TSTP Solution File: SWW619_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW619_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 20:59:28 EDT 2022
% Result : Theorem 15.37s 10.09s
% Output : Proof 15.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWW619_2 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 20:19:01 EDT 2022
% 0.12/0.33 % 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.
% 15.37/10.09 % SZS status Theorem
% 15.37/10.09 % SZS output start Proof
% 15.37/10.09 tff(tptp_fun_Len_16_type, type, (
% 15.37/10.09 tptp_fun_Len_16: $int)).
% 15.37/10.09 tff(tptp_fun_A_12_type, type, (
% 15.37/10.09 tptp_fun_A_12: $int)).
% 15.37/10.09 tff(sorted_sub3_type, type, (
% 15.37/10.09 sorted_sub3: ( array_elt2 * $int * $int ) > $o)).
% 15.37/10.09 tff(min_type, type, (
% 15.37/10.09 min: ( $int * $int ) > $int)).
% 15.37/10.09 tff(tb2t8_type, type, (
% 15.37/10.09 tb2t8: uni > array_elt2)).
% 15.37/10.09 tff(mk_array1_type, type, (
% 15.37/10.09 mk_array1: ( ty * $int * uni ) > uni)).
% 15.37/10.09 tff(t2tb9_type, type, (
% 15.37/10.09 t2tb9: map_int_elt2 > uni)).
% 15.37/10.09 tff(tptp_fun_A2_15_type, type, (
% 15.37/10.09 tptp_fun_A2_15: map_int_elt2)).
% 15.37/10.09 tff(elt5_type, type, (
% 15.37/10.09 elt5: ty)).
% 15.37/10.09 tff(permut_all_type, type, (
% 15.37/10.09 permut_all: ( ty * uni * uni ) > $o)).
% 15.37/10.09 tff(tptp_fun_A1_11_type, type, (
% 15.37/10.09 tptp_fun_A1_11: map_int_elt2)).
% 15.37/10.09 tff(tptp_fun_K_17_type, type, (
% 15.37/10.09 tptp_fun_K_17: $int)).
% 15.37/10.09 tff(tb2t7_type, type, (
% 15.37/10.09 tb2t7: uni > elt4)).
% 15.37/10.09 tff(get_type, type, (
% 15.37/10.09 get: ( ty * ty * uni * uni ) > uni)).
% 15.37/10.09 tff(t2tb_type, type, (
% 15.37/10.09 t2tb: $int > uni)).
% 15.37/10.09 tff(int_type, type, (
% 15.37/10.09 int: ty)).
% 15.37/10.09 tff(tptp_fun_Tmp1_13_type, type, (
% 15.37/10.09 tptp_fun_Tmp1_13: map_int_elt2)).
% 15.37/10.09 tff(tptp_fun_Tmp_14_type, type, (
% 15.37/10.09 tptp_fun_Tmp_14: $int)).
% 15.37/10.09 tff(1,plain,
% 15.37/10.09 (^[K: $int] : refl((sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0))) <=> (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0))))),
% 15.37/10.09 inference(bind,[status(th)],[])).
% 15.37/10.09 tff(2,plain,
% 15.37/10.09 (![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0))) <=> ![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))),
% 15.37/10.09 inference(quant_intro,[status(thm)],[1])).
% 15.37/10.09 tff(3,plain,
% 15.37/10.09 (^[K: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0))) <=> (~((~$greatereq($product(K, Len!16), 0)) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))), ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) <=> (~(~((~$greatereq($product(K, Len!16), 0)) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))))), rewrite((~(~((~$greatereq($product(K, Len!16), 0)) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) <=> ((~$greatereq($product(K, Len!16), 0)) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0))), ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) <=> ((~$greatereq($product(K, Len!16), 0)) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))), (((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))) <=> (((~$greatereq($product(K, Len!16), 0)) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))))), rewrite((((~$greatereq($product(K, Len!16), 0)) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))) <=> (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))), (((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))) <=> (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))))),
% 15.37/10.09 inference(bind,[status(th)],[])).
