tb1(X)) <=> ![X: map_int_int] : sort1(map(int, int), t2tb1(X))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(71,axiom,(![X: map_int_int] : sort1(map(int, int), t2tb1(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2tb_sort1')).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (![X: map_int_int] : sort1(map(int, int), t2tb1(X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.45 tff(73,plain,(
% 0.20/0.45 ![X: map_int_int] : sort1(map(int, int), t2tb1(X))),
% 0.20/0.45 inference(skolemize,[status(sab)],[72])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (![X: map_int_int] : sort1(map(int, int), t2tb1(X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 ((~![X: map_int_int] : sort1(map(int, int), t2tb1(X))) | sort1(map(int, int), t2tb1(A1!4))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (sort1(map(int, int), t2tb1(A1!4))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 (^[A: ty, U: $int, U1: uni] : refl(((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (^[A: ty, U: $int, U1: uni] : rewrite((sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.45 tff(82,axiom,(![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','elts_def1')).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.45 tff(85,plain,(
% 0.20/0.45 ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.45 inference(skolemize,[status(sab)],[84])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb1(A1!4))) | (elts(int, mk_array1(int, A!5, t2tb1(A1!4))) = t2tb1(A1!4)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb1(A1!4))) | (elts(int, mk_array1(int, A!5, t2tb1(A1!4))) = t2tb1(A1!4)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb1(A1!4))) | (elts(int, mk_array1(int, A!5, t2tb1(A1!4))) = t2tb1(A1!4)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb1(A1!4))) | (elts(int, mk_array1(int, A!5, t2tb1(A1!4))) = t2tb1(A1!4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 ((~sort1(map(int, int), t2tb1(A1!4))) | (elts(int, mk_array1(int, A!5, t2tb1(A1!4))) = t2tb1(A1!4))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (elts(int, mk_array1(int, A!5, t2tb1(A1!4))) = t2tb1(A1!4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[90, 76])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (get(int, int, elts(int, mk_array1(int, A!5, t2tb1(A1!4))), t2tb(I!6)) = get(int, int, t2tb1(A1!4), t2tb(I!6))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (^[A: ty, A1: uni, I: $int] : refl((get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(96,axiom,(![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','get_def')).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.46 tff(98,plain,(
% 0.20/0.46 ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[97])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, A!5, t2tb1(A1!4)), I!6) = get(int, int, elts(int, mk_array1(int, A!5, t2tb1(A1!4))), t2tb(I!6)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (get2(int, mk_array1(int, A!5, t2tb1(A1!4)), I!6) = get(int, int, elts(int, mk_array1(int, A!5, t2tb1(A1!4))), t2tb(I!6))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (~$greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)),
% 0.20/0.46 inference(and_elim,[status(thm)],[62])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 ($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0),
% 0.20/0.46 inference(and_elim,[status(thm)],[62])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 ((~($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0)) | $lesseq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)), 0)),
% 0.20/0.46 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 ($lesseq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)), 0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.46 tff(106,assumption,(~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))), introduced(assumption)).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))) | (~$greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (~$greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 ((~$greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0)) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$lesseq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))))), 0)),
% 0.20/0.46 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 (~$greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[109, 108, 105, 102])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (^[A: array_int, L: $int, H: $int, M: $int] : refl((~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))))) <=> (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))))) <=> ![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 (^[A: array_int, L: $int, H: $int, M: $int] : rewrite((~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))))) <=> (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 (![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))))) <=> ![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))))) <=> ![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[114, 112])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 (^[A: array_int, L: $int, H: $int, M: $int] : trans(monotonicity(rewrite(((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & $lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0))))) <=> ((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))), trans(monotonicity(rewrite((~((~($lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) <=> (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0))))), trans(monotonicity(trans(monotonicity(rewrite(($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) <=> (~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0))))), ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) <=> (~(~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0))))))), rewrite((~(~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0))))) <=> ((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))), ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) <=> ((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0))))), rewrite(($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))) <=> ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))), (((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))) <=> (((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))), rewrite((((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))) <=> (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))), (((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))) <=> (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))), ((is_max1(A, L, H, M) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) | ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) <=> (is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))), rewrite((is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))) <=> (is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))), ((is_max1(A, L, H, M) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) | ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) <=> (is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))), ((((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & $lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0))))) & (is_max1(A, L, H, M) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) | ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))) <=> (((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0))))))))) & (is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))))), rewrite((((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0))))))))) & (is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))) <=> (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))), ((((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & $lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0))))) & (is_max1(A, L, H, M) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) | ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))) <=> (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & $lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0))))) & (is_max1(A, L, H, M) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) | ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))) <=> ![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (^[A: array_int, L: $int, H: $int, M: $int] : rewrite((((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & ($greatereq($sum(tptp_fun_K_1(M, H, L, A), $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))) & (((~((~($greatereq($sum(tptp_fun_K_2(M, H, L, A), $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) | ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ((~(~$greatereq($sum(L, $product(-1, H)), 0))) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) | is_max1(A, L, H, M))) <=> (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & $lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0))))) & (is_max1(A, L, H, M) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) | ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 (![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & ($greatereq($sum(tptp_fun_K_1(M, H, L, A), $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))) & (((~((~($greatereq($sum(tptp_fun_K_2(M, H, L, A), $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) | ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ((~(~$greatereq($sum(L, $product(-1, H)), 0))) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) | is_max1(A, L, H, M))) <=> ![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & $lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0))))) & (is_max1(A, L, H, M) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) | ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[118])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (^[A: array_int, L: $int, H: $int, M: $int] : rewrite((((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb2(A), K)), $product(-1, M)), 0)) & (($lesseq($sum(H, $product(-1, L)), 0) & (M = 0)) | ((~$lesseq($sum(H, $product(-1, L)), 0)) & ?[K: $int] : ($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) & ((~(![K: $int] : ((~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb2(A), K)), $product(-1, M)), 0)) & (($lesseq($sum(H, $product(-1, L)), 0) & (M = 0)) | ((~$lesseq($sum(H, $product(-1, L)), 0)) & ?[K: $int] : ($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) | is_max1(A, L, H, M))) <=> (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & ?[K: $int] : ($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) & ((~(![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & ?[K: $int] : ($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) | is_max1(A, L, H, M))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb2(A), K)), $product(-1, M)), 0)) & (($lesseq($sum(H, $product(-1, L)), 0) & (M = 0)) | ((~$lesseq($sum(H, $product(-1, L)), 0)) & ?[K: $int] : ($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) & ((~(![K: $int] : ((~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb2(A), K)), $product(-1, M)), 0)) & (($lesseq($sum(H, $product(-1, L)), 0) & (M = 0)) | ((~$lesseq($sum(H, $product(-1, L)), 0)) & ?[K: $int] : ($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) | is_max1(A, L, H, M))) <=> ![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & ?[K: $int] : ($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) & ((~(![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & ?[K: $int] : ($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) | is_max1(A, L, H, M)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (^[A: array_int, L: $int, H: $int, M: $int] : rewrite((((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) & ((~(![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) | is_max1(A, L, H, M))) <=> (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb2(A), K)), $product(-1, M)), 0)) & (($lesseq($sum(H, $product(-1, L)), 0) & (M = 0)) | ((~$lesseq($sum(H, $product(-1, L)), 0)) & ?[K: $int] : ($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) & ((~(![K: $int] : ((~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb2(A), K)), $product(-1, M)), 0)) & (($lesseq($sum(H, $product(-1, L)), 0) & (M = 0)) | ((~$lesseq($sum(H, $product(-1, L)), 0)) & ?[K: $int] : ($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) | is_max1(A, L, H, M))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) & ((~(![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) | is_max1(A, L, H, M))) <=> ![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb2(A), K)), $product(-1, M)), 0)) & (($lesseq($sum(H, $product(-1, L)), 0) & (M = 0)) | ((~$lesseq($sum(H, $product(-1, L)), 0)) & ?[K: $int] : ($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) & ((~(![K: $int] : ((~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb2(A), K)), $product(-1, M)), 0)) & (($lesseq($sum(H, $product(-1, L)), 0) & (M = 0)) | ((~$lesseq($sum(H, $product(-1, L)), 0)) & ?[K: $int] : ($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) | is_max1(A, L, H, M)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) & ((~(![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) | is_max1(A, L, H, M))) <=> ![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) & ((~(![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) | is_max1(A, L, H, M)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (^[A: array_int, L: $int, H: $int, M: $int] : rewrite(((is_max1(A, L, H, M) => (![K: $int] : (($lesseq(L, K) & $less(K, H)) => $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ($less(L, H) & ?[K: $int] : (($lesseq(L, K) & $less(K, H)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) & ((![K: $int] : (($lesseq(L, K) & $less(K, H)) => $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ($less(L, H) & ?[K: $int] : (($lesseq(L, K) & $less(K, H)) & (M = tb2t(get2(int, t2tb2(A), K))))))) => is_max1(A, L, H, M))) <=> (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) & ((~(![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) | is_max1(A, L, H, M))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (![A: array_int, L: $int, H: $int, M: $int] : ((is_max1(A, L, H, M) => (![K: $int] : (($lesseq(L, K) & $less(K, H)) => $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ($less(L, H) & ?[K: $int] : (($lesseq(L, K) & $less(K, H)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) & ((![K: $int] : (($lesseq(L, K) & $less(K, H)) => $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ($less(L, H) & ?[K: $int] : (($lesseq(L, K) & $less(K, H)) & (M = tb2t(get2(int, t2tb2(A), K))))))) => is_max1(A, L, H, M))) <=> ![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) & ((~(![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) | is_max1(A, L, H, M)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.47 tff(127,axiom,(![A: array_int, L: $int, H: $int, M: $int] : ((is_max1(A, L, H, M) => (![K: $int] : (($lesseq(L, K) & $less(K, H)) => $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ($less(L, H) & ?[K: $int] : (($lesseq(L, K) & $less(K, H)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) & ((![K: $int] : (($lesseq(L, K) & $less(K, H)) => $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ($less(L, H) & ?[K: $int] : (($lesseq(L, K) & $less(K, H)) & (M = tb2t(get2(int, t2tb2(A), K))))))) => is_max1(A, L, H, M)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','is_max_def')).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) & ((~(![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) | is_max1(A, L, H, M)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) & ((~(![K: $int] : ((~($lesseq(L, K) & (~$lesseq(H, K)))) | $lesseq(tb2t(get2(int, t2tb2(A), K)), M)) & (($lesseq(H, L) & (M = 0)) | ((~$lesseq(H, L)) & ?[K: $int] : ($lesseq(L, K) & (~$lesseq(H, K)) & (M = tb2t(get2(int, t2tb2(A), K)))))))) | is_max1(A, L, H, M)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 (![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb2(A), K)), $product(-1, M)), 0)) & (($lesseq($sum(H, $product(-1, L)), 0) & (M = 0)) | ((~$lesseq($sum(H, $product(-1, L)), 0)) & ?[K: $int] : ($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) & ((~(![K: $int] : ((~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb2(A), K)), $product(-1, M)), 0)) & (($lesseq($sum(H, $product(-1, L)), 0) & (M = 0)) | ((~$lesseq($sum(H, $product(-1, L)), 0)) & ?[K: $int] : ($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) | is_max1(A, L, H, M)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[129, 123])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & ?[K: $int] : ($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) & ((~(![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & ?[K: $int] : ($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) | is_max1(A, L, H, M)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[130, 121])).
