TSTP Solution File: SWW574_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW574_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 20:59:19 EDT 2022
% Result : Theorem 0.86s 0.78s
% Output : Proof 1.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW574_2 : TPTP v8.1.0. Released v6.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.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 20:04:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.86/0.78 % SZS status Theorem
% 0.86/0.78 % SZS output start Proof
% 0.86/0.78 tff(tb2t1_type, type, (
% 0.86/0.78 tb2t1: uni > $int)).
% 0.86/0.78 tff(get4_type, type, (
% 0.86/0.78 get4: ( ty * uni * $int ) > uni)).
% 0.86/0.78 tff(tptp_fun_K_16_type, type, (
% 0.86/0.78 tptp_fun_K_16: ( $int * $int * $int * array_int ) > $int)).
% 0.86/0.78 tff(mk_array3_type, type, (
% 0.86/0.78 mk_array3: ( $int * map_int_int ) > array_int)).
% 0.86/0.78 tff(tptp_fun_A4_25_type, type, (
% 0.86/0.78 tptp_fun_A4_25: map_int_int)).
% 0.86/0.78 tff(tptp_fun_A_20_type, type, (
% 0.86/0.78 tptp_fun_A_20: $int)).
% 0.86/0.78 tff(tptp_fun_N_17_type, type, (
% 0.86/0.78 tptp_fun_N_17: $int)).
% 0.86/0.78 tff(tptp_fun_I_22_type, type, (
% 0.86/0.78 tptp_fun_I_22: $int)).
% 0.86/0.78 tff(t2tb2_type, type, (
% 0.86/0.78 t2tb2: array_int > uni)).
% 0.86/0.78 tff(int_type, type, (
% 0.86/0.78 int: ty)).
% 0.86/0.78 tff(tptp_fun_K_14_type, type, (
% 0.86/0.78 tptp_fun_K_14: ( $int * $int * $int * array_int ) > $int)).
% 0.86/0.78 tff(tptp_fun_M_18_type, type, (
% 0.86/0.78 tptp_fun_M_18: $int)).
% 0.86/0.78 tff(tptp_fun_J_23_type, type, (
% 0.86/0.78 tptp_fun_J_23: $int)).
% 0.86/0.78 tff(t2tb1_type, type, (
% 0.86/0.78 t2tb1: $int > uni)).
% 0.86/0.78 tff(tptp_fun_A3_24_type, type, (
% 0.86/0.78 tptp_fun_A3_24: map_int_int)).
% 0.86/0.78 tff(mk_array2_type, type, (
% 0.86/0.78 mk_array2: ( ty * $int * uni ) > uni)).
% 0.86/0.78 tff(elts_type, type, (
% 0.86/0.78 elts: ( ty * uni ) > uni)).
% 0.86/0.78 tff(length1_type, type, (
% 0.86/0.78 length1: ( ty * uni ) > $int)).
% 0.86/0.78 tff(get_type, type, (
% 0.86/0.78 get: ( ty * ty * uni * uni ) > uni)).
% 0.86/0.78 tff(get3_type, type, (
% 0.86/0.78 get3: ( map_int_int * $int ) > $int)).
% 0.86/0.78 tff(tptp_fun_A2_21_type, type, (
% 0.86/0.78 tptp_fun_A2_21: map_int_int)).
% 0.86/0.78 tff(permut_sub3_type, type, (
% 0.86/0.78 permut_sub3: ( array_int * array_int * $int * $int ) > $o)).
% 0.86/0.78 tff(tptp_fun_A1_19_type, type, (
% 0.86/0.78 tptp_fun_A1_19: map_int_int)).
% 0.86/0.78 tff(sorted_sub2_type, type, (
% 0.86/0.78 sorted_sub2: ( map_int_int * $int * $int ) > $o)).
% 0.86/0.78 tff(qs_partition1_type, type, (
% 0.86/0.78 qs_partition1: ( array_int * array_int * $int * $int * $int * $int * $int ) > $o)).
% 0.86/0.78 tff(map_eq_sub1_type, type, (
% 0.86/0.78 map_eq_sub1: ( ty * uni * uni * $int * $int ) > $o)).
% 0.86/0.78 tff(tptp_fun_I_9_type, type, (
% 0.86/0.78 tptp_fun_I_9: ( $int * $int * uni * uni * ty ) > $int)).
% 0.86/0.78 tff(permut3_type, type, (
% 0.86/0.78 permut3: ( ty * uni * uni * $int * $int ) > $o)).
% 0.86/0.78 tff(tptp_fun_J_8_type, type, (
% 0.86/0.78 tptp_fun_J_8: ( $int * $int * $int * uni * uni * ty ) > $int)).
% 0.86/0.78 tff(permut2_type, type, (
% 0.86/0.78 permut2: ( ty * uni * uni * $int * $int ) > $o)).
% 0.86/0.78 tff(tb2t_type, type, (
% 0.86/0.78 tb2t: uni > map_int_int)).
% 0.86/0.78 tff(tptp_fun_K_15_type, type, (
% 0.86/0.78 tptp_fun_K_15: ( $int * $int * $int * array_int ) > $int)).
% 0.86/0.78 tff(1,plain,
% 0.86/0.78 (^[A: ty, U: uni] : refl((U = mk_array2(A, length1(A, U), elts(A, U))) <=> (U = mk_array2(A, length1(A, U), elts(A, U))))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(2,plain,
% 0.86/0.78 (![A: ty, U: uni] : (U = mk_array2(A, length1(A, U), elts(A, U))) <=> ![A: ty, U: uni] : (U = mk_array2(A, length1(A, U), elts(A, U)))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[1])).
% 0.86/0.78 tff(3,plain,
% 0.86/0.78 (![A: ty, U: uni] : (U = mk_array2(A, length1(A, U), elts(A, U))) <=> ![A: ty, U: uni] : (U = mk_array2(A, length1(A, U), elts(A, U)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(4,axiom,(![A: ty, U: uni] : (U = mk_array2(A, length1(A, U), elts(A, U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','array_inversion3')).
% 0.86/0.78 tff(5,plain,
% 0.86/0.78 (![A: ty, U: uni] : (U = mk_array2(A, length1(A, U), elts(A, U)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.86/0.78 tff(6,plain,(
% 0.86/0.78 ![A: ty, U: uni] : (U = mk_array2(A, length1(A, U), elts(A, U)))),
% 0.86/0.78 inference(skolemize,[status(sab)],[5])).
% 0.86/0.78 tff(7,plain,
% 0.86/0.78 (![A: ty, U: uni] : (U = mk_array2(A, length1(A, U), elts(A, U)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.86/0.78 tff(8,plain,
% 0.86/0.78 ((~![A: ty, U: uni] : (U = mk_array2(A, length1(A, U), elts(A, U)))) | (t2tb2(mk_array3(A!20, A4!25)) = mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))))),
% 0.86/0.78 inference(quant_inst,[status(thm)],[])).
% 0.86/0.78 tff(9,plain,
% 0.86/0.78 (t2tb2(mk_array3(A!20, A4!25)) = mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))),
% 0.86/0.78 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.86/0.78 tff(10,plain,
% 0.86/0.78 (mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))) = t2tb2(mk_array3(A!20, A4!25))),
% 0.86/0.78 inference(symmetry,[status(thm)],[9])).
% 0.86/0.78 tff(11,plain,
% 0.86/0.78 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))) = get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))),
% 0.86/0.78 inference(monotonicity,[status(thm)],[10])).
% 0.86/0.78 tff(12,plain,
% 0.86/0.78 (^[A: ty, A1: uni, I: $int] : refl((get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I))) <=> (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I))))),
% 0.86/0.78 inference(bind,[status(th)],[])).
% 0.86/0.78 tff(13,plain,
% 0.86/0.78 (![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I))) <=> ![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))),
% 0.86/0.78 inference(quant_intro,[status(thm)],[12])).
% 0.86/0.78 tff(14,plain,
% 0.86/0.78 (![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I))) <=> ![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(15,axiom,(![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','get_def1')).
% 0.86/0.78 tff(16,plain,
% 0.86/0.78 (![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.86/0.78 tff(17,plain,(
% 0.86/0.78 ![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))),
% 0.86/0.78 inference(skolemize,[status(sab)],[16])).
% 0.86/0.78 tff(18,plain,
% 0.86/0.78 (![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.86/0.78 tff(19,plain,
% 0.86/0.78 ((~![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))) | (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))),
% 0.86/0.78 inference(quant_inst,[status(thm)],[])).
% 0.86/0.78 tff(20,plain,
% 0.86/0.78 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))),
% 0.86/0.78 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.86/0.78 tff(21,plain,
% 0.86/0.78 (get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))) = get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))),
% 0.86/0.78 inference(symmetry,[status(thm)],[20])).
% 0.86/0.78 tff(22,plain,
% 0.86/0.78 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(23,plain,
% 0.86/0.78 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(24,axiom,(![J: uni] : (t2tb1(tb2t1(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR1')).
% 0.86/0.78 tff(25,plain,
% 0.86/0.78 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.86/0.78 tff(26,plain,(
% 0.86/0.78 ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.86/0.78 inference(skolemize,[status(sab)],[25])).
% 0.86/0.78 tff(27,plain,
% 0.86/0.78 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.86/0.78 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.86/0.78 tff(28,plain,
% 0.86/0.78 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))) = t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))),
% 0.86/0.78 inference(quant_inst,[status(thm)],[])).
% 0.86/0.78 tff(29,plain,
% 0.86/0.78 (t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))) = t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))),
% 0.86/0.78 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.86/0.78 tff(30,plain,
% 0.86/0.78 (elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))) = elts(int, t2tb2(mk_array3(A!20, A4!25)))),
% 0.86/0.78 inference(monotonicity,[status(thm)],[10])).
% 0.86/0.78 tff(31,plain,
% 0.86/0.78 (elts(int, t2tb2(mk_array3(A!20, A4!25))) = elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))))),
% 0.86/0.78 inference(symmetry,[status(thm)],[30])).
% 0.86/0.78 tff(32,plain,
% 0.86/0.78 (get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))),
% 0.86/0.78 inference(monotonicity,[status(thm)],[31, 29])).
% 0.86/0.78 tff(33,assumption,(~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))), introduced(assumption)).
% 0.86/0.78 tff(34,plain,
% 0.86/0.78 (((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42)) | $lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)),
% 0.86/0.78 inference(tautology,[status(thm)],[])).
% 0.86/0.78 tff(35,plain,
% 0.86/0.78 ($lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)),
% 0.86/0.78 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.86/0.78 tff(36,plain,
% 0.86/0.78 (((~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & ($greatereq(M!18, 0) & (~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0))) & ((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & $greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & $greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)) & $greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, J!23)), 0)) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$greatereq($sum(R, $product(-1, I!22)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!22)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42))) & ($greatereq(A!20, 0) & $greatereq(M!18, 0) & $greatereq($sum(N!17, $product(-1, M!18)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)))) <=> ((~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & $greatereq(M!18, 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)) & (~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & $greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & $greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, J!23)), 0)) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$greatereq($sum(R, $product(-1, I!22)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!22)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42)) & $greatereq($sum(N!17, $product(-1, M!18)), 0))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(37,plain,
% 0.86/0.78 ((~(~($greatereq(A!20, 0) & $greatereq(M!18, 0) & $greatereq($sum(N!17, $product(-1, M!18)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0))))) <=> ($greatereq(A!20, 0) & $greatereq(M!18, 0) & $greatereq($sum(N!17, $product(-1, M!18)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(38,plain,
% 0.86/0.78 ((~($greatereq(A!20, 0) & $greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0)))) <=> (~($greatereq(A!20, 0) & $greatereq(M!18, 0) & $greatereq($sum(N!17, $product(-1, M!18)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0))))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(39,plain,
% 0.86/0.78 ((~(~($greatereq(A!20, 0) & $greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) <=> (~(~($greatereq(A!20, 0) & $greatereq(M!18, 0) & $greatereq($sum(N!17, $product(-1, M!18)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)))))),
% 0.86/0.78 inference(monotonicity,[status(thm)],[38])).
% 0.86/0.78 tff(40,plain,
% 0.86/0.78 ((~(~($greatereq(A!20, 0) & $greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) <=> ($greatereq(A!20, 0) & $greatereq(M!18, 0) & $greatereq($sum(N!17, $product(-1, M!18)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)))),
% 0.86/0.78 inference(transitivity,[status(thm)],[39, 37])).
% 0.86/0.78 tff(41,plain,
% 0.86/0.78 ((((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & $greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & $greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23))) & ($greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0))) & ($greatereq(A!20, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(I!22, $product(-1, J!23)), 0)) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$greatereq($sum(R, $product(-1, I!22)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!22)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42)))) <=> ((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & $greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & $greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)) & $greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, J!23)), 0)) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$greatereq($sum(R, $product(-1, I!22)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!22)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(42,plain,
% 0.86/0.78 (($greatereq(A!20, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, I!22)), 0)) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, R)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I!22, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42))) <=> ($greatereq(A!20, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(I!22, $product(-1, J!23)), 0)) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$greatereq($sum(R, $product(-1, I!22)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!22)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(43,plain,
% 0.86/0.78 ((~(~($greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0))))) <=> ($greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0)))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(44,plain,
% 0.86/0.78 ((~($greatereq(M!18, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, A!20)), 0)))) <=> (~($greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0))))),
% 0.86/0.78 inference(rewrite,[status(thm)],[])).
% 0.86/0.78 tff(45,plain,
% 0.86/0.78 ((~(~($greatereq(M!18, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, A!20)), 0))))) <=> (~(~($greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0)))))),
% 0.86/0.78 inference(monotonicity,[status(thm)],[44])).
% 0.86/0.78 tff(46,plain,
% 0.86/0.78 ((~(~($greatereq(M!18, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, A!20)), 0))))) <=> ($greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0)))),
% 0.86/0.78 inference(transitivity,[status(thm)],[45, 43])).
% 0.86/0.78 tff(47,plain,
% 0.86/0.78 (((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & ($greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0))) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & ($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)))) <=> ((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & $greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & $greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(48,plain,
% 0.86/0.79 ((~(~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23))))) <=> ($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(49,plain,
% 0.86/0.79 ((~(~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42))) <=> qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(50,plain,
% 0.86/0.79 ((~(~($greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0))))) <=> ($greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(51,plain,
% 0.86/0.79 ((~($greatereq(I!22, 0) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0)))) <=> (~($greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0))))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(52,plain,
% 0.86/0.79 ((~(~($greatereq(I!22, 0) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) <=> (~(~($greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)))))),
% 0.86/0.79 inference(monotonicity,[status(thm)],[51])).
% 0.86/0.79 tff(53,plain,
% 0.86/0.79 ((~(~($greatereq(I!22, 0) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) <=> ($greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)))),
% 0.86/0.79 inference(transitivity,[status(thm)],[52, 50])).
% 0.86/0.79 tff(54,plain,
% 0.86/0.79 (((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(I!22, 0) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) & (~(~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)))))) <=> ((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & ($greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0))) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & ($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23))))),
% 0.86/0.79 inference(monotonicity,[status(thm)],[53, 49, 48])).
% 0.86/0.79 tff(55,plain,
% 0.86/0.79 (((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(I!22, 0) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) & (~(~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)))))) <=> ((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & $greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & $greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)))),
% 0.86/0.79 inference(transitivity,[status(thm)],[54, 47])).
% 0.86/0.79 tff(56,plain,
% 0.86/0.79 ((((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(I!22, 0) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) & (~(~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)))))) & (~(~($greatereq(M!18, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, A!20)), 0))))) & ($greatereq(A!20, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, I!22)), 0)) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, R)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I!22, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42)))) <=> (((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & $greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & $greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23))) & ($greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0))) & ($greatereq(A!20, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(I!22, $product(-1, J!23)), 0)) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$greatereq($sum(R, $product(-1, I!22)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!22)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42))))),
% 0.86/0.79 inference(monotonicity,[status(thm)],[55, 46, 42])).
% 0.86/0.79 tff(57,plain,
% 0.86/0.79 ((((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(I!22, 0) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) & (~(~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)))))) & (~(~($greatereq(M!18, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, A!20)), 0))))) & ($greatereq(A!20, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, I!22)), 0)) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, R)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I!22, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42)))) <=> ((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & $greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & $greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)) & $greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, J!23)), 0)) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$greatereq($sum(R, $product(-1, I!22)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!22)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42)))),
% 0.86/0.79 inference(transitivity,[status(thm)],[56, 41])).
% 0.86/0.79 tff(58,plain,
% 0.86/0.79 ((~(~($greatereq(M!18, 0) & (~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0))))) <=> ($greatereq(M!18, 0) & (~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(59,plain,
% 0.86/0.79 ((~($greatereq(M!18, 0) & (~$greatereq($sum(M!18, $product(-1, N!17)), 0)) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0)))) <=> (~($greatereq(M!18, 0) & (~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0))))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(60,plain,
% 0.86/0.79 ((~(~($greatereq(M!18, 0) & (~$greatereq($sum(M!18, $product(-1, N!17)), 0)) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) <=> (~(~($greatereq(M!18, 0) & (~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)))))),
% 0.86/0.79 inference(monotonicity,[status(thm)],[59])).
% 0.86/0.79 tff(61,plain,
% 0.86/0.79 ((~(~($greatereq(M!18, 0) & (~$greatereq($sum(M!18, $product(-1, N!17)), 0)) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) <=> ($greatereq(M!18, 0) & (~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)))),
% 0.86/0.79 inference(transitivity,[status(thm)],[60, 58])).
% 0.86/0.79 tff(62,plain,
% 0.86/0.79 ((~$greatereq($sum(M!18, $product(-1, N!17)), 0)) <=> (~$lesseq($sum(N!17, $product(-1, M!18)), 0))),
% 0.86/0.79 inference(rewrite,[status(thm)],[])).
% 0.86/0.79 tff(63,plain,
% 0.86/0.79 (((~$greatereq($sum(M!18, $product(-1, N!17)), 0)) & (~(~($greatereq(M!18, 0) & (~$greatereq($sum(M!18, $product(-1, N!17)), 0)) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) & (((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(I!22, 0) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) & (~(~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)))))) & (~(~($greatereq(M!18, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, A!20)), 0))))) & ($greatereq(A!20, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, I!22)), 0)) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, R)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I!22, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42)))) & (~(~($greatereq(A!20, 0) & $greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0)))))) <=> ((~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & ($greatereq(M!18, 0) & (~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0))) & ((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & $greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & $greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)) & $greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, J!23)), 0)) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$greatereq($sum(R, $product(-1, I!22)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!22)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42))) & ($greatereq(A!20, 0) & $greatereq(M!18, 0) & $greatereq($sum(N!17, $product(-1, M!18)), 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0))))),
% 0.86/0.79 inference(monotonicity,[status(thm)],[62, 61, 57, 40])).