% 15.37/10.09 tff(4,plain,
% 15.37/10.09 (![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))) <=> ![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))),
% 15.37/10.09 inference(quant_intro,[status(thm)],[3])).
% 15.37/10.09 tff(5,plain,
% 15.37/10.09 (($greatereq(A!12, 0) & ($greatereq(Tmp!14, 0) & ($sum(A!12, $product(-1, Tmp!14)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp!14)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I))))) & (~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & $greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))))) <=> ($greatereq(A!12, 0) & $greatereq(Tmp!14, 0) & ($sum(A!12, $product(-1, Tmp!14)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp!14)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I))))) & (~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & $greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))))),
% 15.37/10.09 inference(rewrite,[status(thm)],[])).
% 15.37/10.09 tff(6,plain,
% 15.37/10.09 ((($greatereq(Tmp!14, 0) & ($sum(A!12, $product(-1, Tmp!14)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp!14)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I)))))) & ((~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & $greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))))) <=> ($greatereq(Tmp!14, 0) & ($sum(A!12, $product(-1, Tmp!14)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp!14)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I))))) & (~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & $greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))))),
% 15.37/10.09 inference(rewrite,[status(thm)],[])).
% 15.37/10.09 tff(7,plain,
% 15.37/10.09 (((~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & ($greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))))) <=> ((~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & $greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))))),
% 15.37/10.09 inference(rewrite,[status(thm)],[])).
% 15.37/10.09 tff(8,plain,
% 15.37/10.09 (($greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(Len!16, K), 0) & (~$greatereq($sum($product(Len!16, K), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K), min(A!12, $sum(Len!16, $product(Len!16, K)))))) <=> ($greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))))),
% 15.37/10.09 inference(rewrite,[status(thm)],[])).
% 15.37/10.09 tff(9,plain,
% 15.37/10.09 ((~$greatereq($sum(Len!16, $product(-1, A!12)), 0)) <=> (~$lesseq($sum(A!12, $product(-1, Len!16)), 0))),
% 15.37/10.09 inference(rewrite,[status(thm)],[])).
% 15.37/10.09 tff(10,plain,
% 15.37/10.09 ((~((~($greatereq($product(Len!16, K!17), 0) & (~$greatereq($sum($product(Len!16, K!17), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) <=> (~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17))))))),
% 15.37/10.09 inference(rewrite,[status(thm)],[])).
% 15.37/10.09 tff(11,plain,
% 15.37/10.09 (((~((~($greatereq($product(Len!16, K!17), 0) & (~$greatereq($sum($product(Len!16, K!17), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$greatereq($sum(Len!16, $product(-1, A!12)), 0)) & ($greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(Len!16, K), 0) & (~$greatereq($sum($product(Len!16, K), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K), min(A!12, $sum(Len!16, $product(Len!16, K))))))) <=> ((~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & ($greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))))))),
% 15.37/10.09 inference(monotonicity,[status(thm)],[10, 9, 8])).
% 15.37/10.09 tff(12,plain,
% 15.37/10.09 (((~((~($greatereq($product(Len!16, K!17), 0) & (~$greatereq($sum($product(Len!16, K!17), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$greatereq($sum(Len!16, $product(-1, A!12)), 0)) & ($greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(Len!16, K), 0) & (~$greatereq($sum($product(Len!16, K), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K), min(A!12, $sum(Len!16, $product(Len!16, K))))))) <=> ((~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & $greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))))),
% 15.37/10.09 inference(transitivity,[status(thm)],[11, 7])).
% 15.37/10.09 tff(13,plain,
% 15.37/10.09 (($greatereq(Tmp!14, 0) & ($sum(Tmp!14, $product(-1, A!12)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp!14, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I)))))) <=> ($greatereq(Tmp!14, 0) & ($sum(A!12, $product(-1, Tmp!14)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp!14)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I))))))),
% 15.37/10.09 inference(rewrite,[status(thm)],[])).