% 0.20/0.47 tff(132,plain,(
% 0.20/0.47 ![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & ($greatereq($sum(tptp_fun_K_1(M, H, L, A), $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))) & (((~((~($greatereq($sum(tptp_fun_K_2(M, H, L, A), $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) | ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ((~(~$greatereq($sum(L, $product(-1, H)), 0))) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))) | is_max1(A, L, H, M)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[131])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (![A: array_int, L: $int, H: $int, M: $int] : (((~is_max1(A, L, H, M)) | (![K: $int] : ((~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0)) & (($greatereq($sum(L, $product(-1, H)), 0) & (M = 0)) | ((~$greatereq($sum(L, $product(-1, H)), 0)) & $lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0))))) & (is_max1(A, L, H, M) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) & (~$lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0))) | ((~($greatereq($sum(L, $product(-1, H)), 0) & (M = 0))) & ($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : (~($greatereq($sum(K, $product(-1, L)), 0) & (~$lesseq($sum(H, $product(-1, K)), 0)) & ($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[132, 119])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[133, 117])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[134, 115])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 0)))))) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$greatereq(tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))))) <=> ((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 0)))))) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$greatereq(tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 ((~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ($lesseq($sum(I!6, $product(-1, K)), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, I!6)), 0)) | (~(M!8 = 0)))) | (~($greatereq($sum(0, $product(-1, I!6)), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, I!6)), 0)) | (~(M!8 = 0)))) | (~($greatereq($sum(0, $product(-1, I!6)), 0) | ![K: $int] : ($lesseq($sum(I!6, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0))))))))))) <=> (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 0)))))) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$greatereq(tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ($lesseq($sum(I!6, $product(-1, K)), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, I!6)), 0)) | (~(M!8 = 0)))) | (~($greatereq($sum(0, $product(-1, I!6)), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, I!6)), 0)) | (~(M!8 = 0)))) | (~($greatereq($sum(0, $product(-1, I!6)), 0) | ![K: $int] : ($lesseq($sum(I!6, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)))))))))))) <=> ((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 0)))))) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$greatereq(tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[137])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 (((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ($lesseq($sum(I!6, $product(-1, K)), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, I!6)), 0)) | (~(M!8 = 0)))) | (~($greatereq($sum(0, $product(-1, I!6)), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, I!6)), 0)) | (~(M!8 = 0)))) | (~($greatereq($sum(0, $product(-1, I!6)), 0) | ![K: $int] : ($lesseq($sum(I!6, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)))))))))))) <=> ((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 0)))))) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$greatereq(tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[138, 136])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 ((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ($lesseq($sum(I!6, $product(-1, K)), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, I!6)), 0)) | (~(M!8 = 0)))) | (~($greatereq($sum(0, $product(-1, I!6)), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, I!6)), 0)) | (~(M!8 = 0)))) | (~($greatereq($sum(0, $product(-1, I!6)), 0) | ![K: $int] : ($lesseq($sum(I!6, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 ((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 0)))))) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$greatereq(tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 0)))))) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$greatereq(tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[141, 135])).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 (((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 0)))))) | (~($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$greatereq(tptp_fun_K_2(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))) | ((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 ((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 (is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)),
% 0.20/0.49 inference(and_elim,[status(thm)],[62])).
% 0.20/0.49 tff(146,plain,
% 0.20/0.49 ((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 ((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, I!6, M!8)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[147, 144])).
% 0.20/0.49 tff(149,plain,
% 0.20/0.49 (((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~((~((~$lesseq(I!6, 0)) | (~(M!8 = 0)))) | (~($lesseq(I!6, 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | (~$greatereq(tptp_fun_K_1(M!8, I!6, 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))) | ![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(150,plain,
% 0.20/0.49 (![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.50 tff(151,plain,
% 0.20/0.50 (($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))) | $greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 ($greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[151, 106])).
% 0.20/0.50 tff(153,plain,
% 0.20/0.50 (((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | ((~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(154,plain,
% 0.20/0.50 (((~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)) <=> ((~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(155,plain,
% 0.20/0.50 ($greatereq($sum($product(-1, I!6), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4))))), 0) <=> $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(156,plain,
% 0.20/0.50 ($sum(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), $product(-1, I!6)) = $sum($product(-1, I!6), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 ($greatereq($sum(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), $product(-1, I!6)), 0) <=> $greatereq($sum($product(-1, I!6), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4))))), 0)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[156])).