% 0.86/0.79 tff(64,plain,
% 0.86/0.79 (((~$greatereq($sum(M!18, $product(-1, N!17)), 0)) & (~(~($greatereq(M!18, 0) & (~$greatereq($sum(M!18, $product(-1, N!17)), 0)) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) & (((~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(I!22, 0) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0))))) & (~(~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42))) & (~(~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)))))) & (~(~($greatereq(M!18, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, A!20)), 0))))) & ($greatereq(A!20, 0) & $greatereq($sum(J!23, $product(-1, M!18)), 0) & (~$greatereq($sum(J!23, $product(-1, I!22)), 0)) & $lesseq($sum(I!22, $product(-1, N!17)), 0) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, R)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I!22, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42)))) & (~(~($greatereq(A!20, 0) & $greatereq(M!18, 0) & $lesseq($sum(M!18, $product(-1, N!17)), 0) & (~$greatereq($sum(N!17, $product(-1, A!20)), 0)))))) <=> ((~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & $greatereq(M!18, 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)) & (~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & $greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & $greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, J!23)), 0)) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$greatereq($sum(R, $product(-1, I!22)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!22)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42)) & $greatereq($sum(N!17, $product(-1, M!18)), 0))),
% 0.86/0.80 inference(transitivity,[status(thm)],[63, 36])).
% 0.86/0.80 tff(65,plain,
% 0.86/0.80 ((~![A: $int, A1: map_int_int, M: $int, N: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : (![A4: map_int_int] : ((~($greatereq(A, 0) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($greatereq(M, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42))))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))))) <=> (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : (![A4: map_int_int] : ((~($greatereq(A, 0) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($greatereq(M, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42))))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0))))))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(66,plain,
% 0.86/0.80 ((~![A: $int, A1: map_int_int, M: $int, N: $int] : ($lesseq($sum(N, $product(-1, M)), 0) | (~($greatereq(M, 0) & (~$lesseq($sum(N, $product(-1, M)), 0)) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, N)), 0) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : (![A4: map_int_int] : ((~($greatereq(A, 0) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J)))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), 0) & (~$lesseq($sum(A, $product(-1, N)), 0))))) | (~($greatereq(M, 0) & $lesseq($sum(M, $product(-1, J)), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(A, 0) & $lesseq($sum(M, $product(-1, J)), 0) & (~$lesseq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42))))))) <=> (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : (![A4: map_int_int] : ((~($greatereq(A, 0) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($greatereq(M, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42))))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0))))))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(67,plain,
% 0.86/0.80 ((~![A: $int, A1: map_int_int, M: $int, N: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ((~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | ![A4: map_int_int] : ((~($lesseq(0, A) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($lesseq(0, I) & $lesseq(I, N) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($lesseq(0, M) & $lesseq(M, J) & (~$lesseq(A, J)))) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, N) & (~$lesseq(A, N)))))) <=> (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($lesseq($sum(N, $product(-1, M)), 0) | (~($greatereq(M, 0) & (~$lesseq($sum(N, $product(-1, M)), 0)) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, N)), 0) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : (![A4: map_int_int] : ((~($greatereq(A, 0) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J)))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), 0) & (~$lesseq($sum(A, $product(-1, N)), 0))))) | (~($greatereq(M, 0) & $lesseq($sum(M, $product(-1, J)), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(A, 0) & $lesseq($sum(M, $product(-1, J)), 0) & (~$lesseq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42)))))))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(68,plain,
% 0.86/0.80 ((~![A: $int, A1: map_int_int, M: $int, N: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ((~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | ![A4: map_int_int] : ((~($lesseq(0, A) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($lesseq(0, I) & $lesseq(I, N) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($lesseq(0, M) & $lesseq(M, J) & (~$lesseq(A, J)))) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, N) & (~$lesseq(A, N)))))) <=> (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ((~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | ![A4: map_int_int] : ((~($lesseq(0, A) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($lesseq(0, I) & $lesseq(I, N) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($lesseq(0, M) & $lesseq(M, J) & (~$lesseq(A, J)))) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, N) & (~$lesseq(A, N))))))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(69,plain,
% 0.86/0.80 ((~![A: $int, A1: map_int_int, M: $int, N: $int] : (((($lesseq(0, A) & $lesseq(0, M)) & $lesseq(M, N)) & $less(N, A)) => ($less(M, N) => ((($lesseq(0, M) & $less(M, N)) & $less(N, A)) => ![J: $int, I: $int, A2: map_int_int] : (((((((($lesseq(0, A) & $lesseq(M, J)) & $less(J, I)) & $lesseq(I, N)) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(N, 1))) & ![R: $int] : (($lesseq(M, R) & $lesseq(R, J)) => $lesseq(get3(A2, R), 42))) & ![R: $int] : (($less(J, R) & $less(R, I)) => (get3(A2, R) = 42))) & ![R: $int] : (($lesseq(I, R) & $lesseq(R, N)) => $lesseq(42, get3(A2, R)))) => ((($lesseq(0, M) & $lesseq(M, J)) & $less(J, A)) => ![A3: map_int_int] : ((($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(J, 1))) & sorted_sub2(A3, M, $sum(J, 1))) => (qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42) => ((($lesseq(0, I) & $lesseq(I, N)) & $less(N, A)) => ![A4: map_int_int] : ((($lesseq(0, A) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(N, 1))) & sorted_sub2(A4, I, $sum(N, 1))) => qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42))))))))))) <=> (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ((~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | ![A4: map_int_int] : ((~($lesseq(0, A) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($lesseq(0, I) & $lesseq(I, N) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($lesseq(0, M) & $lesseq(M, J) & (~$lesseq(A, J)))) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, N) & (~$lesseq(A, N))))))),
% 0.86/0.80 inference(rewrite,[status(thm)],[])).
% 0.86/0.80 tff(70,axiom,(~![A: $int, A1: map_int_int, M: $int, N: $int] : (((($lesseq(0, A) & $lesseq(0, M)) & $lesseq(M, N)) & $less(N, A)) => ($less(M, N) => ((($lesseq(0, M) & $less(M, N)) & $less(N, A)) => ![J: $int, I: $int, A2: map_int_int] : (((((((($lesseq(0, A) & $lesseq(M, J)) & $less(J, I)) & $lesseq(I, N)) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(N, 1))) & ![R: $int] : (($lesseq(M, R) & $lesseq(R, J)) => $lesseq(get3(A2, R), 42))) & ![R: $int] : (($less(J, R) & $less(R, I)) => (get3(A2, R) = 42))) & ![R: $int] : (($lesseq(I, R) & $lesseq(R, N)) => $lesseq(42, get3(A2, R)))) => ((($lesseq(0, M) & $lesseq(M, J)) & $less(J, A)) => ![A3: map_int_int] : ((($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(J, 1))) & sorted_sub2(A3, M, $sum(J, 1))) => (qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42) => ((($lesseq(0, I) & $lesseq(I, N)) & $less(N, A)) => ![A4: map_int_int] : ((($lesseq(0, A) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(N, 1))) & sorted_sub2(A4, I, $sum(N, 1))) => qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_quicksort')).
% 0.86/0.80 tff(71,plain,
% 0.86/0.80 (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ((~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | ![A4: map_int_int] : ((~($lesseq(0, A) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($lesseq(0, I) & $lesseq(I, N) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($lesseq(0, M) & $lesseq(M, J) & (~$lesseq(A, J)))) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, N) & (~$lesseq(A, N)))))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.86/0.80 tff(72,plain,
% 0.86/0.80 (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ((~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | ![A4: map_int_int] : ((~($lesseq(0, A) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($lesseq(0, I) & $lesseq(I, N) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($lesseq(0, M) & $lesseq(M, J) & (~$lesseq(A, J)))) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, N) & (~$lesseq(A, N)))))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[71, 68])).
% 0.86/0.80 tff(73,plain,
% 0.86/0.80 (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ((~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | ![A4: map_int_int] : ((~($lesseq(0, A) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($lesseq(0, I) & $lesseq(I, N) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($lesseq(0, M) & $lesseq(M, J) & (~$lesseq(A, J)))) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, N) & (~$lesseq(A, N)))))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.86/0.80 tff(74,plain,
% 0.86/0.80 (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ((~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | ![A4: map_int_int] : ((~($lesseq(0, A) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($lesseq(0, I) & $lesseq(I, N) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($lesseq(0, M) & $lesseq(M, J) & (~$lesseq(A, J)))) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, N) & (~$lesseq(A, N)))))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[73, 68])).
% 0.86/0.80 tff(75,plain,
% 0.86/0.80 (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($lesseq($sum(N, $product(-1, M)), 0) | (~($greatereq(M, 0) & (~$lesseq($sum(N, $product(-1, M)), 0)) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, N)), 0) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : (![A4: map_int_int] : ((~($greatereq(A, 0) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J)))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), 0) & (~$lesseq($sum(A, $product(-1, N)), 0))))) | (~($greatereq(M, 0) & $lesseq($sum(M, $product(-1, J)), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(A, 0) & $lesseq($sum(M, $product(-1, J)), 0) & (~$lesseq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42))))))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.86/0.80 tff(76,plain,
% 0.86/0.80 (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : (![A4: map_int_int] : ((~($greatereq(A, 0) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($greatereq(M, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42))))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[75, 66])).
% 0.86/0.80 tff(77,plain,
% 0.86/0.80 (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : (![A4: map_int_int] : ((~($greatereq(A, 0) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($greatereq(M, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42))))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[76, 65])).
% 0.86/0.80 tff(78,plain,
% 0.86/0.80 (~![A: $int, A1: map_int_int, M: $int, N: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : (![A4: map_int_int] : ((~($greatereq(A, 0) & permut_sub3(mk_array3(A, A3), mk_array3(A, A4), I, $sum(1, N)) & sorted_sub2(A4, I, $sum(1, N)))) | qs_partition1(mk_array3(A, A3), mk_array3(A, A4), M, N, I, J, 42)) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~qs_partition1(mk_array3(A, A2), mk_array3(A, A3), M, N, I, J, 42)) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & sorted_sub2(A3, M, $sum(1, J))))) | (~($greatereq(M, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42))))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, N)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))))),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[77, 65])).
% 0.86/0.80 tff(79,plain,
% 0.86/0.80 ((~$lesseq($sum(N!17, $product(-1, M!18)), 0)) & $greatereq(M!18, 0) & (~$lesseq($sum(A!20, $product(-1, N!17)), 0)) & (~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))) & $greatereq(I!22, 0) & $greatereq($sum(N!17, $product(-1, I!22)), 0) & qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) & $greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, J!23)) & sorted_sub2(A3!24, M!18, $sum(1, J!23)) & $lesseq($sum(M!18, $product(-1, J!23)), 0) & (~$lesseq($sum(A!20, $product(-1, J!23)), 0)) & (~$lesseq($sum(I!22, $product(-1, J!23)), 0)) & permut_sub3(mk_array3(A!20, A1!19), mk_array3(A!20, A2!21), M!18, $sum(1, N!17)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!18)), 0) & $lesseq($sum(R, $product(-1, J!23)), 0))) | $lesseq(get3(A2!21, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!23)), 0)) & (~$greatereq($sum(R, $product(-1, I!22)), 0)))) | (get3(A2!21, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!22)), 0) & $lesseq($sum(R, $product(-1, N!17)), 0))) | $greatereq(get3(A2!21, R), 42)) & $greatereq($sum(N!17, $product(-1, M!18)), 0)),
% 0.86/0.80 inference(modus_ponens,[status(thm)],[78, 64])).
% 0.86/0.80 tff(80,plain,
% 0.86/0.80 ($greatereq(M!18, 0)),
% 0.86/0.80 inference(and_elim,[status(thm)],[79])).
% 0.86/0.80 tff(81,assumption,($lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)), introduced(assumption)).
% 0.86/0.80 tff(82,assumption,(~$greatereq(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), 0)), introduced(assumption)).
% 0.86/0.80 tff(83,plain,
% 0.86/0.80 ($false),
% 0.86/0.80 inference(theory_lemma,[status(thm)],[82, 81, 80])).
% 0.86/0.80 tff(84,plain,($greatereq(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.86/0.80 tff(85,plain,
% 0.86/0.80 ($greatereq(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), 0)),
% 0.86/0.80 inference(unit_resolution,[status(thm)],[84, 35])).
% 0.86/0.80 tff(86,plain,
% 0.86/0.80 (^[I: $int] : refl(($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0) <=> ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0))),
% 0.86/0.80 inference(bind,[status(th)],[])).
% 0.86/0.80 tff(87,plain,
% 0.86/0.80 (![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.86/0.80 inference(quant_intro,[status(thm)],[86])).
% 0.86/0.80 tff(88,plain,
% 0.86/0.80 (^[I: $int] : trans(monotonicity(rewrite($sum(tb2t1(t2tb1(I)), $product(-1, I)) = $sum($product(-1, I), tb2t1(t2tb1(I)))), (($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0) <=> ($sum($product(-1, I), tb2t1(t2tb1(I))) = 0))), rewrite(($sum($product(-1, I), tb2t1(t2tb1(I))) = 0) <=> ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)), (($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0) <=> ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)))),
% 0.86/0.80 inference(bind,[status(th)],[])).
% 0.86/0.80 tff(89,plain,
% 0.86/0.80 (![I: $int] : ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.86/0.80 inference(quant_intro,[status(thm)],[88])).
% 0.90/0.80 tff(90,plain,
% 0.90/0.80 (^[I: $int] : rewrite((tb2t1(t2tb1(I)) = I) <=> ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0))),
% 0.90/0.80 inference(bind,[status(th)],[])).
% 0.90/0.80 tff(91,plain,
% 0.90/0.80 (![I: $int] : (tb2t1(t2tb1(I)) = I) <=> ![I: $int] : ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0)),
% 0.90/0.80 inference(quant_intro,[status(thm)],[90])).
% 0.90/0.80 tff(92,plain,
% 0.90/0.80 (![I: $int] : (tb2t1(t2tb1(I)) = I) <=> ![I: $int] : (tb2t1(t2tb1(I)) = I)),
% 0.90/0.80 inference(rewrite,[status(thm)],[])).
% 0.90/0.80 tff(93,axiom,(![I: $int] : (tb2t1(t2tb1(I)) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeL1')).
% 0.90/0.80 tff(94,plain,
% 0.90/0.80 (![I: $int] : (tb2t1(t2tb1(I)) = I)),
% 0.90/0.80 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.90/0.80 tff(95,plain,
% 0.90/0.80 (![I: $int] : ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0)),
% 0.90/0.80 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.90/0.80 tff(96,plain,
% 0.90/0.80 (![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.90/0.80 inference(modus_ponens,[status(thm)],[95, 89])).
% 0.90/0.80 tff(97,plain,(
% 0.90/0.80 ![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.90/0.80 inference(skolemize,[status(sab)],[96])).
% 0.90/0.80 tff(98,plain,
% 0.90/0.80 (![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.90/0.80 inference(modus_ponens,[status(thm)],[97, 87])).
% 0.90/0.80 tff(99,plain,
% 0.90/0.80 ((~![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)) | ($sum(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 0)),
% 0.90/0.80 inference(quant_inst,[status(thm)],[])).
% 0.90/0.80 tff(100,plain,
% 0.90/0.80 ($sum(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 0),
% 0.90/0.80 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.90/0.80 tff(101,plain,
% 0.90/0.80 ((~($sum(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 0)) | $lesseq($sum(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.90/0.80 inference(theory_lemma,[status(thm)],[])).
% 0.90/0.80 tff(102,plain,
% 0.90/0.80 ($lesseq($sum(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.90/0.80 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.90/0.80 tff(103,plain,
% 0.90/0.80 ($greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0) | (~$lesseq($sum(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~$greatereq(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), 0))),
% 0.90/0.80 inference(theory_lemma,[status(thm)],[])).
% 0.90/0.80 tff(104,plain,
% 0.90/0.80 ($greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)),
% 0.90/0.80 inference(unit_resolution,[status(thm)],[103, 102, 85])).
% 0.90/0.80 tff(105,plain,
% 0.90/0.80 (((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42)) | $greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)),
% 0.90/0.80 inference(tautology,[status(thm)],[])).
% 0.90/0.80 tff(106,plain,
% 0.90/0.80 ($greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)),
% 0.90/0.80 inference(unit_resolution,[status(thm)],[105, 33])).
% 0.90/0.80 tff(107,assumption,($greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)), introduced(assumption)).
% 0.90/0.80 tff(108,plain,
% 0.90/0.80 ((~($sum(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 0)) | $greatereq($sum(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.90/0.80 inference(theory_lemma,[status(thm)],[])).
% 0.90/0.80 tff(109,plain,
% 0.90/0.80 ($greatereq($sum(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.90/0.80 inference(unit_resolution,[status(thm)],[108, 100])).
% 0.90/0.80 tff(110,assumption,($lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)), introduced(assumption)).
% 0.90/0.80 tff(111,plain,
% 0.90/0.80 (~$lesseq($sum(I!22, $product(-1, J!23)), 0)),
% 0.90/0.80 inference(and_elim,[status(thm)],[79])).
% 0.90/0.80 tff(112,plain,
% 0.90/0.80 ($false),
% 0.90/0.80 inference(theory_lemma,[status(thm)],[111, 110, 109, 107])).
% 0.90/0.80 tff(113,plain,((~$lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.90/0.80 tff(114,plain,
% 0.90/0.80 (~$lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.90/0.80 inference(unit_resolution,[status(thm)],[113, 106])).
% 0.90/0.80 tff(115,plain,
% 0.90/0.80 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : refl((~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))))) <=> (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))))))),
% 0.90/0.80 inference(bind,[status(th)],[])).
% 0.90/0.80 tff(116,plain,
% 0.90/0.80 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.90/0.80 inference(quant_intro,[status(thm)],[115])).
% 0.90/0.80 tff(117,plain,
% 0.90/0.80 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : rewrite((~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))))) <=> (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))))))),
% 0.90/0.81 inference(bind,[status(th)],[])).
% 0.90/0.81 tff(118,plain,
% 0.90/0.81 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.90/0.81 inference(quant_intro,[status(thm)],[117])).
% 0.90/0.81 tff(119,plain,
% 0.90/0.81 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.90/0.81 inference(transitivity,[status(thm)],[118, 116])).
% 0.90/0.81 tff(120,plain,
% 0.90/0.81 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : trans(monotonicity(rewrite(((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))) <=> ((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))), trans(monotonicity(rewrite((~((~($lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))))) <=> (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))), ((map_eq_sub1(A, A1, A2, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))))))) <=> (map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))), rewrite((map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))) <=> (map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))), ((map_eq_sub1(A, A1, A2, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))))))) <=> (map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))), ((((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))) & (map_eq_sub1(A, A1, A2, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))))))) <=> (((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)))) & (map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))))), rewrite((((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)))) & (map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))) <=> (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))), ((((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))) & (map_eq_sub1(A, A1, A2, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))))))) <=> (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))))),
% 0.90/0.81 inference(bind,[status(th)],[])).
% 0.90/0.81 tff(121,plain,
% 0.90/0.81 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))) & (map_eq_sub1(A, A1, A2, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.90/0.81 inference(quant_intro,[status(thm)],[120])).