% 15.37/10.09 tff(14,plain,
% 15.37/10.09 ((($greatereq(Tmp!14, 0) & ($sum(Tmp!14, $product(-1, A!12)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp!14, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I)))))) & ((~((~($greatereq($product(Len!16, K!17), 0) & (~$greatereq($sum($product(Len!16, K!17), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$greatereq($sum(Len!16, $product(-1, A!12)), 0)) & ($greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(Len!16, K), 0) & (~$greatereq($sum($product(Len!16, K), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K), min(A!12, $sum(Len!16, $product(Len!16, K)))))))) <=> (($greatereq(Tmp!14, 0) & ($sum(A!12, $product(-1, Tmp!14)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp!14)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I)))))) & ((~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & $greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))))))),
% 15.37/10.09 inference(monotonicity,[status(thm)],[13, 12])).
% 15.37/10.09 tff(15,plain,
% 15.37/10.09 ((($greatereq(Tmp!14, 0) & ($sum(Tmp!14, $product(-1, A!12)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp!14, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I)))))) & ((~((~($greatereq($product(Len!16, K!17), 0) & (~$greatereq($sum($product(Len!16, K!17), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$greatereq($sum(Len!16, $product(-1, A!12)), 0)) & ($greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(Len!16, K), 0) & (~$greatereq($sum($product(Len!16, K), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K), min(A!12, $sum(Len!16, $product(Len!16, K)))))))) <=> ($greatereq(Tmp!14, 0) & ($sum(A!12, $product(-1, Tmp!14)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp!14)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I))))) & (~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & $greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))))),
% 15.37/10.09 inference(transitivity,[status(thm)],[14, 6])).
% 15.37/10.09 tff(16,plain,
% 15.37/10.09 ((~(~$greatereq(A!12, 0))) <=> $greatereq(A!12, 0)),
% 15.37/10.09 inference(rewrite,[status(thm)],[])).
% 15.37/10.09 tff(17,plain,
% 15.37/10.09 (((~(~$greatereq(A!12, 0))) & (($greatereq(Tmp!14, 0) & ($sum(Tmp!14, $product(-1, A!12)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp!14, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I)))))) & ((~((~($greatereq($product(Len!16, K!17), 0) & (~$greatereq($sum($product(Len!16, K!17), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$greatereq($sum(Len!16, $product(-1, A!12)), 0)) & ($greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(Len!16, K), 0) & (~$greatereq($sum($product(Len!16, K), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K), min(A!12, $sum(Len!16, $product(Len!16, K))))))))) <=> ($greatereq(A!12, 0) & ($greatereq(Tmp!14, 0) & ($sum(A!12, $product(-1, Tmp!14)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp!14)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I))))) & (~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & $greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))))))),
% 15.37/10.10 inference(monotonicity,[status(thm)],[16, 15])).
% 15.37/10.10 tff(18,plain,
% 15.37/10.10 (((~(~$greatereq(A!12, 0))) & (($greatereq(Tmp!14, 0) & ($sum(Tmp!14, $product(-1, A!12)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp!14, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I)))))) & ((~((~($greatereq($product(Len!16, K!17), 0) & (~$greatereq($sum($product(Len!16, K!17), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$greatereq($sum(Len!16, $product(-1, A!12)), 0)) & ($greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(Len!16, K), 0) & (~$greatereq($sum($product(Len!16, K), $product(-1, A!12)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K), min(A!12, $sum(Len!16, $product(Len!16, K))))))))) <=> ($greatereq(A!12, 0) & $greatereq(Tmp!14, 0) & ($sum(A!12, $product(-1, Tmp!14)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp!14)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I))))) & (~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & $greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16))))))),
% 15.37/10.10 inference(transitivity,[status(thm)],[17, 5])).