% 0.20/0.50 tff(158,plain,
% 0.20/0.50 ($greatereq($sum(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), $product(-1, I!6)), 0) <=> $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)),
% 0.20/0.50 inference(transitivity,[status(thm)],[157, 155])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 (((~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $greatereq($sum(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), $product(-1, I!6)), 0)) <=> ((~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[158])).
% 0.20/0.50 tff(160,plain,
% 0.20/0.50 (((~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $greatereq($sum(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), $product(-1, I!6)), 0)) <=> ((~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0))),
% 0.20/0.50 inference(transitivity,[status(thm)],[159, 154])).
% 0.20/0.50 tff(161,plain,
% 0.20/0.50 (((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | ((~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $greatereq($sum(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), $product(-1, I!6)), 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | ((~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.50 tff(162,plain,
% 0.20/0.50 (((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | ((~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $greatereq($sum(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), $product(-1, I!6)), 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0))),
% 0.20/0.50 inference(transitivity,[status(thm)],[161, 153])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 ((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | ((~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $greatereq($sum(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), $product(-1, I!6)), 0))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 ((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 0))) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)) | $greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 ($greatereq($sum(M!8, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[164, 152, 150])).
% 0.20/0.50 tff(166,plain,
% 0.20/0.50 ($lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[165, 110])).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 (($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))) | (~$lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(168,plain,
% 0.20/0.50 (~$lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[167, 106])).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 (I!6 = tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4))))),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[168, 166])).
% 0.20/0.50 tff(170,plain,
% 0.20/0.50 (tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))) = I!6),
% 0.20/0.50 inference(symmetry,[status(thm)],[169])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 (![J: uni] : (t2tb2(tb2t2(J)) = J) <=> ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(172,plain,
% 0.20/0.50 (![J: uni] : (t2tb2(tb2t2(J)) = J) <=> ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(173,axiom,(![J: uni] : (t2tb2(tb2t2(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR2')).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 (![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.50 tff(175,plain,(
% 0.20/0.50 ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.20/0.50 inference(skolemize,[status(sab)],[174])).
% 0.20/0.50 tff(176,plain,
% 0.20/0.50 (![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.20/0.50 tff(177,plain,
% 0.20/0.50 ((~![J: uni] : (t2tb2(tb2t2(J)) = J)) | (t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))) = mk_array1(int, A!5, t2tb1(A1!4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(178,plain,
% 0.20/0.50 (t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))) = mk_array1(int, A!5, t2tb1(A1!4))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.20/0.50 tff(179,plain,
% 0.20/0.50 (get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4))))) = get2(int, mk_array1(int, A!5, t2tb1(A1!4)), I!6)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[178, 170])).
% 0.20/0.50 tff(180,plain,
% 0.20/0.50 (get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4))))) = get(int, int, t2tb1(A1!4), t2tb(I!6))),
% 0.20/0.50 inference(transitivity,[status(thm)],[179, 101, 92])).
% 0.20/0.50 tff(181,plain,
% 0.20/0.50 (tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))) = tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[180])).
% 0.20/0.50 tff(182,plain,
% 0.20/0.50 (tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))) = tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4))))))),
% 0.20/0.50 inference(symmetry,[status(thm)],[181])).
% 0.20/0.50 tff(183,assumption,($greatereq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0)), introduced(assumption)).
% 0.20/0.50 tff(184,assumption,(~$greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0)), introduced(assumption)).
% 0.20/0.50 tff(185,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[184, 105, 183])).
% 0.20/0.50 tff(186,plain,((~$greatereq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0)) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(187,plain,
% 0.20/0.50 (~$greatereq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[186, 108])).
% 0.20/0.50 tff(188,plain,
% 0.20/0.50 ((~(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))) = tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) | $greatereq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(189,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[188, 187, 182])).