% 0.90/0.81 tff(122,plain,
% 0.90/0.81 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : rewrite((map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))) <=> (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))))),
% 0.90/0.81 inference(bind,[status(th)],[])).
% 0.90/0.81 tff(123,plain,
% 0.90/0.81 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I)))))),
% 0.90/0.81 inference(quant_intro,[status(thm)],[122])).
% 0.90/0.81 tff(124,plain,
% 0.90/0.81 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I)))))),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(125,plain,
% 0.90/0.81 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : rewrite((map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : (($lesseq(L, I) & $less(I, U)) => (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))) <=> (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))))),
% 0.90/0.81 inference(bind,[status(th)],[])).
% 0.90/0.81 tff(126,plain,
% 0.90/0.81 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : (($lesseq(L, I) & $less(I, U)) => (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I)))))),
% 0.90/0.81 inference(quant_intro,[status(thm)],[125])).
% 0.90/0.81 tff(127,axiom,(![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : (($lesseq(L, I) & $less(I, U)) => (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','map_eq_sub_def1')).
% 0.90/0.81 tff(128,plain,
% 0.90/0.81 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I)))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.90/0.81 tff(129,plain,
% 0.90/0.81 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I)))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.90/0.81 tff(130,plain,
% 0.90/0.81 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I)))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[129, 123])).
% 0.90/0.81 tff(131,plain,(
% 0.90/0.81 ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))))) & (map_eq_sub1(A, A1, A2, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))))))))),
% 0.90/0.81 inference(skolemize,[status(sab)],[130])).
% 0.90/0.81 tff(132,plain,
% 0.90/0.81 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[131, 121])).
% 0.90/0.81 tff(133,plain,
% 0.90/0.81 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[132, 119])).
% 0.90/0.81 tff(134,plain,
% 0.90/0.81 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I)))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$greatereq(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), 0))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I)))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$greatereq(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), 0)))))))))),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(135,plain,
% 0.90/0.81 ((~((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))) | $lesseq($sum(I!22, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)))))))) <=> (~((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I)))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$greatereq(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), 0))))))))),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(136,plain,
% 0.90/0.81 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))) | $lesseq($sum(I!22, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I)))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$greatereq(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), 0)))))))))),
% 0.90/0.81 inference(monotonicity,[status(thm)],[135])).
% 0.90/0.81 tff(137,plain,
% 0.90/0.81 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))) | $lesseq($sum(I!22, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I)))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$greatereq(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), 0)))))))))),
% 0.90/0.81 inference(transitivity,[status(thm)],[136, 134])).
% 0.90/0.81 tff(138,plain,
% 0.90/0.81 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))) | $lesseq($sum(I!22, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0))))))))),
% 0.90/0.82 inference(quant_inst,[status(thm)],[])).
% 0.90/0.82 tff(139,plain,
% 0.90/0.82 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb1(I)) = get(A, int, A2, t2tb1(I))) | $lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0))))) | (~(map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb1(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb1(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I)))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$greatereq(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), 0))))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.90/0.82 tff(140,plain,
% 0.90/0.82 (~((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I)))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$greatereq(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), 0)))))))),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[139, 133])).
% 0.90/0.82 tff(141,plain,
% 0.90/0.82 (((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I)))))) | (~(map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22) | (~($lesseq($sum(I!22, $product(-1, tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))) | (~$greatereq(tptp_fun_I_9(I!22, 0, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), 0))))))) | ((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I)))))),
% 0.90/0.82 inference(tautology,[status(thm)],[])).
% 0.90/0.82 tff(142,plain,
% 0.90/0.82 ((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.90/0.82 tff(143,plain,
% 0.90/0.82 (^[A1: array_int, A2: array_int, L: $int, U: $int] : refl((permut_sub3(A1, A2, L, U) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L)) | (~permut3(int, t2tb2(A1), t2tb2(A2), L, U)) | (~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1))))))) <=> (permut_sub3(A1, A2, L, U) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L)) | (~permut3(int, t2tb2(A1), t2tb2(A2), L, U)) | (~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1))))))))),
% 0.90/0.82 inference(bind,[status(th)],[])).
% 0.90/0.82 tff(144,plain,
% 0.90/0.82 (![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L)) | (~permut3(int, t2tb2(A1), t2tb2(A2), L, U)) | (~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1))))))) <=> ![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L)) | (~permut3(int, t2tb2(A1), t2tb2(A2), L, U)) | (~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))))),
% 0.90/0.82 inference(quant_intro,[status(thm)],[143])).
% 0.90/0.82 tff(145,plain,
% 0.90/0.82 (^[A1: array_int, A2: array_int, L: $int, U: $int] : rewrite((permut_sub3(A1, A2, L, U) <=> (map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1))))) <=> (permut_sub3(A1, A2, L, U) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L)) | (~permut3(int, t2tb2(A1), t2tb2(A2), L, U)) | (~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1))))))))),
% 0.90/0.82 inference(bind,[status(th)],[])).
% 0.90/0.82 tff(146,plain,
% 0.90/0.82 (![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1))))) <=> ![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L)) | (~permut3(int, t2tb2(A1), t2tb2(A2), L, U)) | (~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))))),
% 0.90/0.82 inference(quant_intro,[status(thm)],[145])).
% 0.90/0.82 tff(147,plain,
% 0.90/0.82 (![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1))))) <=> ![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(148,plain,
% 0.90/0.82 (^[A1: array_int, A2: array_int, L: $int, U: $int] : rewrite((permut_sub3(A1, A2, L, U) <=> ((map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U)) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1))))) <=> (permut_sub3(A1, A2, L, U) <=> (map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1))))))),
% 0.90/0.82 inference(bind,[status(th)],[])).
% 0.90/0.82 tff(149,plain,
% 0.90/0.82 (![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> ((map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U)) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1))))) <=> ![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))),
% 0.90/0.82 inference(quant_intro,[status(thm)],[148])).
% 0.90/0.82 tff(150,axiom,(![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> ((map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U)) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permut_sub_def')).
% 0.90/0.82 tff(151,plain,
% 0.90/0.82 (![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.90/0.82 tff(152,plain,
% 0.90/0.82 (![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.90/0.82 tff(153,plain,(
% 0.90/0.82 ![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L) & permut3(int, t2tb2(A1), t2tb2(A2), L, U) & map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))),
% 0.90/0.82 inference(skolemize,[status(sab)],[152])).
% 0.90/0.82 tff(154,plain,
% 0.90/0.82 (![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L)) | (~permut3(int, t2tb2(A1), t2tb2(A2), L, U)) | (~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.90/0.82 tff(155,plain,
% 0.90/0.82 (![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L)) | (~permut3(int, t2tb2(A1), t2tb2(A2), L, U)) | (~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[154, 144])).
% 0.90/0.82 tff(156,plain,
% 0.90/0.82 ((~![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L)) | (~permut3(int, t2tb2(A1), t2tb2(A2), L, U)) | (~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))))) | (permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | (~permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), $sum(1, N!17), length1(int, t2tb2(mk_array3(A!20, A3!24))))))))),
% 0.90/0.82 inference(quant_inst,[status(thm)],[])).
% 0.90/0.82 tff(157,plain,
% 0.90/0.82 (permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | (~permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), $sum(1, N!17), length1(int, t2tb2(mk_array3(A!20, A3!24)))))))),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.90/0.82 tff(158,plain,
% 0.90/0.82 (~((~($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17)))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42))),
% 0.90/0.82 inference(and_elim,[status(thm)],[79])).
% 0.90/0.82 tff(159,plain,
% 0.90/0.82 ($greatereq(A!20, 0) & permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) & sorted_sub2(A4!25, I!22, $sum(1, N!17))),
% 0.90/0.82 inference(or_elim,[status(thm)],[158])).
% 0.90/0.82 tff(160,plain,
% 0.90/0.82 (permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17))),
% 0.90/0.82 inference(and_elim,[status(thm)],[159])).
% 0.90/0.82 tff(161,plain,
% 0.90/0.82 ((~(permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | (~permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), $sum(1, N!17), length1(int, t2tb2(mk_array3(A!20, A3!24))))))))) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17))) | (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | (~permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), $sum(1, N!17), length1(int, t2tb2(mk_array3(A!20, A3!24)))))))),
% 0.90/0.82 inference(tautology,[status(thm)],[])).
% 0.90/0.82 tff(162,plain,
% 0.90/0.82 ((~(permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | (~permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), $sum(1, N!17), length1(int, t2tb2(mk_array3(A!20, A3!24))))))))) | (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | (~permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), $sum(1, N!17), length1(int, t2tb2(mk_array3(A!20, A3!24)))))))),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.90/0.82 tff(163,plain,
% 0.90/0.82 (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | (~permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), $sum(1, N!17), length1(int, t2tb2(mk_array3(A!20, A3!24))))))),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[162, 157])).
% 0.90/0.82 tff(164,plain,
% 0.90/0.82 (((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | (~permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), $sum(1, N!17), length1(int, t2tb2(mk_array3(A!20, A3!24)))))) | map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)),
% 0.90/0.82 inference(tautology,[status(thm)],[])).
% 0.90/0.82 tff(165,plain,
% 0.90/0.82 (map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.90/0.82 tff(166,plain,
% 0.90/0.82 ((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I)))))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))),
% 0.90/0.82 inference(tautology,[status(thm)],[])).
% 0.90/0.82 tff(167,plain,
% 0.90/0.82 ((~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I)))))) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.90/0.82 tff(168,plain,
% 0.90/0.82 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[167, 142])).
% 0.90/0.82 tff(169,plain,
% 0.90/0.82 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | ((~$greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | (~$greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(170,plain,
% 0.90/0.82 (((~$greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) <=> ((~$greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(171,plain,
% 0.90/0.82 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | ((~$greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | ((~$greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))))),
% 0.90/0.82 inference(monotonicity,[status(thm)],[170])).
% 0.90/0.82 tff(172,plain,
% 0.90/0.82 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | ((~$greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | (~$greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))))),
% 0.90/0.82 inference(transitivity,[status(thm)],[171, 169])).
% 0.90/0.82 tff(173,plain,
% 0.90/0.82 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | ((~$greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))))),
% 0.90/0.83 inference(quant_inst,[status(thm)],[])).
% 0.90/0.83 tff(174,plain,
% 0.90/0.83 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | (~$greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.90/0.83 tff(175,plain,
% 0.90/0.83 ((~$greatereq(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[174, 168])).
% 0.90/0.83 tff(176,plain,
% 0.90/0.83 (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[175, 114, 104])).
% 0.90/0.83 tff(177,plain,
% 0.90/0.83 (t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))) = t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))),
% 0.90/0.83 inference(symmetry,[status(thm)],[29])).
% 0.90/0.83 tff(178,plain,
% 0.90/0.83 (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[177])).
% 0.90/0.83 tff(179,plain,
% 0.90/0.83 ((~![A: ty, U: uni] : (U = mk_array2(A, length1(A, U), elts(A, U)))) | (t2tb2(mk_array3(A!20, A3!24)) = mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))))),
% 0.90/0.83 inference(quant_inst,[status(thm)],[])).
% 0.90/0.83 tff(180,plain,
% 0.90/0.83 (t2tb2(mk_array3(A!20, A3!24)) = mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[179, 7])).
% 0.90/0.83 tff(181,plain,
% 0.90/0.83 (mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))) = t2tb2(mk_array3(A!20, A3!24))),
% 0.90/0.83 inference(symmetry,[status(thm)],[180])).
% 0.90/0.83 tff(182,plain,
% 0.90/0.83 (elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))) = elts(int, t2tb2(mk_array3(A!20, A3!24)))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[181])).
% 0.90/0.83 tff(183,plain,
% 0.90/0.83 (get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[182, 29])).
% 0.90/0.83 tff(184,plain,
% 0.90/0.83 ((~![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))) | (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))),
% 0.90/0.83 inference(quant_inst,[status(thm)],[])).
% 0.90/0.83 tff(185,plain,
% 0.90/0.83 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[184, 18])).
% 0.90/0.83 tff(186,plain,
% 0.90/0.83 (get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))) = get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[180])).
% 0.90/0.83 tff(187,plain,
% 0.90/0.83 (get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))) = get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))),
% 0.90/0.83 inference(transitivity,[status(thm)],[186, 185, 183, 178, 176, 32, 21, 11])).
% 0.90/0.83 tff(188,plain,
% 0.90/0.83 (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[187])).
% 0.90/0.83 tff(189,plain,
% 0.90/0.83 (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))) = tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))),
% 0.90/0.83 inference(symmetry,[status(thm)],[188])).
% 0.90/0.83 tff(190,plain,
% 0.90/0.83 ((~(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))) = tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))), 0)),
% 0.90/0.83 inference(theory_lemma,[status(thm)],[])).
% 0.90/0.83 tff(191,plain,
% 0.90/0.83 ($lesseq($sum(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))), 0)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.90/0.83 tff(192,plain,
% 0.90/0.83 (((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42)) | (~$lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))),
% 0.90/0.83 inference(tautology,[status(thm)],[])).
% 0.90/0.83 tff(193,plain,
% 0.90/0.83 (~$lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[192, 33])).
% 0.90/0.83 tff(194,plain,
% 0.90/0.83 ((~$lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42) | (~$lesseq($sum(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))), 0))),
% 0.90/0.83 inference(theory_lemma,[status(thm)],[])).
% 0.90/0.83 tff(195,plain,
% 0.90/0.83 (~$lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[194, 193, 191])).
% 0.90/0.83 tff(196,plain,
% 0.90/0.83 ($lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0))),
% 0.90/0.83 inference(theory_lemma,[status(thm)],[])).
% 0.90/0.83 tff(197,plain,
% 0.90/0.83 ($lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[196, 102, 35])).
% 0.90/0.83 tff(198,plain,
% 0.90/0.83 ($greatereq($sum(N!17, $product(-1, I!22)), 0)),
% 0.90/0.83 inference(and_elim,[status(thm)],[79])).
% 0.90/0.83 tff(199,plain,
% 0.90/0.83 ((~$lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1)) | (~$greatereq($sum(N!17, $product(-1, I!22)), 0)) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.90/0.83 inference(theory_lemma,[status(thm)],[])).
% 0.90/0.83 tff(200,plain,
% 0.90/0.83 (~$lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[199, 114, 198])).
% 0.90/0.83 tff(201,plain,
% 0.90/0.83 (elts(int, t2tb2(mk_array3(A!20, A3!24))) = elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))))),
% 0.90/0.83 inference(symmetry,[status(thm)],[182])).
% 0.90/0.83 tff(202,plain,
% 0.90/0.83 (permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17)) <=> permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[201, 31])).
% 0.90/0.83 tff(203,plain,
% 0.90/0.83 (permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) <=> permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))),
% 0.90/0.83 inference(symmetry,[status(thm)],[202])).
% 0.90/0.83 tff(204,plain,
% 0.90/0.83 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : refl((permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U))))) <=> (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U))))))),
% 0.90/0.83 inference(bind,[status(th)],[])).
% 0.90/0.83 tff(205,plain,
% 0.90/0.83 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))),
% 0.90/0.83 inference(quant_intro,[status(thm)],[204])).
% 0.90/0.83 tff(206,plain,
% 0.90/0.83 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : rewrite((permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U))))))),
% 0.90/0.83 inference(bind,[status(th)],[])).
% 0.90/0.83 tff(207,plain,
% 0.90/0.83 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))),
% 0.90/0.83 inference(quant_intro,[status(thm)],[206])).
% 0.90/0.83 tff(208,plain,
% 0.90/0.83 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : rewrite((permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> (permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U))))),
% 0.90/0.83 inference(bind,[status(th)],[])).
% 0.90/0.83 tff(209,plain,
% 0.90/0.83 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.90/0.83 inference(quant_intro,[status(thm)],[208])).
% 0.90/0.83 tff(210,plain,
% 0.90/0.83 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(211,plain,
% 0.90/0.83 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : rewrite((permut3(A, A1, A2, L, U) <=> ((((((length1(A, A1) = length1(A, A2)) & $lesseq(0, L)) & $lesseq(L, length1(A, A1))) & $lesseq(0, U)) & $lesseq(U, length1(A, A1))) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U))))),
% 0.90/0.83 inference(bind,[status(th)],[])).
% 0.90/0.83 tff(212,plain,
% 0.90/0.83 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((((((length1(A, A1) = length1(A, A2)) & $lesseq(0, L)) & $lesseq(L, length1(A, A1))) & $lesseq(0, U)) & $lesseq(U, length1(A, A1))) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.90/0.83 inference(quant_intro,[status(thm)],[211])).
% 0.90/0.83 tff(213,axiom,(![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((((((length1(A, A1) = length1(A, A2)) & $lesseq(0, L)) & $lesseq(L, length1(A, A1))) & $lesseq(0, U)) & $lesseq(U, length1(A, A1))) & permut2(A, elts(A, A1), elts(A, A2), L, U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permut_def1')).
% 0.90/0.83 tff(214,plain,
% 0.90/0.83 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.90/0.83 tff(215,plain,
% 0.90/0.83 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.90/0.83 tff(216,plain,
% 0.90/0.83 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[215, 209])).
% 0.90/0.83 tff(217,plain,(
% 0.90/0.83 ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.90/0.83 inference(skolemize,[status(sab)],[216])).
% 0.90/0.83 tff(218,plain,
% 0.90/0.83 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[217, 207])).
% 0.90/0.83 tff(219,plain,
% 0.90/0.83 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[218, 205])).
% 0.90/0.83 tff(220,plain,
% 0.90/0.83 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq(M!18, 0)) | (~$greatereq(N!17, -1)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~$lesseq($sum(N!17, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), -1)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq(M!18, 0)) | (~$greatereq(N!17, -1)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~$lesseq($sum(N!17, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), -1))))))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(221,plain,
% 0.90/0.83 ((permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq($sum(1, N!17), 0)) | (~$greatereq(M!18, 0)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)))))) <=> (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq(M!18, 0)) | (~$greatereq(N!17, -1)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~$lesseq($sum(N!17, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), -1)))))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(222,plain,
% 0.90/0.83 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq($sum(1, N!17), 0)) | (~$greatereq(M!18, 0)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq(M!18, 0)) | (~$greatereq(N!17, -1)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~$lesseq($sum(N!17, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), -1))))))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[221])).
% 0.90/0.83 tff(223,plain,
% 0.90/0.83 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq($sum(1, N!17), 0)) | (~$greatereq(M!18, 0)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq(M!18, 0)) | (~$greatereq(N!17, -1)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~$lesseq($sum(N!17, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), -1))))))),
% 0.90/0.84 inference(transitivity,[status(thm)],[222, 220])).
% 0.90/0.84 tff(224,plain,
% 0.90/0.84 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq($sum(1, N!17), 0)) | (~$greatereq(M!18, 0)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))))))),
% 0.90/0.84 inference(quant_inst,[status(thm)],[])).