% 15.37/10.10 tff(19,plain,
% 15.37/10.10 ((~![A: $int, A1: map_int_elt2] : ((~$greatereq(A, 0)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($greatereq(Tmp, 0) & ($sum(Tmp, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K))))) | $greatereq($sum(Len, $product(-1, A)), 0) | (~($greatereq(Len, 1) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K))))))))))) <=> (~![A: $int, A1: map_int_elt2] : ((~$greatereq(A, 0)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($greatereq(Tmp, 0) & ($sum(Tmp, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K))))) | $greatereq($sum(Len, $product(-1, A)), 0) | (~($greatereq(Len, 1) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K)))))))))))),
% 15.37/10.10 inference(rewrite,[status(thm)],[])).
% 15.37/10.10 tff(20,plain,
% 15.37/10.10 ((~![A: $int, A1: map_int_elt2] : ((~$greatereq(A, 0)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($greatereq(Tmp, 0) & ($sum(Tmp, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : ($lesseq($sum(A, $product(-1, Len)), 0) | ![K: $int] : ((~($greatereq($product(K, Len), 0) & (~$lesseq($sum(A, $product(-1, $product(K, Len))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))) | (~($greatereq(Len, 1) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($greatereq($product(K, Len), 0) & (~$lesseq($sum(A, $product(-1, $product(K, Len))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))))))))) <=> (~![A: $int, A1: map_int_elt2] : ((~$greatereq(A, 0)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($greatereq(Tmp, 0) & ($sum(Tmp, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K))))) | $greatereq($sum(Len, $product(-1, A)), 0) | (~($greatereq(Len, 1) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K)))))))))))),
% 15.37/10.10 inference(rewrite,[status(thm)],[])).
% 15.37/10.10 tff(21,plain,
% 15.37/10.10 ((~![A: $int, A1: map_int_elt2] : ((~$lesseq(0, A)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($lesseq(0, Tmp) & (Tmp = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))) | $lesseq(A, Len) | (~($lesseq(1, Len) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))))))))) <=> (~![A: $int, A1: map_int_elt2] : ((~$greatereq(A, 0)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($greatereq(Tmp, 0) & ($sum(Tmp, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : ($lesseq($sum(A, $product(-1, Len)), 0) | ![K: $int] : ((~($greatereq($product(K, Len), 0) & (~$lesseq($sum(A, $product(-1, $product(K, Len))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))) | (~($greatereq(Len, 1) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($greatereq($product(K, Len), 0) & (~$lesseq($sum(A, $product(-1, $product(K, Len))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len))))))))))),
% 15.37/10.10 inference(rewrite,[status(thm)],[])).
% 15.37/10.10 tff(22,plain,
% 15.37/10.10 ((~![A: $int, A1: map_int_elt2] : ((~$lesseq(0, A)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($lesseq(0, Tmp) & (Tmp = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))) | $lesseq(A, Len) | (~($lesseq(1, Len) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))))))))) <=> (~![A: $int, A1: map_int_elt2] : ((~$lesseq(0, A)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($lesseq(0, Tmp) & (Tmp = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))) | $lesseq(A, Len) | (~($lesseq(1, Len) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len))))))))))),
% 15.37/10.10 inference(rewrite,[status(thm)],[])).
% 15.37/10.10 tff(23,plain,
% 15.37/10.10 ((~![A: $int, A1: map_int_elt2] : ($lesseq(0, A) => ![Tmp: $int, Tmp1: map_int_elt2] : ((($lesseq(0, Tmp) & (Tmp = A)) & ![I: $int] : (($lesseq(0, I) & $less(I, Tmp)) => (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I)))))) => ![Len: $int, A2: map_int_elt2] : ((($lesseq(1, Len) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2)))) & ![K: $int] : (($lesseq(0, $product(K, Len)) & $less($product(K, Len), A)) => sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len))))) => ($less(Len, A) => ![K: $int] : (($lesseq(0, $product(K, Len)) & $less($product(K, Len), A)) => sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len))))))))) <=> (~![A: $int, A1: map_int_elt2] : ((~$lesseq(0, A)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($lesseq(0, Tmp) & (Tmp = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))) | $lesseq(A, Len) | (~($lesseq(1, Len) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len))))))))))),
% 15.37/10.10 inference(rewrite,[status(thm)],[])).