% 0.20/0.50 tff(190,plain,($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(191,plain,
% 0.20/0.50 (((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 1))) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~((~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | $lesseq(I!6, -1) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))))) <=> ((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 1))) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~((~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | $lesseq(I!6, -1) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(192,plain,
% 0.20/0.51 ((~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ($lesseq($sum($sum(1, I!6), $product(-1, K)), 0) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, $sum(1, I!6))), 0)) | (~(M1!9 = 0)))) | (~($greatereq($sum(0, $product(-1, $sum(1, I!6))), 0) | $lesseq($sum($sum(1, I!6), $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~($lesseq($sum($sum(1, I!6), $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, $sum(1, I!6))), 0)) | (~(M1!9 = 0)))) | (~($greatereq($sum(0, $product(-1, $sum(1, I!6))), 0) | ![K: $int] : ($lesseq($sum($sum(1, I!6), $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0))))))))))) <=> (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 1))) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~((~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | $lesseq(I!6, -1) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(193,plain,
% 0.20/0.51 (((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ($lesseq($sum($sum(1, I!6), $product(-1, K)), 0) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, $sum(1, I!6))), 0)) | (~(M1!9 = 0)))) | (~($greatereq($sum(0, $product(-1, $sum(1, I!6))), 0) | $lesseq($sum($sum(1, I!6), $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~($lesseq($sum($sum(1, I!6), $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, $sum(1, I!6))), 0)) | (~(M1!9 = 0)))) | (~($greatereq($sum(0, $product(-1, $sum(1, I!6))), 0) | ![K: $int] : ($lesseq($sum($sum(1, I!6), $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)))))))))))) <=> ((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 1))) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~((~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | $lesseq(I!6, -1) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[192])).
% 0.20/0.51 tff(194,plain,
% 0.20/0.51 (((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ($lesseq($sum($sum(1, I!6), $product(-1, K)), 0) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, $sum(1, I!6))), 0)) | (~(M1!9 = 0)))) | (~($greatereq($sum(0, $product(-1, $sum(1, I!6))), 0) | $lesseq($sum($sum(1, I!6), $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~($lesseq($sum($sum(1, I!6), $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, $sum(1, I!6))), 0)) | (~(M1!9 = 0)))) | (~($greatereq($sum(0, $product(-1, $sum(1, I!6))), 0) | ![K: $int] : ($lesseq($sum($sum(1, I!6), $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)))))))))))) <=> ((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 1))) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~((~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | $lesseq(I!6, -1) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[193, 191])).
% 0.20/0.51 tff(195,plain,
% 0.20/0.51 ((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ($lesseq($sum($sum(1, I!6), $product(-1, K)), 0) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, $sum(1, I!6))), 0)) | (~(M1!9 = 0)))) | (~($greatereq($sum(0, $product(-1, $sum(1, I!6))), 0) | $lesseq($sum($sum(1, I!6), $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~($lesseq($sum($sum(1, I!6), $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), 0)))) | (~((~((~$greatereq($sum(0, $product(-1, $sum(1, I!6))), 0)) | (~(M1!9 = 0)))) | (~($greatereq($sum(0, $product(-1, $sum(1, I!6))), 0) | ![K: $int] : ($lesseq($sum($sum(1, I!6), $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)))))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(196,plain,
% 0.20/0.51 ((~![A: array_int, L: $int, H: $int, M: $int] : (~((~((~is_max1(A, L, H, M)) | (~((~![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | $lesseq($sum(H, $product(-1, tptp_fun_K_1(M, H, L, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_1(M, H, L, A))), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_1(M, H, L, A))))) = 0)))))))))) | (~(is_max1(A, L, H, M) | (~($lesseq($sum(H, $product(-1, tptp_fun_K_2(M, H, L, A))), 0) | $greatereq($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), tptp_fun_K_2(M, H, L, A))))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_2(M, H, L, A))), 0)))) | (~((~((~$greatereq($sum(L, $product(-1, H)), 0)) | (~(M = 0)))) | (~($greatereq($sum(L, $product(-1, H)), 0) | ![K: $int] : ($lesseq($sum(H, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, L)), 0)) | (~($sum(M, $product(-1, tb2t(get2(int, t2tb2(A), K)))) = 0)))))))))))) | (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 1))) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~((~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | $lesseq(I!6, -1) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.52 tff(197,plain,
% 0.20/0.52 (~((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 1))) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~((~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | $lesseq(I!6, -1) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[196, 135])).