% 0.90/0.84 tff(225,plain,
% 0.90/0.84 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq(M!18, 0)) | (~$greatereq(N!17, -1)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~$lesseq($sum(N!17, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), -1)))))),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.94/0.84 tff(226,plain,
% 0.94/0.84 (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq(M!18, 0)) | (~$greatereq(N!17, -1)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~$lesseq($sum(N!17, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), -1))))),
% 0.94/0.84 inference(unit_resolution,[status(thm)],[225, 219])).
% 0.94/0.84 tff(227,plain,
% 0.94/0.84 (^[U: array_int] : refl((U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U))))) <=> (U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U))))))),
% 0.94/0.84 inference(bind,[status(th)],[])).
% 0.94/0.84 tff(228,plain,
% 0.94/0.84 (![U: array_int] : (U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U))))) <=> ![U: array_int] : (U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U)))))),
% 0.94/0.84 inference(quant_intro,[status(thm)],[227])).
% 0.94/0.84 tff(229,plain,
% 0.94/0.84 (![U: array_int] : (U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U))))) <=> ![U: array_int] : (U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U)))))),
% 0.94/0.84 inference(rewrite,[status(thm)],[])).
% 0.94/0.84 tff(230,axiom,(![U: array_int] : (U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','array_inversion2')).
% 0.94/0.84 tff(231,plain,
% 0.94/0.84 (![U: array_int] : (U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U)))))),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.94/0.84 tff(232,plain,(
% 0.94/0.84 ![U: array_int] : (U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U)))))),
% 0.94/0.84 inference(skolemize,[status(sab)],[231])).
% 0.94/0.84 tff(233,plain,
% 0.94/0.84 (![U: array_int] : (U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U)))))),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.94/0.84 tff(234,plain,
% 0.94/0.84 ((~![U: array_int] : (U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U)))))) | (mk_array3(A!20, A4!25) = mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))),
% 0.94/0.84 inference(quant_inst,[status(thm)],[])).
% 0.94/0.84 tff(235,plain,
% 0.94/0.84 (mk_array3(A!20, A4!25) = mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))),
% 0.94/0.84 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.94/0.84 tff(236,plain,
% 0.94/0.84 (mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))) = mk_array3(A!20, A4!25)),
% 0.94/0.84 inference(symmetry,[status(thm)],[235])).
% 0.94/0.84 tff(237,plain,
% 0.94/0.84 (t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))) = t2tb2(mk_array3(A!20, A4!25))),
% 0.94/0.84 inference(monotonicity,[status(thm)],[236])).
% 0.94/0.84 tff(238,plain,
% 0.94/0.84 (t2tb2(mk_array3(A!20, A4!25)) = t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))),
% 0.94/0.84 inference(symmetry,[status(thm)],[237])).
% 0.94/0.84 tff(239,plain,
% 0.94/0.84 (mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))) = t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))),
% 0.94/0.84 inference(transitivity,[status(thm)],[10, 238])).
% 0.94/0.84 tff(240,plain,
% 0.94/0.84 ((~![U: array_int] : (U = mk_array3(length1(int, t2tb2(U)), tb2t(elts(int, t2tb2(U)))))) | (mk_array3(A!20, A3!24) = mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))),
% 0.94/0.84 inference(quant_inst,[status(thm)],[])).
% 0.94/0.84 tff(241,plain,
% 0.94/0.84 (mk_array3(A!20, A3!24) = mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))),
% 0.94/0.84 inference(unit_resolution,[status(thm)],[240, 233])).
% 0.94/0.84 tff(242,plain,
% 0.94/0.84 (mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))) = mk_array3(A!20, A3!24)),
% 0.94/0.84 inference(symmetry,[status(thm)],[241])).
% 0.94/0.84 tff(243,plain,
% 0.94/0.84 (t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))) = t2tb2(mk_array3(A!20, A3!24))),
% 0.94/0.84 inference(monotonicity,[status(thm)],[242])).
% 0.94/0.84 tff(244,plain,
% 0.94/0.84 (t2tb2(mk_array3(A!20, A3!24)) = t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))),
% 0.94/0.84 inference(symmetry,[status(thm)],[243])).
% 0.94/0.84 tff(245,plain,
% 0.94/0.84 (mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))) = t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))),
% 0.94/0.84 inference(transitivity,[status(thm)],[181, 244])).
% 0.94/0.84 tff(246,plain,
% 0.94/0.84 (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17))),
% 0.94/0.84 inference(monotonicity,[status(thm)],[245, 239])).
% 0.94/0.84 tff(247,plain,
% 0.94/0.84 (permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17)) <=> permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17))),
% 0.94/0.84 inference(symmetry,[status(thm)],[246])).
% 0.94/0.84 tff(248,plain,
% 0.94/0.84 ((~![A1: array_int, A2: array_int, L: $int, U: $int] : (permut_sub3(A1, A2, L, U) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), 0, L)) | (~permut3(int, t2tb2(A1), t2tb2(A2), L, U)) | (~map_eq_sub1(int, elts(int, t2tb2(A1)), elts(int, t2tb2(A2)), U, length1(int, t2tb2(A1)))))))) | (permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), 0, M!18)) | (~permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), $sum(1, N!17), length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))))))),
% 0.94/0.84 inference(quant_inst,[status(thm)],[])).
% 0.94/0.84 tff(249,plain,
% 0.94/0.84 (permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), 0, M!18)) | (~permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), $sum(1, N!17), length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))))))))),
% 0.94/0.84 inference(unit_resolution,[status(thm)],[248, 155])).
% 0.94/0.84 tff(250,assumption,(~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))), introduced(assumption)).
% 0.94/0.84 tff(251,plain,
% 0.94/0.84 (permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17)) <=> permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17))),
% 0.94/0.84 inference(monotonicity,[status(thm)],[242, 236])).
% 0.94/0.84 tff(252,plain,
% 0.94/0.84 (permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), I!22, $sum(1, N!17)) <=> permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))),
% 0.94/0.84 inference(symmetry,[status(thm)],[251])).
% 0.94/0.84 tff(253,plain,
% 0.94/0.84 (permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[160, 252])).
% 0.94/0.84 tff(254,plain,
% 0.94/0.84 ($lesseq($sum(M!18, $product(-1, J!23)), 0)),
% 0.94/0.84 inference(and_elim,[status(thm)],[79])).
% 0.94/0.84 tff(255,assumption,(~$lesseq($sum(M!18, $product(-1, I!22)), 0)), introduced(assumption)).
% 0.94/0.84 tff(256,plain,
% 0.94/0.84 ($false),
% 0.94/0.84 inference(theory_lemma,[status(thm)],[255, 111, 254])).
% 0.94/0.84 tff(257,plain,($lesseq($sum(M!18, $product(-1, I!22)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.94/0.84 tff(258,plain,
% 0.94/0.84 (~$lesseq($sum(A!20, $product(-1, N!17)), 0)),
% 0.94/0.84 inference(and_elim,[status(thm)],[79])).
% 0.94/0.84 tff(259,plain,
% 0.94/0.84 (^[U: $int, U1: map_int_int] : refl(($sum(U, $product(-1, length1(int, t2tb2(mk_array3(U, U1))))) = 0) <=> ($sum(U, $product(-1, length1(int, t2tb2(mk_array3(U, U1))))) = 0))),
% 0.94/0.84 inference(bind,[status(th)],[])).
% 0.94/0.84 tff(260,plain,
% 0.94/0.84 (![U: $int, U1: map_int_int] : ($sum(U, $product(-1, length1(int, t2tb2(mk_array3(U, U1))))) = 0) <=> ![U: $int, U1: map_int_int] : ($sum(U, $product(-1, length1(int, t2tb2(mk_array3(U, U1))))) = 0)),
% 0.94/0.84 inference(quant_intro,[status(thm)],[259])).
% 0.94/0.84 tff(261,plain,
% 0.94/0.84 (^[U: $int, U1: map_int_int] : trans(monotonicity(rewrite($sum(length1(int, t2tb2(mk_array3(U, U1))), $product(-1, U)) = $sum($product(-1, U), length1(int, t2tb2(mk_array3(U, U1))))), (($sum(length1(int, t2tb2(mk_array3(U, U1))), $product(-1, U)) = 0) <=> ($sum($product(-1, U), length1(int, t2tb2(mk_array3(U, U1)))) = 0))), rewrite(($sum($product(-1, U), length1(int, t2tb2(mk_array3(U, U1)))) = 0) <=> ($sum(U, $product(-1, length1(int, t2tb2(mk_array3(U, U1))))) = 0)), (($sum(length1(int, t2tb2(mk_array3(U, U1))), $product(-1, U)) = 0) <=> ($sum(U, $product(-1, length1(int, t2tb2(mk_array3(U, U1))))) = 0)))),
% 0.94/0.84 inference(bind,[status(th)],[])).
% 0.94/0.84 tff(262,plain,
% 0.94/0.84 (![U: $int, U1: map_int_int] : ($sum(length1(int, t2tb2(mk_array3(U, U1))), $product(-1, U)) = 0) <=> ![U: $int, U1: map_int_int] : ($sum(U, $product(-1, length1(int, t2tb2(mk_array3(U, U1))))) = 0)),
% 0.94/0.84 inference(quant_intro,[status(thm)],[261])).
% 0.94/0.84 tff(263,plain,
% 0.94/0.84 (^[U: $int, U1: map_int_int] : rewrite((length1(int, t2tb2(mk_array3(U, U1))) = U) <=> ($sum(length1(int, t2tb2(mk_array3(U, U1))), $product(-1, U)) = 0))),
% 0.94/0.84 inference(bind,[status(th)],[])).
% 0.94/0.84 tff(264,plain,
% 0.94/0.84 (![U: $int, U1: map_int_int] : (length1(int, t2tb2(mk_array3(U, U1))) = U) <=> ![U: $int, U1: map_int_int] : ($sum(length1(int, t2tb2(mk_array3(U, U1))), $product(-1, U)) = 0)),
% 0.94/0.84 inference(quant_intro,[status(thm)],[263])).
% 0.94/0.84 tff(265,plain,
% 0.94/0.84 (![U: $int, U1: map_int_int] : (length1(int, t2tb2(mk_array3(U, U1))) = U) <=> ![U: $int, U1: map_int_int] : (length1(int, t2tb2(mk_array3(U, U1))) = U)),
% 0.94/0.84 inference(rewrite,[status(thm)],[])).
% 0.94/0.84 tff(266,axiom,(![U: $int, U1: map_int_int] : (length1(int, t2tb2(mk_array3(U, U1))) = U)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','length_def2')).
% 0.94/0.84 tff(267,plain,
% 0.94/0.84 (![U: $int, U1: map_int_int] : (length1(int, t2tb2(mk_array3(U, U1))) = U)),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.94/0.84 tff(268,plain,
% 0.94/0.84 (![U: $int, U1: map_int_int] : ($sum(length1(int, t2tb2(mk_array3(U, U1))), $product(-1, U)) = 0)),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[267, 264])).
% 0.94/0.84 tff(269,plain,
% 0.94/0.84 (![U: $int, U1: map_int_int] : ($sum(U, $product(-1, length1(int, t2tb2(mk_array3(U, U1))))) = 0)),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[268, 262])).
% 0.94/0.84 tff(270,plain,(
% 0.94/0.84 ![U: $int, U1: map_int_int] : ($sum(U, $product(-1, length1(int, t2tb2(mk_array3(U, U1))))) = 0)),
% 0.94/0.84 inference(skolemize,[status(sab)],[269])).
% 0.94/0.84 tff(271,plain,
% 0.94/0.84 (![U: $int, U1: map_int_int] : ($sum(U, $product(-1, length1(int, t2tb2(mk_array3(U, U1))))) = 0)),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[270, 260])).
% 0.94/0.84 tff(272,plain,
% 0.94/0.84 ((~![U: $int, U1: map_int_int] : ($sum(U, $product(-1, length1(int, t2tb2(mk_array3(U, U1))))) = 0)) | ($sum(A!20, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))) = 0)),
% 0.94/0.84 inference(quant_inst,[status(thm)],[])).
% 0.94/0.84 tff(273,plain,
% 0.94/0.84 ($sum(A!20, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))) = 0),
% 0.94/0.84 inference(unit_resolution,[status(thm)],[272, 271])).
% 0.94/0.84 tff(274,plain,
% 0.94/0.84 ((~($sum(A!20, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))) = 0)) | $lesseq($sum(A!20, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)),
% 0.94/0.84 inference(theory_lemma,[status(thm)],[])).
% 0.94/0.84 tff(275,plain,
% 0.94/0.84 ($lesseq($sum(A!20, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)),
% 0.94/0.84 inference(unit_resolution,[status(thm)],[274, 273])).
% 0.94/0.84 tff(276,plain,
% 0.94/0.84 (length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))) = length1(int, t2tb2(mk_array3(A!20, A3!24)))),
% 0.94/0.84 inference(monotonicity,[status(thm)],[243])).
% 0.94/0.84 tff(277,plain,
% 0.94/0.84 (length1(int, t2tb2(mk_array3(A!20, A3!24))) = length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))))),
% 0.94/0.84 inference(symmetry,[status(thm)],[276])).
% 0.94/0.84 tff(278,plain,
% 0.94/0.84 ((~(length1(int, t2tb2(mk_array3(A!20, A3!24))) = length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))) | $lesseq($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), 0)),
% 0.94/0.84 inference(theory_lemma,[status(thm)],[])).
% 0.94/0.84 tff(279,plain,
% 0.94/0.84 ($lesseq($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), 0)),
% 0.94/0.84 inference(unit_resolution,[status(thm)],[278, 277])).
% 0.94/0.84 tff(280,plain,
% 0.94/0.84 ($lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1) | (~$lesseq($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), 0)) | (~$lesseq($sum(A!20, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | $lesseq($sum(A!20, $product(-1, N!17)), 0)),
% 0.94/0.84 inference(theory_lemma,[status(thm)],[])).
% 0.94/0.84 tff(281,plain,
% 0.94/0.84 ($lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1)),
% 0.94/0.84 inference(unit_resolution,[status(thm)],[280, 279, 275, 258])).
% 0.94/0.84 tff(282,plain,
% 0.94/0.84 (^[A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : refl((permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0))) <=> (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0))))),
% 0.94/0.84 inference(bind,[status(th)],[])).
% 0.94/0.84 tff(283,plain,
% 0.94/0.84 (![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0))) <=> ![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))),
% 0.94/0.84 inference(quant_intro,[status(thm)],[282])).
% 0.94/0.84 tff(284,plain,
% 0.94/0.84 (^[A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : trans(monotonicity(trans(monotonicity(rewrite(($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) <=> (~((~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))))), ((~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) <=> (~(~((~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))))))), rewrite((~(~((~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))))) <=> ((~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)))), ((~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) <=> ((~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))))), trans(monotonicity(rewrite(($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0)) <=> (~((~$greatereq(L2, 0)) | (~$lesseq($sum(L2, $product(-1, L1)), 0))))), ((~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0))) <=> (~(~((~$greatereq(L2, 0)) | (~$lesseq($sum(L2, $product(-1, L1)), 0))))))), rewrite((~(~((~$greatereq(L2, 0)) | (~$lesseq($sum(L2, $product(-1, L1)), 0))))) <=> ((~$greatereq(L2, 0)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))), ((~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0))) <=> ((~$greatereq(L2, 0)) | (~$lesseq($sum(L2, $product(-1, L1)), 0))))), ((permut_sub3(A1, A2, L2, U2) | (~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | (~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0))) | (~permut_sub3(A1, A2, L1, U1))) <=> (permut_sub3(A1, A2, L2, U2) | ((~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | ((~$greatereq(L2, 0)) | (~$lesseq($sum(L2, $product(-1, L1)), 0))) | (~permut_sub3(A1, A2, L1, U1))))), rewrite((permut_sub3(A1, A2, L2, U2) | ((~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | ((~$greatereq(L2, 0)) | (~$lesseq($sum(L2, $product(-1, L1)), 0))) | (~permut_sub3(A1, A2, L1, U1))) <=> (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))), ((permut_sub3(A1, A2, L2, U2) | (~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | (~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0))) | (~permut_sub3(A1, A2, L1, U1))) <=> (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))))),
% 0.94/0.84 inference(bind,[status(th)],[])).
% 0.94/0.84 tff(285,plain,
% 0.94/0.84 (![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | (~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0))) | (~permut_sub3(A1, A2, L1, U1))) <=> ![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))),
% 0.94/0.84 inference(quant_intro,[status(thm)],[284])).
% 0.94/0.84 tff(286,plain,
% 0.94/0.84 (^[A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : trans(monotonicity(rewrite((~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) <=> (~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)))), rewrite((~($lesseq(0, L2) & $lesseq(L2, L1))) <=> (~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0)))), ((permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1)))) <=> (permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | (~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0)))))), rewrite((permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | (~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0)))) <=> (permut_sub3(A1, A2, L2, U2) | (~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | (~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0))) | (~permut_sub3(A1, A2, L1, U1)))), ((permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1)))) <=> (permut_sub3(A1, A2, L2, U2) | (~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | (~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0))) | (~permut_sub3(A1, A2, L1, U1)))))),
% 0.94/0.84 inference(bind,[status(th)],[])).
% 0.94/0.84 tff(287,plain,
% 0.94/0.84 (![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1)))) <=> ![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | (~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0))) | (~permut_sub3(A1, A2, L1, U1)))),
% 0.94/0.84 inference(quant_intro,[status(thm)],[286])).
% 0.94/0.84 tff(288,plain,
% 0.94/0.84 (![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1)))) <=> ![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1))))),
% 0.94/0.84 inference(rewrite,[status(thm)],[])).
% 0.94/0.84 tff(289,plain,
% 0.94/0.84 (^[A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : trans(monotonicity(trans(monotonicity(rewrite((($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1)))) => permut_sub3(A1, A2, L2, U2)) <=> ((~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | permut_sub3(A1, A2, L2, U2))), ((($lesseq(0, L2) & $lesseq(L2, L1)) => (($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1)))) => permut_sub3(A1, A2, L2, U2))) <=> (($lesseq(0, L2) & $lesseq(L2, L1)) => ((~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | permut_sub3(A1, A2, L2, U2))))), rewrite((($lesseq(0, L2) & $lesseq(L2, L1)) => ((~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | permut_sub3(A1, A2, L2, U2))) <=> (permut_sub3(A1, A2, L2, U2) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1))))), ((($lesseq(0, L2) & $lesseq(L2, L1)) => (($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1)))) => permut_sub3(A1, A2, L2, U2))) <=> (permut_sub3(A1, A2, L2, U2) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1)))))), ((permut_sub3(A1, A2, L1, U1) => (($lesseq(0, L2) & $lesseq(L2, L1)) => (($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1)))) => permut_sub3(A1, A2, L2, U2)))) <=> (permut_sub3(A1, A2, L1, U1) => (permut_sub3(A1, A2, L2, U2) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1))))))), rewrite((permut_sub3(A1, A2, L1, U1) => (permut_sub3(A1, A2, L2, U2) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1))))) <=> (permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1))))), ((permut_sub3(A1, A2, L1, U1) => (($lesseq(0, L2) & $lesseq(L2, L1)) => (($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1)))) => permut_sub3(A1, A2, L2, U2)))) <=> (permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1))))))),
% 0.94/0.84 inference(bind,[status(th)],[])).