% 15.37/10.10 tff(24,axiom,(~![A: $int, A1: map_int_elt2] : ($lesseq(0, A) => ![Tmp: $int, Tmp1: map_int_elt2] : ((($lesseq(0, Tmp) & (Tmp = A)) & ![I: $int] : (($lesseq(0, I) & $less(I, Tmp)) => (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I)))))) => ![Len: $int, A2: map_int_elt2] : ((($lesseq(1, Len) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2)))) & ![K: $int] : (($lesseq(0, $product(K, Len)) & $less($product(K, Len), A)) => sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len))))) => ($less(Len, A) => ![K: $int] : (($lesseq(0, $product(K, Len)) & $less($product(K, Len), A)) => sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_bottom_up_mergesort')).
% 15.37/10.10 tff(25,plain,
% 15.37/10.10 (~![A: $int, A1: map_int_elt2] : ((~$lesseq(0, A)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($lesseq(0, Tmp) & (Tmp = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))) | $lesseq(A, Len) | (~($lesseq(1, Len) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))))))))),
% 15.37/10.10 inference(modus_ponens,[status(thm)],[24, 23])).
% 15.37/10.10 tff(26,plain,
% 15.37/10.10 (~![A: $int, A1: map_int_elt2] : ((~$lesseq(0, A)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($lesseq(0, Tmp) & (Tmp = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))) | $lesseq(A, Len) | (~($lesseq(1, Len) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))))))))),
% 15.37/10.10 inference(modus_ponens,[status(thm)],[25, 22])).
% 15.37/10.10 tff(27,plain,
% 15.37/10.10 (~![A: $int, A1: map_int_elt2] : ((~$lesseq(0, A)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($lesseq(0, Tmp) & (Tmp = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))) | $lesseq(A, Len) | (~($lesseq(1, Len) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))))))))),
% 15.37/10.10 inference(modus_ponens,[status(thm)],[26, 22])).
% 15.37/10.10 tff(28,plain,
% 15.37/10.10 (~![A: $int, A1: map_int_elt2] : ((~$lesseq(0, A)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($lesseq(0, Tmp) & (Tmp = A) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))) | $lesseq(A, Len) | (~($lesseq(1, Len) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($lesseq(0, $product(K, Len)) & (~$lesseq(A, $product(K, Len))))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))))))))),
% 15.37/10.10 inference(modus_ponens,[status(thm)],[27, 22])).
% 15.37/10.10 tff(29,plain,
% 15.37/10.10 (~![A: $int, A1: map_int_elt2] : ((~$greatereq(A, 0)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($greatereq(Tmp, 0) & ($sum(Tmp, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : ($lesseq($sum(A, $product(-1, Len)), 0) | ![K: $int] : ((~($greatereq($product(K, Len), 0) & (~$lesseq($sum(A, $product(-1, $product(K, Len))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))) | (~($greatereq(Len, 1) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($greatereq($product(K, Len), 0) & (~$lesseq($sum(A, $product(-1, $product(K, Len))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(K, Len), min(A, $sum($product(K, Len), Len)))))))))),
% 15.37/10.10 inference(modus_ponens,[status(thm)],[28, 21])).
% 15.37/10.10 tff(30,plain,
% 15.37/10.10 (~![A: $int, A1: map_int_elt2] : ((~$greatereq(A, 0)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($greatereq(Tmp, 0) & ($sum(Tmp, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K))))) | $greatereq($sum(Len, $product(-1, A)), 0) | (~($greatereq(Len, 1) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K))))))))))),
% 15.37/10.10 inference(modus_ponens,[status(thm)],[29, 20])).
% 15.37/10.10 tff(31,plain,
% 15.37/10.10 (~![A: $int, A1: map_int_elt2] : ((~$greatereq(A, 0)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($greatereq(Tmp, 0) & ($sum(Tmp, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K))))) | $greatereq($sum(Len, $product(-1, A)), 0) | (~($greatereq(Len, 1) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K))))))))))),
% 15.37/10.10 inference(modus_ponens,[status(thm)],[30, 19])).