% 0.20/0.52 tff(198,plain,
% 0.20/0.52 (((~((~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)) | (~((~![K: $int] : ((~$greatereq(K, 0)) | $greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))), 0) | $greatereq($sum(K, $product(-1, I!6)), 1))) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~((~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))) = 0)) | $lesseq(I!6, -1) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_1(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))))))) | (~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))))) | (is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(199,plain,
% 0.20/0.52 (is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.20/0.52 tff(200,plain,
% 0.20/0.52 (~((~($sum(S!7, $sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, S1!10))) = 0)) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9))),
% 0.20/0.52 inference(and_elim,[status(thm)],[62])).
% 0.20/0.52 tff(201,plain,
% 0.20/0.52 (~is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9)),
% 0.20/0.52 inference(or_elim,[status(thm)],[200])).
% 0.20/0.52 tff(202,plain,
% 0.20/0.52 ((~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))) | is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(203,plain,
% 0.20/0.52 ((~(is_max1(tb2t2(mk_array1(int, A!5, t2tb1(A1!4))), 0, $sum(1, I!6), M1!9) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0)))))) | (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.20/0.52 tff(204,plain,
% 0.20/0.52 ((~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))) | (~($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))))), 0) | $lesseq($sum(I!6, $product(-1, tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))))), -1) | (~$greatereq(tptp_fun_K_2(M1!9, $sum(1, I!6), 0, tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), 0))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[203, 199])).
% 0.20/0.52 tff(205,plain,
% 0.20/0.52 (~((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[204, 190])).
% 0.20/0.52 tff(206,plain,
% 0.20/0.52 (((~((~$lesseq(I!6, -1)) | (~(M1!9 = 0)))) | (~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))))) | ($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(207,plain,
% 0.20/0.52 ($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.20/0.52 tff(208,plain,
% 0.20/0.52 ((~$lesseq(I!6, -1)) | (~$greatereq(I!6, 0))),
% 0.20/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.52 tff(209,plain,
% 0.20/0.52 (~$lesseq(I!6, -1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[208, 63])).
% 0.20/0.52 tff(210,plain,
% 0.20/0.52 ((~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))) | $lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(211,plain,
% 0.20/0.52 ((~($lesseq(I!6, -1) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1)))) | ![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.20/0.52 tff(212,plain,
% 0.20/0.52 (![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[211, 207])).
% 0.20/0.52 tff(213,plain,
% 0.20/0.52 (((~![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))) | ((~$greatereq(tb2t(t2tb(I!6)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0)) | $lesseq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), -1))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))) | (~$greatereq(tb2t(t2tb(I!6)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0)) | $lesseq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), -1))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(214,plain,
% 0.20/0.52 (((~$greatereq(tb2t(t2tb(I!6)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0)) | $greatereq($sum(tb2t(t2tb(I!6)), $product(-1, I!6)), 1)) <=> ((~$greatereq(tb2t(t2tb(I!6)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0)) | $lesseq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), -1))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(215,plain,
% 0.20/0.52 (((~![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))) | ((~$greatereq(tb2t(t2tb(I!6)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0)) | $greatereq($sum(tb2t(t2tb(I!6)), $product(-1, I!6)), 1))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))) | ((~$greatereq(tb2t(t2tb(I!6)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0)) | $lesseq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), -1)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[214])).