% 0.94/0.84 tff(290,plain,
% 0.94/0.84 (![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L1, U1) => (($lesseq(0, L2) & $lesseq(L2, L1)) => (($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1)))) => permut_sub3(A1, A2, L2, U2)))) <=> ![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1))))),
% 0.94/0.84 inference(quant_intro,[status(thm)],[289])).
% 0.94/0.84 tff(291,axiom,(![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L1, U1) => (($lesseq(0, L2) & $lesseq(L2, L1)) => (($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1)))) => permut_sub3(A1, A2, L2, U2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permut_sub_weakening')).
% 0.94/0.84 tff(292,plain,
% 0.94/0.84 (![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1))))),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.94/0.84 tff(293,plain,
% 0.94/0.84 (![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~permut_sub3(A1, A2, L1, U1)) | (~($lesseq(U1, U2) & $lesseq(U2, length1(int, t2tb2(A1))))) | (~($lesseq(0, L2) & $lesseq(L2, L1))))),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.94/0.84 tff(294,plain,
% 0.94/0.84 (![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | (~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0))) | (~permut_sub3(A1, A2, L1, U1)))),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[293, 287])).
% 0.94/0.84 tff(295,plain,(
% 0.94/0.84 ![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~($lesseq($sum(U1, $product(-1, U2)), 0) & $lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0))) | (~($greatereq(L2, 0) & $lesseq($sum(L2, $product(-1, L1)), 0))) | (~permut_sub3(A1, A2, L1, U1)))),
% 0.94/0.84 inference(skolemize,[status(sab)],[294])).
% 0.94/0.84 tff(296,plain,
% 0.94/0.84 (![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[295, 285])).
% 0.94/0.84 tff(297,plain,
% 0.94/0.84 (![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))),
% 0.94/0.84 inference(modus_ponens,[status(thm)],[296, 283])).
% 0.94/0.84 tff(298,plain,
% 0.94/0.84 (((~![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))) | ((~$greatereq(M!18, 0)) | permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1)))) <=> ((~![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))) | (~$greatereq(M!18, 0)) | permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1)))),
% 0.94/0.85 inference(rewrite,[status(thm)],[])).
% 0.94/0.85 tff(299,plain,
% 0.94/0.85 ((permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | $false | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1)) | (~$greatereq(M!18, 0)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0))) <=> ((~$greatereq(M!18, 0)) | permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1)))),
% 0.94/0.85 inference(rewrite,[status(thm)],[])).
% 0.94/0.85 tff(300,plain,
% 0.94/0.85 ((~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), 0)) <=> (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1))),
% 0.94/0.85 inference(rewrite,[status(thm)],[])).
% 0.94/0.85 tff(301,plain,
% 0.94/0.85 ((~$true) <=> $false),
% 0.94/0.85 inference(rewrite,[status(thm)],[])).
% 0.94/0.85 tff(302,plain,
% 0.94/0.85 ($lesseq(0, 0) <=> $true),
% 0.94/0.85 inference(rewrite,[status(thm)],[])).
% 0.94/0.85 tff(303,plain,
% 0.94/0.85 ($sum($sum(1, N!17), $sum(-1, $product(-1, N!17))) = 0),
% 0.94/0.85 inference(rewrite,[status(thm)],[])).
% 0.94/0.85 tff(304,plain,
% 0.94/0.85 ($sum($product(-1, 1), $product(-1, N!17)) = $sum(-1, $product(-1, N!17))),
% 0.94/0.85 inference(rewrite,[status(thm)],[])).
% 0.94/0.85 tff(305,plain,
% 0.94/0.85 ($product(-1, $sum(1, N!17)) = $sum($product(-1, 1), $product(-1, N!17))),
% 0.94/0.85 inference(rewrite,[status(thm)],[])).
% 0.94/0.85 tff(306,plain,
% 0.94/0.85 ($product(-1, $sum(1, N!17)) = $sum(-1, $product(-1, N!17))),
% 0.94/0.85 inference(transitivity,[status(thm)],[305, 304])).
% 0.94/0.85 tff(307,plain,
% 0.94/0.85 ($sum($sum(1, N!17), $product(-1, $sum(1, N!17))) = $sum($sum(1, N!17), $sum(-1, $product(-1, N!17)))),
% 0.94/0.85 inference(monotonicity,[status(thm)],[306])).
% 0.94/0.85 tff(308,plain,
% 0.94/0.85 ($sum($sum(1, N!17), $product(-1, $sum(1, N!17))) = 0),
% 0.94/0.85 inference(transitivity,[status(thm)],[307, 303])).
% 0.94/0.85 tff(309,plain,
% 0.94/0.85 ($lesseq($sum($sum(1, N!17), $product(-1, $sum(1, N!17))), 0) <=> $lesseq(0, 0)),
% 0.94/0.85 inference(monotonicity,[status(thm)],[308])).
% 0.94/0.85 tff(310,plain,
% 0.94/0.85 ($lesseq($sum($sum(1, N!17), $product(-1, $sum(1, N!17))), 0) <=> $true),
% 0.94/0.85 inference(transitivity,[status(thm)],[309, 302])).
% 0.94/0.85 tff(311,plain,
% 0.94/0.85 ((~$lesseq($sum($sum(1, N!17), $product(-1, $sum(1, N!17))), 0)) <=> (~$true)),
% 0.94/0.85 inference(monotonicity,[status(thm)],[310])).
% 0.94/0.85 tff(312,plain,
% 0.94/0.85 ((~$lesseq($sum($sum(1, N!17), $product(-1, $sum(1, N!17))), 0)) <=> $false),
% 0.94/0.85 inference(transitivity,[status(thm)],[311, 301])).
% 0.94/0.85 tff(313,plain,
% 0.94/0.85 ((permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~$lesseq($sum($sum(1, N!17), $product(-1, $sum(1, N!17))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), 0)) | (~$greatereq(M!18, 0)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0))) <=> (permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | $false | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1)) | (~$greatereq(M!18, 0)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0)))),
% 0.94/0.85 inference(monotonicity,[status(thm)],[312, 300])).
% 0.94/0.85 tff(314,plain,
% 0.94/0.85 ((permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~$lesseq($sum($sum(1, N!17), $product(-1, $sum(1, N!17))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), 0)) | (~$greatereq(M!18, 0)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0))) <=> ((~$greatereq(M!18, 0)) | permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1)))),
% 0.94/0.85 inference(transitivity,[status(thm)],[313, 299])).
% 0.94/0.85 tff(315,plain,
% 0.94/0.85 (((~![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))) | (permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~$lesseq($sum($sum(1, N!17), $product(-1, $sum(1, N!17))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), 0)) | (~$greatereq(M!18, 0)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0)))) <=> ((~![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))) | ((~$greatereq(M!18, 0)) | permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1))))),
% 0.94/0.85 inference(monotonicity,[status(thm)],[314])).
% 0.94/0.85 tff(316,plain,
% 0.94/0.85 (((~![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))) | (permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~$lesseq($sum($sum(1, N!17), $product(-1, $sum(1, N!17))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), 0)) | (~$greatereq(M!18, 0)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0)))) <=> ((~![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))) | (~$greatereq(M!18, 0)) | permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1)))),
% 0.94/0.85 inference(transitivity,[status(thm)],[315, 298])).
% 0.94/0.85 tff(317,plain,
% 0.94/0.85 ((~![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))) | (permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~$lesseq($sum($sum(1, N!17), $product(-1, $sum(1, N!17))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), 0)) | (~$greatereq(M!18, 0)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0)))),
% 0.94/0.85 inference(quant_inst,[status(thm)],[])).
% 0.94/0.85 tff(318,plain,
% 0.94/0.85 ((~![A1: array_int, A2: array_int, L1: $int, U1: $int, L2: $int, U2: $int] : (permut_sub3(A1, A2, L2, U2) | (~$lesseq($sum(U1, $product(-1, U2)), 0)) | (~$lesseq($sum(U2, $product(-1, length1(int, t2tb2(A1)))), 0)) | (~$greatereq(L2, 0)) | (~permut_sub3(A1, A2, L1, U1)) | (~$lesseq($sum(L2, $product(-1, L1)), 0)))) | (~$greatereq(M!18, 0)) | permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17))) | (~$lesseq($sum(M!18, $product(-1, I!22)), 0)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))), -1))),
% 0.94/0.85 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.94/0.85 tff(319,plain,
% 0.94/0.85 (permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), I!22, $sum(1, N!17)))),
% 0.94/0.85 inference(unit_resolution,[status(thm)],[318, 297, 80, 281, 257])).
% 0.94/0.85 tff(320,plain,
% 0.94/0.85 ($false),
% 0.94/0.85 inference(unit_resolution,[status(thm)],[319, 253, 250])).
% 0.94/0.85 tff(321,plain,(permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))), inference(lemma,lemma(discharge,[]))).
% 0.94/0.85 tff(322,plain,
% 0.94/0.85 ((~(permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), 0, M!18)) | (~permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), $sum(1, N!17), length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))))))) | (~permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), 0, M!18)) | (~permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), $sum(1, N!17), length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))))))))),
% 0.94/0.85 inference(tautology,[status(thm)],[])).
% 0.94/0.85 tff(323,plain,
% 0.94/0.85 ((~(permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) <=> (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), 0, M!18)) | (~permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), $sum(1, N!17), length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))))))) | (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), 0, M!18)) | (~permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), $sum(1, N!17), length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))))))))),
% 0.94/0.85 inference(unit_resolution,[status(thm)],[322, 321])).
% 0.94/0.85 tff(324,plain,
% 0.94/0.85 (~((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), 0, M!18)) | (~permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), $sum(1, N!17), length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))))))),
% 0.94/0.85 inference(unit_resolution,[status(thm)],[323, 249])).
% 0.94/0.85 tff(325,plain,
% 0.94/0.85 (((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), 0, M!18)) | (~permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))))), elts(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))))), $sum(1, N!17), length1(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))))))) | permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17))),
% 0.94/0.85 inference(tautology,[status(thm)],[])).
% 0.94/0.85 tff(326,plain,
% 0.94/0.85 (permut3(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25)))))), M!18, $sum(1, N!17))),
% 0.94/0.85 inference(unit_resolution,[status(thm)],[325, 324])).
% 0.94/0.85 tff(327,plain,
% 0.94/0.85 (permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17))),
% 0.94/0.85 inference(modus_ponens,[status(thm)],[326, 247])).
% 0.94/0.85 tff(328,plain,
% 0.94/0.85 ((~(permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17)) <=> (~((~$greatereq(M!18, 0)) | (~$greatereq(N!17, -1)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~$lesseq($sum(N!17, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), -1)))))) | (~permut3(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), M!18, $sum(1, N!17))) | (~((~$greatereq(M!18, 0)) | (~$greatereq(N!17, -1)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~$lesseq($sum(N!17, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), -1))))),
% 0.94/0.86 inference(tautology,[status(thm)],[])).
% 0.94/0.86 tff(329,plain,
% 0.94/0.86 (~((~$greatereq(M!18, 0)) | (~$greatereq(N!17, -1)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~$lesseq($sum(N!17, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), -1)))),
% 0.94/0.86 inference(unit_resolution,[status(thm)],[328, 327, 226])).
% 0.94/0.86 tff(330,plain,
% 0.94/0.86 (((~$greatereq(M!18, 0)) | (~$greatereq(N!17, -1)) | (~($sum(length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))))) = 0)) | (~$lesseq($sum(M!18, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), 0)) | (~permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))) | (~$lesseq($sum(N!17, $product(-1, length1(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))))), -1))) | permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))),
% 0.94/0.86 inference(tautology,[status(thm)],[])).
% 0.94/0.86 tff(331,plain,
% 0.94/0.86 (permut2(int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17))),
% 0.94/0.86 inference(unit_resolution,[status(thm)],[330, 329])).
% 0.94/0.86 tff(332,plain,
% 0.94/0.86 (permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))),
% 0.94/0.86 inference(modus_ponens,[status(thm)],[331, 203])).
% 0.94/0.86 tff(333,plain,
% 0.94/0.86 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : refl(($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))))) <=> ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))))))),
% 0.94/0.86 inference(bind,[status(th)],[])).
% 0.94/0.86 tff(334,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))),
% 0.94/0.86 inference(quant_intro,[status(thm)],[333])).
% 0.94/0.86 tff(335,plain,
% 0.94/0.86 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : trans(monotonicity(trans(monotonicity(rewrite(($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0))) <=> (~((~$lesseq($sum(L, $product(-1, I)), 0)) | $lesseq($sum(U, $product(-1, I)), 0)))), ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) <=> (~(~((~$lesseq($sum(L, $product(-1, I)), 0)) | $lesseq($sum(U, $product(-1, I)), 0)))))), rewrite((~(~((~$lesseq($sum(L, $product(-1, I)), 0)) | $lesseq($sum(U, $product(-1, I)), 0)))) <=> ((~$lesseq($sum(L, $product(-1, I)), 0)) | $lesseq($sum(U, $product(-1, I)), 0))), ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) <=> ((~$lesseq($sum(L, $product(-1, I)), 0)) | $lesseq($sum(U, $product(-1, I)), 0)))), rewrite(($lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) & (get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))) <=> (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))))), (((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ($lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) & (get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))) <=> ((~permut2(A, A1, A2, L, U)) | ((~$lesseq($sum(L, $product(-1, I)), 0)) | $lesseq($sum(U, $product(-1, I)), 0)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))))))), rewrite(((~permut2(A, A1, A2, L, U)) | ((~$lesseq($sum(L, $product(-1, I)), 0)) | $lesseq($sum(U, $product(-1, I)), 0)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))))) <=> ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))), (((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ($lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) & (get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))) <=> ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))))),
% 0.94/0.86 inference(bind,[status(th)],[])).
% 0.94/0.86 tff(336,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ($lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) & (get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))),
% 0.94/0.86 inference(quant_intro,[status(thm)],[335])).
% 0.94/0.86 tff(337,plain,
% 0.94/0.86 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : rewrite(((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ($greatereq($sum(tptp_fun_J_8(I, U, L, A2, A1, A), $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) & (get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))) <=> ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ($lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) & (get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))))),
% 0.94/0.86 inference(bind,[status(th)],[])).
% 0.94/0.86 tff(338,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ($greatereq($sum(tptp_fun_J_8(I, U, L, A2, A1, A), $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) & (get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ($lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) & (get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))),
% 0.94/0.86 inference(quant_intro,[status(thm)],[337])).
% 0.94/0.86 tff(339,plain,
% 0.94/0.86 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : rewrite(((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ?[J: $int] : ($lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))) <=> ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ?[J: $int] : ($greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))))),
% 0.94/0.86 inference(bind,[status(th)],[])).
% 0.94/0.86 tff(340,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ?[J: $int] : ($lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ?[J: $int] : ($greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))),
% 0.94/0.86 inference(quant_intro,[status(thm)],[339])).
% 0.94/0.86 tff(341,plain,
% 0.94/0.86 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : rewrite(((~permut2(A, A1, A2, L, U)) | (~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))) <=> ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ?[J: $int] : ($lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))))),
% 0.94/0.86 inference(bind,[status(th)],[])).
% 0.94/0.86 tff(342,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ?[J: $int] : ($lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))),
% 0.94/0.86 inference(quant_intro,[status(thm)],[341])).
% 0.94/0.86 tff(343,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))),
% 0.94/0.86 inference(rewrite,[status(thm)],[])).
% 0.94/0.86 tff(344,plain,
% 0.94/0.86 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : trans(monotonicity(trans(monotonicity(rewrite(($lesseq(L, I) & $less(I, U)) <=> ($lesseq(L, I) & (~$lesseq(U, I)))), quant_intro(proof_bind(^[J: $int] : trans(monotonicity(rewrite(($lesseq(L, J) & $less(J, U)) <=> ($lesseq(L, J) & (~$lesseq(U, J)))), ((($lesseq(L, J) & $less(J, U)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))) <=> (($lesseq(L, J) & (~$lesseq(U, J))) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))), rewrite((($lesseq(L, J) & (~$lesseq(U, J))) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))) <=> ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))), ((($lesseq(L, J) & $less(J, U)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))) <=> ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))))), (?[J: $int] : (($lesseq(L, J) & $less(J, U)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))) <=> ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))), ((($lesseq(L, I) & $less(I, U)) => ?[J: $int] : (($lesseq(L, J) & $less(J, U)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))) <=> (($lesseq(L, I) & (~$lesseq(U, I))) => ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))))), rewrite((($lesseq(L, I) & (~$lesseq(U, I))) => ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))) <=> ((~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))), ((($lesseq(L, I) & $less(I, U)) => ?[J: $int] : (($lesseq(L, J) & $less(J, U)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))) <=> ((~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))))), ((permut2(A, A1, A2, L, U) => (($lesseq(L, I) & $less(I, U)) => ?[J: $int] : (($lesseq(L, J) & $less(J, U)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))) <=> (permut2(A, A1, A2, L, U) => ((~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))))), rewrite((permut2(A, A1, A2, L, U) => ((~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))) <=> ((~permut2(A, A1, A2, L, U)) | (~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))), ((permut2(A, A1, A2, L, U) => (($lesseq(L, I) & $less(I, U)) => ?[J: $int] : (($lesseq(L, J) & $less(J, U)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))) <=> ((~permut2(A, A1, A2, L, U)) | (~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))))),
% 0.94/0.86 inference(bind,[status(th)],[])).
% 0.94/0.86 tff(345,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : (permut2(A, A1, A2, L, U) => (($lesseq(L, I) & $less(I, U)) => ?[J: $int] : (($lesseq(L, J) & $less(J, U)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))),
% 0.94/0.86 inference(quant_intro,[status(thm)],[344])).
% 0.94/0.86 tff(346,axiom,(![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : (permut2(A, A1, A2, L, U) => (($lesseq(L, I) & $less(I, U)) => ?[J: $int] : (($lesseq(L, J) & $less(J, U)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permut_exists1')).
% 0.94/0.86 tff(347,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))),
% 0.94/0.86 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.94/0.86 tff(348,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq(L, I) & (~$lesseq(U, I)))) | ?[J: $int] : ($lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))),
% 0.94/0.86 inference(modus_ponens,[status(thm)],[347, 343])).
% 0.94/0.86 tff(349,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ?[J: $int] : ($lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))),
% 0.94/0.86 inference(modus_ponens,[status(thm)],[348, 342])).
% 0.94/0.86 tff(350,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ?[J: $int] : ($greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb1(J)) = get(A, int, A2, t2tb1(I)))))),
% 0.94/0.86 inference(modus_ponens,[status(thm)],[349, 340])).
% 0.94/0.86 tff(351,plain,(
% 0.94/0.86 ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ($greatereq($sum(tptp_fun_J_8(I, U, L, A2, A1, A), $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) & (get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))),
% 0.94/0.86 inference(skolemize,[status(sab)],[350])).