% 15.37/10.10 tff(32,plain,
% 15.37/10.10 (~![A: $int, A1: map_int_elt2] : ((~$greatereq(A, 0)) | ![Tmp: $int, Tmp1: map_int_elt2] : ((~($greatereq(Tmp, 0) & ($sum(Tmp, $product(-1, A)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1), t2tb(I))))))) | ![Len: $int, A2: map_int_elt2] : (![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K))))) | $greatereq($sum(Len, $product(-1, A)), 0) | (~($greatereq(Len, 1) & permut_all(elt5, mk_array1(elt5, A, t2tb9(A1)), mk_array1(elt5, A, t2tb9(A2))) & ![K: $int] : ((~($greatereq($product(Len, K), 0) & (~$greatereq($sum($product(Len, K), $product(-1, A)), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A, t2tb9(A2))), $product(Len, K), min(A, $sum(Len, $product(Len, K))))))))))),
% 15.37/10.10 inference(modus_ponens,[status(thm)],[31, 19])).
% 15.37/10.10 tff(33,plain,
% 15.37/10.10 ($greatereq(A!12, 0) & $greatereq(Tmp!14, 0) & ($sum(A!12, $product(-1, Tmp!14)) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp!14)), 0)))) | (tb2t7(get(elt5, int, t2tb9(Tmp1!13), t2tb(I))) = tb2t7(get(elt5, int, t2tb9(A1!11), t2tb(I))))) & (~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))) & (~$lesseq($sum(A!12, $product(-1, Len!16)), 0)) & $greatereq(Len!16, 1) & permut_all(elt5, mk_array1(elt5, A!12, t2tb9(A1!11)), mk_array1(elt5, A!12, t2tb9(A2!15))) & ![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))))),
% 15.37/10.10 inference(modus_ponens,[status(thm)],[32, 18])).
% 15.37/10.10 tff(34,plain,
% 15.37/10.10 (![K: $int] : ((~($greatereq($product(K, Len!16), 0) & (~$lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))))),
% 15.37/10.10 inference(and_elim,[status(thm)],[33])).
% 15.37/10.10 tff(35,plain,
% 15.37/10.10 (![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))),
% 15.37/10.10 inference(modus_ponens,[status(thm)],[34, 4])).
% 15.37/10.10 tff(36,plain,
% 15.37/10.10 (![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))),
% 15.37/10.10 inference(modus_ponens,[status(thm)],[35, 2])).
% 15.37/10.10 tff(37,plain,
% 15.37/10.10 (~((~($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))))),
% 15.37/10.10 inference(and_elim,[status(thm)],[33])).
% 15.37/10.10 tff(38,plain,
% 15.37/10.10 (~sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17))))),
% 15.37/10.10 inference(or_elim,[status(thm)],[37])).
% 15.37/10.10 tff(39,plain,
% 15.37/10.10 ($greatereq($product(Len!16, K!17), 0) & (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0))),
% 15.37/10.10 inference(or_elim,[status(thm)],[37])).
% 15.37/10.10 tff(40,plain,
% 15.37/10.10 (~$lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)),
% 15.37/10.10 inference(and_elim,[status(thm)],[39])).
% 15.37/10.10 tff(41,plain,
% 15.37/10.10 ($greatereq($product(Len!16, K!17), 0)),
% 15.37/10.10 inference(and_elim,[status(thm)],[39])).
% 15.37/10.10 tff(42,plain,
% 15.37/10.10 (((~![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))) | (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))) | $lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0) | (~$greatereq($product(Len!16, K!17), 0)))) <=> ((~![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))) | $lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0) | (~$greatereq($product(Len!16, K!17), 0)))),
% 15.37/10.10 inference(rewrite,[status(thm)],[])).
% 15.37/10.10 tff(43,plain,
% 15.37/10.10 ((sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))) | $lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0) | (~$greatereq($product(Len!16, K!17), 0))) <=> (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))) | $lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0) | (~$greatereq($product(Len!16, K!17), 0)))),
% 15.37/10.10 inference(rewrite,[status(thm)],[])).