% 0.20/0.52 tff(216,plain,
% 0.20/0.52 (((~![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))) | ((~$greatereq(tb2t(t2tb(I!6)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0)) | $greatereq($sum(tb2t(t2tb(I!6)), $product(-1, I!6)), 1))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))) | (~$greatereq(tb2t(t2tb(I!6)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0)) | $lesseq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), -1))),
% 0.20/0.52 inference(transitivity,[status(thm)],[215, 213])).
% 0.20/0.52 tff(217,plain,
% 0.20/0.52 ((~![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))) | ((~$greatereq(tb2t(t2tb(I!6)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0)) | $greatereq($sum(tb2t(t2tb(I!6)), $product(-1, I!6)), 1))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(218,plain,
% 0.20/0.52 ((~![K: $int] : ((~$greatereq(K, 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), K)))) = 0)) | $greatereq($sum(K, $product(-1, I!6)), 1))) | (~$greatereq(tb2t(t2tb(I!6)), 0)) | (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0)) | $lesseq($sum(I!6, $product(-1, tb2t(t2tb(I!6)))), -1)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.20/0.52 tff(219,plain,
% 0.20/0.52 (~($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[218, 212, 67, 19])).
% 0.20/0.52 tff(220,plain,
% 0.20/0.52 (I!6 = tb2t(t2tb(I!6))),
% 0.20/0.52 inference(theory_lemma,[status(thm)],[17, 65])).
% 0.20/0.52 tff(221,plain,
% 0.20/0.52 (tb2t(t2tb(I!6)) = I!6),
% 0.20/0.52 inference(symmetry,[status(thm)],[220])).
% 0.20/0.52 tff(222,plain,
% 0.20/0.52 (get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6))) = get2(int, mk_array1(int, A!5, t2tb1(A1!4)), I!6)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[178, 221])).
% 0.20/0.52 tff(223,plain,
% 0.20/0.52 (get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6))) = get(int, int, t2tb1(A1!4), t2tb(I!6))),
% 0.20/0.53 inference(transitivity,[status(thm)],[222, 101, 92])).
% 0.20/0.53 tff(224,plain,
% 0.20/0.53 (tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))) = tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[223])).
% 0.20/0.53 tff(225,plain,
% 0.20/0.53 (tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))) = tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6))))),
% 0.20/0.53 inference(symmetry,[status(thm)],[224])).
% 0.20/0.53 tff(226,plain,
% 0.20/0.53 ((~(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))) = tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) | $greatereq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0)),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(227,plain,
% 0.20/0.53 ($greatereq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.20/0.53 tff(228,plain,
% 0.20/0.53 ($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0) | (~$lesseq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0))),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(229,plain,
% 0.20/0.53 ($greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[228, 227, 105])).
% 0.20/0.53 tff(230,plain,
% 0.20/0.53 ((~($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)) = 0)) | $greatereq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)), 0)),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(231,plain,
% 0.20/0.53 ($greatereq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[230, 103])).
% 0.20/0.53 tff(232,plain,
% 0.20/0.53 ((~(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))) = tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) | $lesseq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0)),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(233,plain,
% 0.20/0.53 ($lesseq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[232, 225])).
% 0.20/0.53 tff(234,plain,
% 0.20/0.53 ($lesseq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0) | (~$greatereq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, M1!9)), 0)) | (~$lesseq($sum(tb2t(get(int, int, t2tb1(A1!4), t2tb(I!6))), $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0))),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(235,plain,
% 0.20/0.53 ($lesseq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[234, 233, 231])).
% 0.20/0.53 tff(236,plain,
% 0.20/0.53 (($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))) = 0) | (~$lesseq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0)) | (~$greatereq($sum(M1!9, $product(-1, tb2t(get2(int, t2tb2(tb2t2(mk_array1(int, A!5, t2tb1(A1!4)))), tb2t(t2tb(I!6)))))), 0))),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(237,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[236, 235, 229, 219])).
% 0.20/0.53 % SZS output end Proof
%------------------------------------------------------------------------------