% 0.94/0.86 tff(352,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ((~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | ($lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) & (get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))),
% 0.94/0.86 inference(modus_ponens,[status(thm)],[351, 338])).
% 0.94/0.86 tff(353,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))),
% 0.94/0.86 inference(modus_ponens,[status(thm)],[352, 336])).
% 0.94/0.86 tff(354,plain,
% 0.94/0.86 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))),
% 0.94/0.86 inference(modus_ponens,[status(thm)],[353, 334])).
% 0.94/0.86 tff(355,plain,
% 0.94/0.86 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | ((~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))),
% 0.94/0.86 inference(rewrite,[status(thm)],[])).
% 0.94/0.86 tff(356,plain,
% 0.94/0.86 (($lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)))) <=> ((~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))),
% 0.94/0.86 inference(rewrite,[status(thm)],[])).
% 0.94/0.86 tff(357,plain,
% 0.94/0.86 ((~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))))) <=> (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)))),
% 0.94/0.86 inference(rewrite,[status(thm)],[])).
% 0.94/0.86 tff(358,plain,
% 0.94/0.86 ($lesseq($sum(1, $sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))), 0) <=> $lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1)),
% 0.94/0.86 inference(rewrite,[status(thm)],[])).
% 0.94/0.86 tff(359,plain,
% 0.94/0.86 ($sum($sum(1, N!17), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = $sum(1, $sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))),
% 0.94/0.86 inference(rewrite,[status(thm)],[])).
% 0.94/0.86 tff(360,plain,
% 0.94/0.86 ($lesseq($sum($sum(1, N!17), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) <=> $lesseq($sum(1, $sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))), 0)),
% 0.94/0.86 inference(monotonicity,[status(thm)],[359])).
% 0.94/0.86 tff(361,plain,
% 0.94/0.86 ($lesseq($sum($sum(1, N!17), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) <=> $lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1)),
% 0.94/0.86 inference(transitivity,[status(thm)],[360, 358])).
% 0.94/0.86 tff(362,plain,
% 0.94/0.86 (($lesseq($sum($sum(1, N!17), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | (~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))))))) <=> ($lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[361, 357])).
% 0.94/0.87 tff(363,plain,
% 0.94/0.87 (($lesseq($sum($sum(1, N!17), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | (~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))))))) <=> ((~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))),
% 0.94/0.87 inference(transitivity,[status(thm)],[362, 356])).
% 0.94/0.87 tff(364,plain,
% 0.94/0.87 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | ($lesseq($sum($sum(1, N!17), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | (~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | ((~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)))))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[363])).
% 0.94/0.87 tff(365,plain,
% 0.94/0.87 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | ($lesseq($sum($sum(1, N!17), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | (~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))),
% 0.94/0.87 inference(transitivity,[status(thm)],[364, 355])).
% 0.94/0.87 tff(366,plain,
% 0.94/0.87 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | ($lesseq($sum($sum(1, N!17), $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | (~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))))))),
% 0.94/0.87 inference(quant_inst,[status(thm)],[])).
% 0.94/0.87 tff(367,plain,
% 0.94/0.87 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), M!18, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.94/0.87 tff(368,plain,
% 0.94/0.87 ($lesseq($sum(N!17, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), -1) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)))),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[367, 354, 332])).
% 0.94/0.87 tff(369,plain,
% 0.94/0.87 (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[368, 200, 197])).
% 0.94/0.87 tff(370,plain,
% 0.94/0.87 (((~$lesseq($sum(M!18, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))))),
% 0.94/0.87 inference(tautology,[status(thm)],[])).
% 0.94/0.87 tff(371,plain,
% 0.94/0.87 (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[370, 369])).
% 0.94/0.87 tff(372,plain,
% 0.94/0.87 (tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)) = tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))),
% 0.94/0.87 inference(theory_lemma,[status(thm)],[109, 102])).
% 0.94/0.87 tff(373,plain,
% 0.94/0.87 (tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))) = tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))),
% 0.94/0.87 inference(symmetry,[status(thm)],[372])).
% 0.94/0.87 tff(374,plain,
% 0.94/0.87 (tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int) = tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)),
% 0.94/0.87 inference(monotonicity,[status(thm)],[373])).
% 0.94/0.87 tff(375,plain,
% 0.94/0.87 (t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)) = t2tb1(tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[374])).
% 0.94/0.87 tff(376,plain,
% 0.94/0.87 (t2tb1(tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)) = t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))),
% 0.94/0.87 inference(symmetry,[status(thm)],[375])).
% 0.94/0.87 tff(377,plain,
% 0.94/0.87 (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[376])).
% 0.94/0.87 tff(378,plain,
% 0.94/0.87 (get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[182])).
% 0.94/0.87 tff(379,plain,
% 0.94/0.87 ((~![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))) | (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))))),
% 0.94/0.87 inference(quant_inst,[status(thm)],[])).
% 0.94/0.87 tff(380,plain,
% 0.94/0.87 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[379, 18])).
% 0.94/0.87 tff(381,plain,
% 0.94/0.87 (get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)) = get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[180])).
% 0.94/0.87 tff(382,plain,
% 0.94/0.87 (get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)) = get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))),
% 0.94/0.87 inference(transitivity,[status(thm)],[381, 380, 378, 377, 371, 32, 21, 11])).
% 0.94/0.87 tff(383,plain,
% 0.94/0.87 (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[382])).
% 0.94/0.87 tff(384,plain,
% 0.94/0.87 (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))))),
% 0.94/0.87 inference(transitivity,[status(thm)],[383, 189])).
% 0.94/0.87 tff(385,plain,
% 0.94/0.87 ((tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = 42) <=> (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42)),
% 0.94/0.87 inference(monotonicity,[status(thm)],[384])).
% 0.94/0.87 tff(386,plain,
% 0.94/0.87 ((~(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = 42)) <=> (~(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[385])).
% 0.94/0.87 tff(387,plain,
% 0.94/0.88 (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))) = tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))),
% 0.94/0.88 inference(symmetry,[status(thm)],[383])).
% 0.94/0.88 tff(388,plain,
% 0.94/0.88 ((~(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))) = tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))))) | $lesseq($sum(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))))), 0)),
% 0.94/0.88 inference(theory_lemma,[status(thm)],[])).
% 0.94/0.88 tff(389,plain,
% 0.94/0.88 ($lesseq($sum(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))))), 0)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[388, 387])).
% 0.94/0.88 tff(390,plain,
% 0.94/0.88 ((~$lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42) | (~$lesseq($sum(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))))), 0))),
% 0.94/0.88 inference(theory_lemma,[status(thm)],[])).
% 0.94/0.88 tff(391,plain,
% 0.94/0.88 (~$lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[390, 389, 193])).
% 0.94/0.88 tff(392,plain,
% 0.94/0.88 ((~(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = 42)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42)),
% 0.94/0.88 inference(theory_lemma,[status(thm)],[])).
% 0.94/0.88 tff(393,plain,
% 0.94/0.88 (~(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)), $sum(1, N!17), M!18, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = 42)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[392, 391])).
% 0.94/0.88 tff(394,plain,
% 0.94/0.88 (~(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[393, 386])).
% 0.94/0.88 tff(395,plain,
% 0.94/0.88 (^[T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : rewrite((~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))))) <=> (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(396,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))))) <=> ![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[395])).
% 0.94/0.88 tff(397,plain,
% 0.94/0.88 (^[T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : refl((~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))))) <=> (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(398,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))))) <=> ![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))))))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[397])).
% 0.94/0.88 tff(399,plain,
% 0.94/0.88 (^[T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : rewrite((~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))))) <=> (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(400,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))))) <=> ![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))))))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[399])).
% 0.94/0.88 tff(401,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))))) <=> ![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))))))),
% 0.94/0.88 inference(transitivity,[status(thm)],[400, 398])).
% 0.94/0.88 tff(402,plain,
% 0.94/0.88 (^[T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : trans(monotonicity(rewrite(((~qs_partition1(T1, T2, M, N, I, J, X)) | (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) <=> ((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))), trans(monotonicity(rewrite((~((~($lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) <=> (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))))), rewrite((~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) <=> (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)))), rewrite((~((~($lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0) & $greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0))) <=> (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))), ((qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~((~($lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0) & $greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0)))) <=> (qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))))), rewrite((qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))) <=> (qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))), ((qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~((~($lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0) & $greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0)))) <=> (qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))))), ((((~qs_partition1(T1, T2, M, N, I, J, X)) | (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) & (qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~((~($lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0) & $greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0))))) <=> (((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))) & (qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))))), rewrite((((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))) & (qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) <=> (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))))))), ((((~qs_partition1(T1, T2, M, N, I, J, X)) | (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) & (qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~((~($lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0) & $greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0))))) <=> (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))))))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(403,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (((~qs_partition1(T1, T2, M, N, I, J, X)) | (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) & (qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~((~($lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0) & $greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0))))) <=> ![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))))))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[402])).
% 0.94/0.88 tff(404,plain,
% 0.94/0.88 (^[T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : rewrite((((~qs_partition1(T1, T2, M, N, I, J, X)) | (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) & (qs_partition1(T1, T2, M, N, I, J, X) | ((~permut_sub3(T1, T2, M, $sum(1, N))) | (~((~($greatereq($sum(tptp_fun_K_14(X, J, M, T2), $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$greatereq($sum(tptp_fun_K_15(X, J, I, T2), $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) | (~((~($greatereq($sum(tptp_fun_K_16(X, I, N, T2), $product(-1, I)), 0) & $lesseq($sum(tptp_fun_K_16(X, I, N, T2), $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0)))))) <=> (((~qs_partition1(T1, T2, M, N, I, J, X)) | (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) & (qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~((~($lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0) & $greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0))))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(405,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (((~qs_partition1(T1, T2, M, N, I, J, X)) | (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) & (qs_partition1(T1, T2, M, N, I, J, X) | ((~permut_sub3(T1, T2, M, $sum(1, N))) | (~((~($greatereq($sum(tptp_fun_K_14(X, J, M, T2), $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$greatereq($sum(tptp_fun_K_15(X, J, I, T2), $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) | (~((~($greatereq($sum(tptp_fun_K_16(X, I, N, T2), $product(-1, I)), 0) & $lesseq($sum(tptp_fun_K_16(X, I, N, T2), $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0)))))) <=> ![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (((~qs_partition1(T1, T2, M, N, I, J, X)) | (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) & (qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~((~($lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0) & $greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0)))))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[404])).
% 0.94/0.88 tff(406,plain,
% 0.94/0.88 (^[T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : rewrite((qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq($sum(M, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, J)), 0))) | $lesseq($sum(tb2t1(get4(int, t2tb2(T2), K)), $product(-1, X)), 0)) & ![K: $int] : ((~((~$lesseq($sum(K, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | ($sum(tb2t1(get4(int, t2tb2(T2), K)), $product(-1, X)) = 0)) & ![K: $int] : ((~($lesseq($sum(I, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) <=> (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(407,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq($sum(M, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, J)), 0))) | $lesseq($sum(tb2t1(get4(int, t2tb2(T2), K)), $product(-1, X)), 0)) & ![K: $int] : ((~((~$lesseq($sum(K, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | ($sum(tb2t1(get4(int, t2tb2(T2), K)), $product(-1, X)) = 0)) & ![K: $int] : ((~($lesseq($sum(I, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) <=> ![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0))))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[406])).
% 0.94/0.88 tff(408,plain,
% 0.94/0.88 (^[T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : rewrite((qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq(M, K) & $lesseq(K, J))) | $lesseq(tb2t1(get4(int, t2tb2(T2), K)), X)) & ![K: $int] : ((~((~$lesseq(K, J)) & (~$lesseq(I, K)))) | (tb2t1(get4(int, t2tb2(T2), K)) = X)) & ![K: $int] : ((~($lesseq(I, K) & $lesseq(K, N))) | $lesseq(X, tb2t1(get4(int, t2tb2(T2), K)))))) <=> (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq($sum(M, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, J)), 0))) | $lesseq($sum(tb2t1(get4(int, t2tb2(T2), K)), $product(-1, X)), 0)) & ![K: $int] : ((~((~$lesseq($sum(K, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | ($sum(tb2t1(get4(int, t2tb2(T2), K)), $product(-1, X)) = 0)) & ![K: $int] : ((~($lesseq($sum(I, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(409,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq(M, K) & $lesseq(K, J))) | $lesseq(tb2t1(get4(int, t2tb2(T2), K)), X)) & ![K: $int] : ((~((~$lesseq(K, J)) & (~$lesseq(I, K)))) | (tb2t1(get4(int, t2tb2(T2), K)) = X)) & ![K: $int] : ((~($lesseq(I, K) & $lesseq(K, N))) | $lesseq(X, tb2t1(get4(int, t2tb2(T2), K)))))) <=> ![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq($sum(M, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, J)), 0))) | $lesseq($sum(tb2t1(get4(int, t2tb2(T2), K)), $product(-1, X)), 0)) & ![K: $int] : ((~((~$lesseq($sum(K, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | ($sum(tb2t1(get4(int, t2tb2(T2), K)), $product(-1, X)) = 0)) & ![K: $int] : ((~($lesseq($sum(I, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0))))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[408])).
% 0.94/0.88 tff(410,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq(M, K) & $lesseq(K, J))) | $lesseq(tb2t1(get4(int, t2tb2(T2), K)), X)) & ![K: $int] : ((~((~$lesseq(K, J)) & (~$lesseq(I, K)))) | (tb2t1(get4(int, t2tb2(T2), K)) = X)) & ![K: $int] : ((~($lesseq(I, K) & $lesseq(K, N))) | $lesseq(X, tb2t1(get4(int, t2tb2(T2), K)))))) <=> ![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq(M, K) & $lesseq(K, J))) | $lesseq(tb2t1(get4(int, t2tb2(T2), K)), X)) & ![K: $int] : ((~((~$lesseq(K, J)) & (~$lesseq(I, K)))) | (tb2t1(get4(int, t2tb2(T2), K)) = X)) & ![K: $int] : ((~($lesseq(I, K) & $lesseq(K, N))) | $lesseq(X, tb2t1(get4(int, t2tb2(T2), K))))))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(411,plain,
% 0.94/0.88 (^[T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : rewrite((qs_partition1(T1, T2, M, N, I, J, X) <=> (((permut_sub3(T1, T2, M, $sum(N, 1)) & ![K: $int] : (($lesseq(M, K) & $lesseq(K, J)) => $lesseq(tb2t1(get4(int, t2tb2(T2), K)), X))) & ![K: $int] : (($less(J, K) & $less(K, I)) => (tb2t1(get4(int, t2tb2(T2), K)) = X))) & ![K: $int] : (($lesseq(I, K) & $lesseq(K, N)) => $lesseq(X, tb2t1(get4(int, t2tb2(T2), K)))))) <=> (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq(M, K) & $lesseq(K, J))) | $lesseq(tb2t1(get4(int, t2tb2(T2), K)), X)) & ![K: $int] : ((~((~$lesseq(K, J)) & (~$lesseq(I, K)))) | (tb2t1(get4(int, t2tb2(T2), K)) = X)) & ![K: $int] : ((~($lesseq(I, K) & $lesseq(K, N))) | $lesseq(X, tb2t1(get4(int, t2tb2(T2), K)))))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(412,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (((permut_sub3(T1, T2, M, $sum(N, 1)) & ![K: $int] : (($lesseq(M, K) & $lesseq(K, J)) => $lesseq(tb2t1(get4(int, t2tb2(T2), K)), X))) & ![K: $int] : (($less(J, K) & $less(K, I)) => (tb2t1(get4(int, t2tb2(T2), K)) = X))) & ![K: $int] : (($lesseq(I, K) & $lesseq(K, N)) => $lesseq(X, tb2t1(get4(int, t2tb2(T2), K)))))) <=> ![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq(M, K) & $lesseq(K, J))) | $lesseq(tb2t1(get4(int, t2tb2(T2), K)), X)) & ![K: $int] : ((~((~$lesseq(K, J)) & (~$lesseq(I, K)))) | (tb2t1(get4(int, t2tb2(T2), K)) = X)) & ![K: $int] : ((~($lesseq(I, K) & $lesseq(K, N))) | $lesseq(X, tb2t1(get4(int, t2tb2(T2), K))))))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[411])).
% 0.94/0.88 tff(413,axiom,(![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (((permut_sub3(T1, T2, M, $sum(N, 1)) & ![K: $int] : (($lesseq(M, K) & $lesseq(K, J)) => $lesseq(tb2t1(get4(int, t2tb2(T2), K)), X))) & ![K: $int] : (($less(J, K) & $less(K, I)) => (tb2t1(get4(int, t2tb2(T2), K)) = X))) & ![K: $int] : (($lesseq(I, K) & $lesseq(K, N)) => $lesseq(X, tb2t1(get4(int, t2tb2(T2), K))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qs_partition_def')).
% 0.94/0.88 tff(414,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq(M, K) & $lesseq(K, J))) | $lesseq(tb2t1(get4(int, t2tb2(T2), K)), X)) & ![K: $int] : ((~((~$lesseq(K, J)) & (~$lesseq(I, K)))) | (tb2t1(get4(int, t2tb2(T2), K)) = X)) & ![K: $int] : ((~($lesseq(I, K) & $lesseq(K, N))) | $lesseq(X, tb2t1(get4(int, t2tb2(T2), K))))))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.94/0.88 tff(415,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq(M, K) & $lesseq(K, J))) | $lesseq(tb2t1(get4(int, t2tb2(T2), K)), X)) & ![K: $int] : ((~((~$lesseq(K, J)) & (~$lesseq(I, K)))) | (tb2t1(get4(int, t2tb2(T2), K)) = X)) & ![K: $int] : ((~($lesseq(I, K) & $lesseq(K, N))) | $lesseq(X, tb2t1(get4(int, t2tb2(T2), K))))))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[414, 410])).
% 0.94/0.88 tff(416,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($lesseq($sum(M, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, J)), 0))) | $lesseq($sum(tb2t1(get4(int, t2tb2(T2), K)), $product(-1, X)), 0)) & ![K: $int] : ((~((~$lesseq($sum(K, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | ($sum(tb2t1(get4(int, t2tb2(T2), K)), $product(-1, X)) = 0)) & ![K: $int] : ((~($lesseq($sum(I, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0))))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[415, 409])).
% 0.94/0.88 tff(417,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (qs_partition1(T1, T2, M, N, I, J, X) <=> (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0))))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[416, 407])).
% 0.94/0.88 tff(418,plain,(
% 0.94/0.88 ![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (((~qs_partition1(T1, T2, M, N, I, J, X)) | (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) & (qs_partition1(T1, T2, M, N, I, J, X) | ((~permut_sub3(T1, T2, M, $sum(1, N))) | (~((~($greatereq($sum(tptp_fun_K_14(X, J, M, T2), $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$greatereq($sum(tptp_fun_K_15(X, J, I, T2), $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) | (~((~($greatereq($sum(tptp_fun_K_16(X, I, N, T2), $product(-1, I)), 0) & $lesseq($sum(tptp_fun_K_16(X, I, N, T2), $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0))))))),
% 0.94/0.88 inference(skolemize,[status(sab)],[417])).