% 15.37/10.10 tff(44,plain,
% 15.37/10.10 ((~$greatereq($product(K!17, Len!16), 0)) <=> (~$greatereq($product(Len!16, K!17), 0))),
% 15.37/10.10 inference(rewrite,[status(thm)],[])).
% 15.37/10.10 tff(45,plain,
% 15.37/10.10 ($lesseq($sum(A!12, $product(-1, $product(K!17, Len!16))), 0) <=> $lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0)),
% 15.37/10.10 inference(rewrite,[status(thm)],[])).
% 15.37/10.10 tff(46,plain,
% 15.37/10.10 (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K!17, Len!16), min(A!12, $sum(Len!16, $product(K!17, Len!16)))) <=> sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17))))),
% 15.37/10.10 inference(rewrite,[status(thm)],[])).
% 15.37/10.10 tff(47,plain,
% 15.37/10.10 ((sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K!17, Len!16), min(A!12, $sum(Len!16, $product(K!17, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K!17, Len!16))), 0) | (~$greatereq($product(K!17, Len!16), 0))) <=> (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))) | $lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0) | (~$greatereq($product(Len!16, K!17), 0)))),
% 15.37/10.10 inference(monotonicity,[status(thm)],[46, 45, 44])).
% 15.37/10.10 tff(48,plain,
% 15.37/10.10 ((sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K!17, Len!16), min(A!12, $sum(Len!16, $product(K!17, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K!17, Len!16))), 0) | (~$greatereq($product(K!17, Len!16), 0))) <=> (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))) | $lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0) | (~$greatereq($product(Len!16, K!17), 0)))),
% 15.37/10.10 inference(transitivity,[status(thm)],[47, 43])).
% 15.37/10.10 tff(49,plain,
% 15.37/10.10 (((~![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))) | (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K!17, Len!16), min(A!12, $sum(Len!16, $product(K!17, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K!17, Len!16))), 0) | (~$greatereq($product(K!17, Len!16), 0)))) <=> ((~![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))) | (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))) | $lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0) | (~$greatereq($product(Len!16, K!17), 0))))),
% 15.37/10.10 inference(monotonicity,[status(thm)],[48])).
% 15.37/10.10 tff(50,plain,
% 15.37/10.10 (((~![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))) | (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K!17, Len!16), min(A!12, $sum(Len!16, $product(K!17, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K!17, Len!16))), 0) | (~$greatereq($product(K!17, Len!16), 0)))) <=> ((~![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))) | $lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0) | (~$greatereq($product(Len!16, K!17), 0)))),
% 15.37/10.10 inference(transitivity,[status(thm)],[49, 42])).
% 15.37/10.10 tff(51,plain,
% 15.37/10.10 ((~![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))) | (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K!17, Len!16), min(A!12, $sum(Len!16, $product(K!17, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K!17, Len!16))), 0) | (~$greatereq($product(K!17, Len!16), 0)))),
% 15.37/10.11 inference(quant_inst,[status(thm)],[])).
% 15.37/10.11 tff(52,plain,
% 15.37/10.11 ((~![K: $int] : (sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(K, Len!16), min(A!12, $sum(Len!16, $product(K, Len!16)))) | $lesseq($sum(A!12, $product(-1, $product(K, Len!16))), 0) | (~$greatereq($product(K, Len!16), 0)))) | sorted_sub3(tb2t8(mk_array1(elt5, A!12, t2tb9(A2!15))), $product(Len!16, K!17), min(A!12, $sum(Len!16, $product(Len!16, K!17)))) | $lesseq($sum(A!12, $product(-1, $product(Len!16, K!17))), 0) | (~$greatereq($product(Len!16, K!17), 0))),
% 15.37/10.11 inference(modus_ponens,[status(thm)],[51, 50])).
% 15.37/10.11 tff(53,plain,
% 15.37/10.11 ($false),
% 15.37/10.11 inference(unit_resolution,[status(thm)],[52, 41, 40, 38, 36])).
% 15.37/10.11 % SZS output end Proof
%------------------------------------------------------------------------------