% 0.94/0.88 tff(419,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (((~qs_partition1(T1, T2, M, N, I, J, X)) | (permut_sub3(T1, T2, M, $sum(1, N)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)) & ![K: $int] : ((~((~$greatereq($sum(J, $product(-1, K)), 0)) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & $lesseq($sum(K, $product(-1, N)), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0)))) & (qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~((~($lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0))) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)) & (~$lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0)))) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0))) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0) & $greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0)))))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[418, 405])).
% 0.94/0.88 tff(420,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))))))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[419, 403])).
% 0.94/0.88 tff(421,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0)))))))) | (~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0))))))))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[420, 401])).
% 0.94/0.88 tff(422,plain,
% 0.94/0.88 (![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[421, 396])).
% 0.94/0.88 tff(423,plain,
% 0.94/0.88 (((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42)))))))))) <=> ((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))))))))))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(424,plain,
% 0.94/0.89 ((~((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~($greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))))) = 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0))) | (~($lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$greatereq($sum(J!23, $product(-1, K)), 0)) | $greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))), 0) | (~$greatereq($sum(K, $product(-1, M!18)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I!22)), 0) | $greatereq($sum(J!23, $product(-1, K)), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | $lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))), 0) | (~$lesseq($sum(K, $product(-1, N!17)), 0)))))))))) <=> (~((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42)))))))))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(425,plain,
% 0.94/0.89 (((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~($greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))))) = 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0))) | (~($lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$greatereq($sum(J!23, $product(-1, K)), 0)) | $greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))), 0) | (~$greatereq($sum(K, $product(-1, M!18)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I!22)), 0) | $greatereq($sum(J!23, $product(-1, K)), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | $lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))), 0) | (~$lesseq($sum(K, $product(-1, N!17)), 0))))))))))) <=> ((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))))))))))),
% 0.94/0.89 inference(monotonicity,[status(thm)],[424])).
% 0.94/0.89 tff(426,plain,
% 0.94/0.89 (((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~($greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))))) = 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0))) | (~($lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$greatereq($sum(J!23, $product(-1, K)), 0)) | $greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))), 0) | (~$greatereq($sum(K, $product(-1, M!18)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I!22)), 0) | $greatereq($sum(J!23, $product(-1, K)), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | $lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))), 0) | (~$lesseq($sum(K, $product(-1, N!17)), 0))))))))))) <=> ((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))))))))))),
% 0.94/0.89 inference(transitivity,[status(thm)],[425, 423])).
% 0.94/0.89 tff(427,plain,
% 0.94/0.89 ((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~($greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))))) = 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0))) | (~($lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$greatereq($sum(J!23, $product(-1, K)), 0)) | $greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))), 0) | (~$greatereq($sum(K, $product(-1, M!18)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I!22)), 0) | $greatereq($sum(J!23, $product(-1, K)), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | $lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)))), 0) | (~$lesseq($sum(K, $product(-1, N!17)), 0))))))))))),
% 0.94/0.89 inference(quant_inst,[status(thm)],[])).
% 0.94/0.89 tff(428,plain,
% 0.94/0.89 ((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42)))))))))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.94/0.90 tff(429,plain,
% 0.94/0.90 (~((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))))))))),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[428, 422])).
% 0.94/0.90 tff(430,plain,
% 0.94/0.90 (((~(qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A3!24)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A3!24)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A3!24)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42)))))))) | ((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))))))),
% 0.94/0.90 inference(tautology,[status(thm)],[])).
% 0.94/0.90 tff(431,plain,
% 0.94/0.90 ((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42)))))),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[430, 429])).
% 0.94/0.90 tff(432,plain,
% 0.94/0.90 (qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)),
% 0.94/0.90 inference(and_elim,[status(thm)],[79])).
% 0.94/0.90 tff(433,plain,
% 0.94/0.90 ((~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))))))) | (~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42)))))),
% 0.94/0.90 inference(tautology,[status(thm)],[])).
% 0.94/0.90 tff(434,plain,
% 0.94/0.90 ((~((~qs_partition1(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))))))) | (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42)))))),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[433, 432])).
% 0.94/0.90 tff(435,plain,
% 0.94/0.90 (~((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))))),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[434, 431])).
% 0.94/0.90 tff(436,plain,
% 0.94/0.90 (((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42)))) | ![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))),
% 0.94/0.90 inference(tautology,[status(thm)],[])).
% 0.94/0.90 tff(437,plain,
% 0.94/0.90 (![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[436, 435])).
% 0.94/0.90 tff(438,plain,
% 0.94/0.90 (((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | ($lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | $greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42))) <=> ((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | $greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(439,plain,
% 0.94/0.90 (($greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42)) <=> ($lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | $greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(440,plain,
% 0.94/0.90 ($greatereq($sum($product(-1, I!22), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))), 0) <=> $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(441,plain,
% 0.94/0.90 ($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)) = $sum($product(-1, I!22), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(442,plain,
% 0.94/0.90 ($greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)), 0) <=> $greatereq($sum($product(-1, I!22), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))), 0)),
% 0.94/0.90 inference(monotonicity,[status(thm)],[441])).
% 0.94/0.90 tff(443,plain,
% 0.94/0.90 ($greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)), 0) <=> $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.94/0.90 inference(transitivity,[status(thm)],[442, 440])).
% 0.94/0.90 tff(444,plain,
% 0.94/0.90 ($lesseq($sum($product(-1, J!23), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))), 0) <=> $greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(445,plain,
% 0.94/0.90 ($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)) = $sum($product(-1, J!23), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(446,plain,
% 0.94/0.90 ($lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0) <=> $lesseq($sum($product(-1, J!23), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25))))), 0)),
% 0.94/0.90 inference(monotonicity,[status(thm)],[445])).
% 0.94/0.90 tff(447,plain,
% 0.94/0.90 ($lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0) <=> $greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.94/0.90 inference(transitivity,[status(thm)],[446, 444])).
% 0.94/0.90 tff(448,plain,
% 0.94/0.90 (($lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42)) <=> ($greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42))),
% 0.94/0.90 inference(monotonicity,[status(thm)],[447, 443])).
% 0.94/0.90 tff(449,plain,
% 0.94/0.90 (($lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42)) <=> ($lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | $greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42))),
% 0.94/0.90 inference(transitivity,[status(thm)],[448, 439])).
% 0.94/0.90 tff(450,plain,
% 0.94/0.90 (((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | ($lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42))) <=> ((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | ($lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | $greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42)))),
% 0.94/0.90 inference(monotonicity,[status(thm)],[449])).
% 0.94/0.90 tff(451,plain,
% 0.94/0.90 (((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | ($lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42))) <=> ((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | $greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42))),
% 0.94/0.90 inference(transitivity,[status(thm)],[450, 438])).
% 0.94/0.90 tff(452,plain,
% 0.94/0.90 ((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | ($lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0) | $greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42))),
% 0.94/0.90 inference(quant_inst,[status(thm)],[])).
% 0.94/0.90 tff(453,plain,
% 0.94/0.90 ((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | $lesseq($sum(I!22, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | $greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.94/0.90 tff(454,plain,
% 0.94/0.90 ($greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))) = 42)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[453, 437, 114])).
% 0.94/0.90 tff(455,plain,
% 0.94/0.90 ($greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[454, 394])).
% 0.94/0.90 tff(456,plain,
% 0.94/0.90 (((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42)))) | ![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))),
% 0.94/0.90 inference(tautology,[status(thm)],[])).
% 0.94/0.90 tff(457,plain,
% 0.94/0.90 (![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[456, 435])).
% 0.94/0.90 tff(458,plain,
% 0.94/0.90 (((~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | ((~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42) | (~$greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)))) <=> ((~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42) | (~$greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(459,plain,
% 0.94/0.90 (((~$greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42)) <=> ((~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42) | (~$greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(460,plain,
% 0.94/0.90 ((~$greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, M!18)), 0)) <=> (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(461,plain,
% 0.94/0.90 ((~$lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0)) <=> (~$greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(462,plain,
% 0.94/0.90 (((~$lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0)) | (~$greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42)) <=> ((~$greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42))),
% 0.94/0.90 inference(monotonicity,[status(thm)],[461, 460])).
% 0.94/0.90 tff(463,plain,
% 0.94/0.90 (((~$lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0)) | (~$greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42)) <=> ((~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42) | (~$greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)))),
% 0.94/0.90 inference(transitivity,[status(thm)],[462, 459])).
% 0.94/0.90 tff(464,plain,
% 0.94/0.90 (((~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | ((~$lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0)) | (~$greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42))) <=> ((~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | ((~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42) | (~$greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0))))),
% 0.94/0.90 inference(monotonicity,[status(thm)],[463])).
% 0.94/0.90 tff(465,plain,
% 0.94/0.90 (((~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | ((~$lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0)) | (~$greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42))) <=> ((~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42) | (~$greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)))),
% 0.94/0.90 inference(transitivity,[status(thm)],[464, 458])).
% 0.94/0.90 tff(466,plain,
% 0.94/0.90 ((~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | ((~$lesseq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, J!23)), 0)) | (~$greatereq($sum(tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(467,plain,
% 0.94/0.91 ((~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~$lesseq($sum(M!18, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42) | (~$greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0))),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.94/0.91 tff(468,plain,
% 0.94/0.91 ($lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 42) | (~$greatereq($sum(J!23, $product(-1, tb2t1(t2tb1(tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0))),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[467, 457, 197])).
% 0.94/0.91 tff(469,plain,
% 0.94/0.91 ($false),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[468, 455, 195])).
% 0.94/0.91 tff(470,plain,((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42)), inference(lemma,lemma(discharge,[]))).
% 0.94/0.91 tff(471,assumption,(~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))), introduced(assumption)).
% 0.94/0.91 tff(472,plain,
% 0.94/0.91 (($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42)) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0))),
% 0.94/0.91 inference(tautology,[status(thm)],[])).
% 0.94/0.91 tff(473,plain,
% 0.94/0.91 (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[472, 471])).
% 0.94/0.91 tff(474,plain,
% 0.94/0.91 (($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0))),
% 0.94/0.91 inference(tautology,[status(thm)],[])).
% 0.94/0.91 tff(475,plain,
% 0.94/0.91 (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[474, 471])).
% 0.94/0.91 tff(476,plain,
% 0.94/0.91 (((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | ($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) <=> ((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | $greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(477,plain,
% 0.94/0.91 (($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42)) <=> ($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(478,plain,
% 0.94/0.91 ($greatereq($sum($product(-1, I!22), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))), 0) <=> $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0)),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(479,plain,
% 0.94/0.91 ($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)) = $sum($product(-1, I!22), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(480,plain,
% 0.94/0.91 ($greatereq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)), 0) <=> $greatereq($sum($product(-1, I!22), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))), 0)),
% 0.94/0.91 inference(monotonicity,[status(thm)],[479])).
% 0.94/0.91 tff(481,plain,
% 0.94/0.91 ($greatereq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)), 0) <=> $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0)),
% 0.94/0.91 inference(transitivity,[status(thm)],[480, 478])).
% 0.94/0.91 tff(482,plain,
% 0.94/0.91 ($lesseq($sum($product(-1, J!23), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))), 0) <=> $greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0)),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(483,plain,
% 0.94/0.91 ($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, J!23)) = $sum($product(-1, J!23), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(484,plain,
% 0.94/0.91 ($lesseq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, J!23)), 0) <=> $lesseq($sum($product(-1, J!23), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))), 0)),
% 0.94/0.91 inference(monotonicity,[status(thm)],[483])).
% 0.94/0.91 tff(485,plain,
% 0.94/0.91 ($lesseq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, J!23)), 0) <=> $greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0)),
% 0.94/0.91 inference(transitivity,[status(thm)],[484, 482])).
% 0.94/0.91 tff(486,plain,
% 0.94/0.91 (($lesseq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, J!23)), 0) | $greatereq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42)) <=> ($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[485, 481])).
% 0.94/0.91 tff(487,plain,
% 0.94/0.91 (($lesseq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, J!23)), 0) | $greatereq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42)) <=> ($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))),
% 0.94/0.91 inference(transitivity,[status(thm)],[486, 477])).
% 0.94/0.91 tff(488,plain,
% 0.94/0.91 (((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | ($lesseq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, J!23)), 0) | $greatereq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) <=> ((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | ($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42)))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[487])).
% 0.94/0.91 tff(489,plain,
% 0.94/0.91 (((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | ($lesseq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, J!23)), 0) | $greatereq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) <=> ((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | $greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))),
% 0.94/0.91 inference(transitivity,[status(thm)],[488, 476])).
% 0.94/0.91 tff(490,plain,
% 0.94/0.91 ((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | ($lesseq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, J!23)), 0) | $greatereq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(491,plain,
% 0.94/0.91 ((~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42))) | $greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42)),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.94/0.91 tff(492,plain,
% 0.94/0.91 (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[491, 475, 473, 437])).
% 0.94/0.91 tff(493,plain,
% 0.94/0.91 (get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[180])).
% 0.94/0.91 tff(494,plain,
% 0.94/0.91 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))),
% 0.94/0.91 inference(symmetry,[status(thm)],[493])).
% 0.94/0.91 tff(495,plain,
% 0.94/0.91 (t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))) = mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))),
% 0.94/0.91 inference(transitivity,[status(thm)],[243, 180])).
% 0.94/0.91 tff(496,plain,
% 0.94/0.91 (get4(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[495])).
% 0.94/0.91 tff(497,plain,
% 0.94/0.91 (get4(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))),
% 0.94/0.91 inference(transitivity,[status(thm)],[496, 494])).
% 0.94/0.91 tff(498,plain,
% 0.94/0.91 (tb2t1(get4(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[497])).
% 0.94/0.91 tff(499,plain,
% 0.94/0.91 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get4(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))),
% 0.94/0.91 inference(symmetry,[status(thm)],[496])).
% 0.94/0.91 tff(500,plain,
% 0.94/0.91 ((~![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))) | (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(501,plain,
% 0.94/0.91 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[500, 18])).
% 0.94/0.91 tff(502,plain,
% 0.94/0.91 (get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))),
% 0.94/0.91 inference(symmetry,[status(thm)],[501])).
% 0.94/0.91 tff(503,plain,
% 0.94/0.91 (get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[182])).
% 0.94/0.91 tff(504,plain,
% 0.94/0.91 (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))),
% 0.94/0.91 inference(symmetry,[status(thm)],[503])).
% 0.94/0.91 tff(505,assumption,(~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)), introduced(assumption)).
% 0.94/0.91 tff(506,assumption,(~$greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0)), introduced(assumption)).
% 0.94/0.91 tff(507,plain,
% 0.94/0.91 ($false),
% 0.94/0.91 inference(theory_lemma,[status(thm)],[80, 254, 506, 505])).
% 0.94/0.91 tff(508,plain,($greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0) | $greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.94/0.91 tff(509,plain,
% 0.94/0.91 ($greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[508, 475])).
% 0.94/0.91 tff(510,plain,
% 0.94/0.91 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | ((~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | (~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(511,plain,
% 0.94/0.91 (((~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)) | $greatereq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))))) <=> ((~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(512,plain,
% 0.94/0.91 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | ((~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)) | $greatereq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | ((~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))))))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[511])).
% 0.94/0.91 tff(513,plain,
% 0.94/0.91 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | ((~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)) | $greatereq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | (~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))))),
% 0.94/0.91 inference(transitivity,[status(thm)],[512, 510])).
% 0.94/0.91 tff(514,plain,
% 0.94/0.91 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | ((~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)) | $greatereq($sum(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(515,plain,
% 0.94/0.91 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, I!22)), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(I)) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(I))))) | (~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))))),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.94/0.91 tff(516,plain,
% 0.94/0.91 ((~$greatereq(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)), 0)) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))))),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[515, 473, 168])).
% 0.94/0.91 tff(517,plain,
% 0.94/0.91 (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[516, 509])).
% 0.94/0.91 tff(518,plain,
% 0.94/0.91 (get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))),
% 0.94/0.91 inference(symmetry,[status(thm)],[517])).
% 0.94/0.91 tff(519,plain,
% 0.94/0.91 (get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))),
% 0.94/0.92 inference(monotonicity,[status(thm)],[31])).
% 0.94/0.92 tff(520,plain,
% 0.94/0.92 (get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))),
% 0.94/0.92 inference(symmetry,[status(thm)],[519])).
% 0.94/0.92 tff(521,plain,
% 0.94/0.92 ((~![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))) | (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))))),
% 0.94/0.92 inference(quant_inst,[status(thm)],[])).
% 0.94/0.92 tff(522,plain,
% 0.94/0.92 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[521, 18])).
% 0.94/0.92 tff(523,plain,
% 0.94/0.92 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))),
% 0.94/0.92 inference(monotonicity,[status(thm)],[10])).
% 0.94/0.92 tff(524,plain,
% 0.94/0.92 (get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))),
% 0.94/0.92 inference(symmetry,[status(thm)],[523])).
% 0.94/0.92 tff(525,plain,
% 0.94/0.92 (get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))) = get4(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))),
% 0.94/0.92 inference(transitivity,[status(thm)],[524, 522, 520, 518, 504, 502, 499])).
% 0.94/0.92 tff(526,plain,
% 0.94/0.92 (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = tb2t1(get4(int, t2tb2(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24)))))), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25))))),
% 0.94/0.92 inference(monotonicity,[status(thm)],[525])).
% 0.94/0.92 tff(527,plain,
% 0.94/0.92 (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42),
% 0.94/0.92 inference(transitivity,[status(thm)],[526, 498, 492])).
% 0.94/0.92 tff(528,plain,
% 0.94/0.92 (($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42)) | (~(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))),
% 0.94/0.92 inference(tautology,[status(thm)],[])).
% 0.94/0.92 tff(529,plain,
% 0.94/0.92 (~(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[528, 471])).
% 0.94/0.92 tff(530,plain,
% 0.94/0.92 ($false),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[529, 527])).
% 0.94/0.92 tff(531,plain,($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42)), inference(lemma,lemma(discharge,[]))).
% 0.94/0.92 tff(532,plain,
% 0.94/0.92 (permut_sub3(mk_array3(length1(int, t2tb2(mk_array3(A!20, A3!24))), tb2t(elts(int, t2tb2(mk_array3(A!20, A3!24))))), mk_array3(length1(int, t2tb2(mk_array3(A!20, A4!25))), tb2t(elts(int, t2tb2(mk_array3(A!20, A4!25))))), M!18, $sum(1, N!17)) <=> permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))),
% 0.94/0.92 inference(monotonicity,[status(thm)],[242, 236])).
% 0.94/0.92 tff(533,plain,
% 0.94/0.92 (permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[321, 532])).
% 0.94/0.92 tff(534,plain,
% 0.94/0.92 (((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)) = 42)))))))))) <=> ((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)) = 42))))))))))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(535,plain,
% 0.94/0.92 ((~((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~($greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))))) = 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0))) | (~($lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$greatereq($sum(J!23, $product(-1, K)), 0)) | $greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))), 0) | (~$greatereq($sum(K, $product(-1, M!18)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I!22)), 0) | $greatereq($sum(J!23, $product(-1, K)), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | $lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))), 0) | (~$lesseq($sum(K, $product(-1, N!17)), 0)))))))))) <=> (~((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)) = 42)))))))))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(536,plain,
% 0.94/0.92 (((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~($greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))))) = 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0))) | (~($lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$greatereq($sum(J!23, $product(-1, K)), 0)) | $greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))), 0) | (~$greatereq($sum(K, $product(-1, M!18)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I!22)), 0) | $greatereq($sum(J!23, $product(-1, K)), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | $lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))), 0) | (~$lesseq($sum(K, $product(-1, N!17)), 0))))))))))) <=> ((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)) = 42))))))))))),
% 0.94/0.92 inference(monotonicity,[status(thm)],[535])).
% 0.94/0.92 tff(537,plain,
% 0.94/0.92 (((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~($greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))))) = 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0))) | (~($lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$greatereq($sum(J!23, $product(-1, K)), 0)) | $greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))), 0) | (~$greatereq($sum(K, $product(-1, M!18)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I!22)), 0) | $greatereq($sum(J!23, $product(-1, K)), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | $lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))), 0) | (~$lesseq($sum(K, $product(-1, N!17)), 0))))))))))) <=> ((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)) = 42))))))))))),
% 0.94/0.93 inference(transitivity,[status(thm)],[536, 534])).
% 0.94/0.93 tff(538,plain,
% 0.94/0.93 ((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~($greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))))) = 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0))) | (~($lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$greatereq($sum(J!23, $product(-1, K)), 0)) | $greatereq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))), 0) | (~$greatereq($sum(K, $product(-1, M!18)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I!22)), 0) | $greatereq($sum(J!23, $product(-1, K)), 0) | ($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | $lesseq($sum(42, $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)))), 0) | (~$lesseq($sum(K, $product(-1, N!17)), 0))))))))))),
% 0.94/0.93 inference(quant_inst,[status(thm)],[])).
% 0.94/0.93 tff(539,plain,
% 0.94/0.93 ((~![T1: array_int, T2: array_int, M: $int, N: $int, I: $int, J: $int, X: $int] : (~((~(qs_partition1(T1, T2, M, N, I, J, X) | (~permut_sub3(T1, T2, M, $sum(1, N))) | (~($greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_14(X, J, M, T2))))), 0) | (~$lesseq($sum(M, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_K_14(X, J, M, T2))), 0)))) | (~($greatereq($sum(J, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_15(X, J, I, T2))))) = 0) | $lesseq($sum(I, $product(-1, tptp_fun_K_15(X, J, I, T2))), 0))) | (~($lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), tptp_fun_K_16(X, I, N, T2))))), 0) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)) | (~$greatereq($sum(N, $product(-1, tptp_fun_K_16(X, I, N, T2))), 0)))))) | (~((~qs_partition1(T1, T2, M, N, I, J, X)) | (~((~permut_sub3(T1, T2, M, $sum(1, N))) | (~![K: $int] : ((~$greatereq($sum(J, $product(-1, K)), 0)) | $greatereq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$greatereq($sum(K, $product(-1, M)), 0)))) | (~![K: $int] : ($greatereq($sum(K, $product(-1, I)), 0) | $greatereq($sum(J, $product(-1, K)), 0) | ($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))) = 0))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(X, $product(-1, tb2t1(get4(int, t2tb2(T2), K)))), 0) | (~$lesseq($sum(K, $product(-1, N)), 0))))))))))) | (~((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)) = 42)))))))))),
% 0.94/0.93 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.94/0.93 tff(540,plain,
% 0.94/0.93 (~((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)) = 42))))))))),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[539, 422])).
% 0.94/0.93 tff(541,plain,
% 0.94/0.93 (((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))))) | (~((~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)) | (~((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), K)) = 42)))))))) | (qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))))),
% 1.03/0.93 inference(tautology,[status(thm)],[])).
% 1.03/0.93 tff(542,plain,
% 1.03/0.93 (qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)))),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[541, 540])).
% 1.03/0.93 tff(543,plain,
% 1.03/0.93 (~qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42)),
% 1.03/0.93 inference(or_elim,[status(thm)],[158])).
% 1.03/0.93 tff(544,plain,
% 1.03/0.93 ((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))))) | qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)))),
% 1.03/0.93 inference(tautology,[status(thm)],[])).
% 1.03/0.93 tff(545,plain,
% 1.03/0.93 ((~(qs_partition1(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, N!17, I!22, J!23, 42) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))))) | (~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)))),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[544, 543])).
% 1.03/0.93 tff(546,plain,
% 1.03/0.93 ((~permut_sub3(mk_array3(A!20, A3!24), mk_array3(A!20, A4!25), M!18, $sum(1, N!17))) | (~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)))),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[545, 542])).
% 1.03/0.93 tff(547,plain,
% 1.03/0.93 ((~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~($greatereq($sum(J!23, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_15(42, J!23, I!22, mk_array3(A!20, A4!25)))) = 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)))),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[546, 533])).
% 1.03/0.93 tff(548,plain,
% 1.03/0.93 ((~((~$lesseq($sum(M!18, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(J!23, $product(-1, tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_14(42, J!23, M!18, mk_array3(A!20, A4!25)))), 42))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)))),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[547, 531])).
% 1.03/0.93 tff(549,plain,
% 1.03/0.93 (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[548, 470])).
% 1.03/0.93 tff(550,plain,
% 1.03/0.93 (((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)) | (~$greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))),
% 1.03/0.93 inference(tautology,[status(thm)],[])).
% 1.03/0.93 tff(551,plain,
% 1.03/0.93 (~$greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[550, 549])).
% 1.03/0.93 tff(552,assumption,(~$greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)), introduced(assumption)).
% 1.03/0.93 tff(553,plain,
% 1.03/0.93 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25))) = get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))),
% 1.03/0.93 inference(monotonicity,[status(thm)],[10])).
% 1.03/0.93 tff(554,plain,
% 1.03/0.93 ((~![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))) | (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))),
% 1.03/0.93 inference(quant_inst,[status(thm)],[])).
% 1.03/0.93 tff(555,plain,
% 1.03/0.93 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25))))),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[554, 18])).
% 1.03/0.93 tff(556,plain,
% 1.03/0.93 (get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))) = get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25)))), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))),
% 1.03/0.93 inference(symmetry,[status(thm)],[555])).
% 1.03/0.93 tff(557,plain,
% 1.03/0.93 (get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A4!25))))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25))))),
% 1.03/0.93 inference(monotonicity,[status(thm)],[31])).
% 1.03/0.94 tff(558,assumption,(~((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42))), introduced(assumption)).
% 1.03/0.94 tff(559,plain,
% 1.03/0.94 (((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)) | $greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)),
% 1.03/0.94 inference(tautology,[status(thm)],[])).
% 1.03/0.94 tff(560,plain,
% 1.03/0.94 ($greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[559, 558])).
% 1.03/0.94 tff(561,plain,
% 1.03/0.94 ((~$lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0))),
% 1.03/0.94 inference(theory_lemma,[status(thm)],[])).
% 1.03/0.94 tff(562,plain,
% 1.03/0.94 (~$lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[561, 560])).
% 1.03/0.94 tff(563,plain,
% 1.03/0.94 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17)))))))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(564,plain,
% 1.03/0.94 ((permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq($sum(1, N!17), 0)) | (~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17)))))) <=> (permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))))))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(565,plain,
% 1.03/0.94 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq($sum(1, N!17), 0)) | (~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17)))))))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[564])).
% 1.03/0.94 tff(566,plain,
% 1.03/0.94 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq($sum(1, N!17), 0)) | (~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17)))))))),
% 1.03/0.94 inference(transitivity,[status(thm)],[565, 563])).
% 1.03/0.94 tff(567,plain,
% 1.03/0.94 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq($sum(1, N!17), 0)) | (~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~$lesseq($sum($sum(1, N!17), $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))))))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(568,plain,
% 1.03/0.94 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))))))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[567, 566])).
% 1.03/0.94 tff(569,plain,
% 1.03/0.94 (permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17)))))),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[568, 219])).
% 1.03/0.94 tff(570,plain,
% 1.03/0.94 (((~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), 0, I!22)) | (~permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))) | (~map_eq_sub1(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), $sum(1, N!17), length1(int, t2tb2(mk_array3(A!20, A3!24)))))) | permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))),
% 1.03/0.94 inference(tautology,[status(thm)],[])).
% 1.03/0.94 tff(571,plain,
% 1.03/0.94 (permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[570, 163])).
% 1.03/0.94 tff(572,plain,
% 1.03/0.94 ((~(permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))))))) | (~permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17))) | (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17)))))),
% 1.03/0.94 inference(tautology,[status(thm)],[])).
% 1.03/0.94 tff(573,plain,
% 1.03/0.94 ((~(permut3(int, t2tb2(mk_array3(A!20, A3!24)), t2tb2(mk_array3(A!20, A4!25)), I!22, $sum(1, N!17)) <=> (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))))))) | (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17)))))),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[572, 571])).
% 1.03/0.94 tff(574,plain,
% 1.03/0.94 (~((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))))),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[573, 569])).
% 1.03/0.94 tff(575,plain,
% 1.03/0.94 (((~$greatereq(I!22, 0)) | (~($sum(length1(int, t2tb2(mk_array3(A!20, A3!24))), $product(-1, length1(int, t2tb2(mk_array3(A!20, A4!25))))) = 0)) | (~$greatereq(N!17, -1)) | (~$lesseq($sum(N!17, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), -1)) | (~$lesseq($sum(I!22, $product(-1, length1(int, t2tb2(mk_array3(A!20, A3!24))))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17)))) | permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))),
% 1.03/0.94 inference(tautology,[status(thm)],[])).
% 1.03/0.94 tff(576,plain,
% 1.03/0.94 (permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[575, 574])).
% 1.03/0.94 tff(577,plain,
% 1.03/0.94 (((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)) | $lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)),
% 1.03/0.94 inference(tautology,[status(thm)],[])).
% 1.03/0.94 tff(578,plain,
% 1.03/0.94 ($lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[577, 558])).
% 1.03/0.94 tff(579,plain,
% 1.03/0.94 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | ((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(580,plain,
% 1.03/0.94 (($lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)))) <=> ((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(581,plain,
% 1.03/0.94 ((~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))))) <=> (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(582,plain,
% 1.03/0.94 ($lesseq($sum(1, $sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25))))), 0) <=> $lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1)),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(583,plain,
% 1.03/0.94 ($sum($sum(1, N!17), $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))) = $sum(1, $sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(584,plain,
% 1.03/0.94 ($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0) <=> $lesseq($sum(1, $sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25))))), 0)),
% 1.03/0.94 inference(monotonicity,[status(thm)],[583])).
% 1.03/0.94 tff(585,plain,
% 1.03/0.94 ($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0) <=> $lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1)),
% 1.03/0.94 inference(transitivity,[status(thm)],[584, 582])).
% 1.03/0.94 tff(586,plain,
% 1.03/0.94 (($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | (~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25))))))))) <=> ($lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[585, 581])).
% 1.03/0.95 tff(587,plain,
% 1.03/0.95 (($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | (~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25))))))))) <=> ((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))),
% 1.03/0.95 inference(transitivity,[status(thm)],[586, 580])).
% 1.03/0.95 tff(588,plain,
% 1.03/0.95 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | ($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | (~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | ((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[587])).
% 1.03/0.95 tff(589,plain,
% 1.03/0.95 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | ($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | (~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))))),
% 1.03/0.95 inference(transitivity,[status(thm)],[588, 579])).
% 1.03/0.95 tff(590,plain,
% 1.03/0.95 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | ($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | (~($lesseq($sum($sum(1, N!17), $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))))))),
% 1.03/0.95 inference(quant_inst,[status(thm)],[])).
% 1.03/0.95 tff(591,plain,
% 1.03/0.95 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int] : ($lesseq($sum(U, $product(-1, I)), 0) | (~$lesseq($sum(L, $product(-1, I)), 0)) | (~permut2(A, A1, A2, L, U)) | (~($lesseq($sum(U, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_J_8(I, U, L, A2, A1, A))), 0)) | (~(get(A, int, A1, t2tb1(tptp_fun_J_8(I, U, L, A2, A1, A))) = get(A, int, A2, t2tb1(I)))))))) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~permut2(int, elts(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A4!25))), I!22, $sum(1, N!17))) | $lesseq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), -1) | (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[590, 589])).
% 1.03/0.95 tff(592,plain,
% 1.03/0.95 (~((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[591, 354, 578, 576, 562])).
% 1.03/0.95 tff(593,plain,
% 1.03/0.95 (((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)) | (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))),
% 1.03/0.95 inference(tautology,[status(thm)],[])).
% 1.03/0.95 tff(594,plain,
% 1.03/0.95 (get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25))))),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[593, 592])).
% 1.03/0.95 tff(595,plain,
% 1.03/0.95 (get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[182])).
% 1.03/0.95 tff(596,plain,
% 1.03/0.95 ((~![A: ty, A1: uni, I: $int] : (get4(A, A1, I) = get(A, int, elts(A, A1), t2tb1(I)))) | (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))))),
% 1.03/0.95 inference(quant_inst,[status(thm)],[])).
% 1.03/0.95 tff(597,plain,
% 1.03/0.95 (get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)) = get(int, int, elts(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24))))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[596, 18])).
% 1.03/0.95 tff(598,plain,
% 1.03/0.95 (get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)) = get4(int, mk_array2(int, length1(int, t2tb2(mk_array3(A!20, A3!24))), elts(int, t2tb2(mk_array3(A!20, A3!24)))), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[180])).
% 1.03/0.95 tff(599,plain,
% 1.03/0.95 (get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)) = get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))),
% 1.03/0.95 inference(transitivity,[status(thm)],[598, 597, 595, 594, 557, 556, 553])).
% 1.03/0.95 tff(600,plain,
% 1.03/0.95 (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[599])).
% 1.03/0.95 tff(601,plain,
% 1.03/0.95 (tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))) = tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int)))),
% 1.03/0.95 inference(symmetry,[status(thm)],[600])).
% 1.03/0.95 tff(602,plain,
% 1.03/0.95 ((~(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))) = tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))))) | $greatereq($sum(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))))), 0)),
% 1.03/0.95 inference(theory_lemma,[status(thm)],[])).
% 1.03/0.95 tff(603,plain,
% 1.03/0.95 ($greatereq($sum(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), $product(-1, tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))))), 0)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[602, 601])).
% 1.03/0.95 tff(604,plain,
% 1.03/0.95 (((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)) | (~$lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1))),
% 1.03/0.95 inference(tautology,[status(thm)],[])).
% 1.03/0.95 tff(605,plain,
% 1.03/0.95 (~$lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[604, 592])).
% 1.03/0.95 tff(606,plain,
% 1.03/0.95 ($greatereq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)),
% 1.03/0.96 inference(theory_lemma,[status(thm)],[])).
% 1.03/0.96 tff(607,plain,
% 1.03/0.96 ($greatereq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[606, 605])).
% 1.03/0.96 tff(608,plain,
% 1.03/0.96 (((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~(get(int, int, elts(int, t2tb2(mk_array3(A!20, A3!24))), t2tb1(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))) = get(int, int, elts(int, t2tb2(mk_array3(A!20, A4!25))), t2tb1(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))))) | $lesseq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), -1)) | $lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)),
% 1.03/0.96 inference(tautology,[status(thm)],[])).
% 1.03/0.96 tff(609,plain,
% 1.03/0.96 ($lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[608, 592])).
% 1.03/0.96 tff(610,plain,
% 1.03/0.96 (((~permut_sub3(mk_array3(A!20, A2!21), mk_array3(A!20, A3!24), M!18, $sum(1, N!17))) | (~![K: $int] : ((~$lesseq($sum(K, $product(-1, J!23)), 0)) | (~$greatereq($sum(K, $product(-1, M!18)), 0)) | $lesseq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~![K: $int] : ($lesseq($sum(K, $product(-1, J!23)), 0) | $greatereq($sum(K, $product(-1, I!22)), 0) | (tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)) = 42)))) | ![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))),
% 1.03/0.96 inference(tautology,[status(thm)],[])).
% 1.03/0.96 tff(611,plain,
% 1.03/0.96 (![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[610, 435])).
% 1.03/0.96 tff(612,plain,
% 1.03/0.96 (((~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | ((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42))) <=> ((~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(613,plain,
% 1.03/0.96 (((~$greatereq($sum(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), $product(-1, I!22)), 0)) | (~$lesseq($sum(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42)) <=> ((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(614,plain,
% 1.03/0.96 (((~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | ((~$greatereq($sum(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), $product(-1, I!22)), 0)) | (~$lesseq($sum(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42))) <=> ((~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | ((~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42)))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[613])).
% 1.03/0.96 tff(615,plain,
% 1.03/0.96 (((~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | ((~$greatereq($sum(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), $product(-1, I!22)), 0)) | (~$lesseq($sum(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42))) <=> ((~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42))),
% 1.03/0.97 inference(transitivity,[status(thm)],[614, 612])).
% 1.03/0.97 tff(616,plain,
% 1.03/0.97 ((~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | ((~$greatereq($sum(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), $product(-1, I!22)), 0)) | (~$lesseq($sum(tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int), $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(617,plain,
% 1.03/0.97 ((~![K: $int] : ((~$greatereq($sum(K, $product(-1, I!22)), 0)) | (~$lesseq($sum(K, $product(-1, N!17)), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), K)), 42))) | (~$lesseq($sum(I!22, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[616, 615])).
% 1.03/0.97 tff(618,plain,
% 1.03/0.97 ($greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A3!24)), tptp_fun_J_8(tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)), $sum(1, N!17), I!22, elts(int, t2tb2(mk_array3(A!20, A4!25))), elts(int, t2tb2(mk_array3(A!20, A3!24))), int))), 42)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[617, 611, 609, 607])).
% 1.03/0.97 tff(619,plain,
% 1.03/0.97 ($false),
% 1.03/0.97 inference(theory_lemma,[status(thm)],[618, 603, 552])).
% 1.03/0.97 tff(620,plain,(((~$lesseq($sum(I!22, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | (~$greatereq($sum(N!17, $product(-1, tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 0)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)) | $greatereq(tb2t1(get4(int, t2tb2(mk_array3(A!20, A4!25)), tptp_fun_K_16(42, I!22, N!17, mk_array3(A!20, A4!25)))), 42)), inference(lemma,lemma(discharge,[]))).
% 1.03/0.97 tff(621,plain,
% 1.03/0.97 ($false),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[620, 551, 549])).
% 1.03/0.97 % SZS output end Proof
%------------------------------------------------------------------------------