TSTP Solution File: SWW623_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW623_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:28 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW623_2 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 20:21:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 tff(get_type, type, (
% 0.20/0.52 get: ( ty * ty * uni * uni ) > uni)).
% 0.20/0.52 tff(t2tb_type, type, (
% 0.20/0.52 t2tb: $int > uni)).
% 0.20/0.52 tff(tptp_fun_I_9_type, type, (
% 0.20/0.52 tptp_fun_I_9: ( $int * $int * uni * uni * ty ) > $int)).
% 0.20/0.52 tff(elt7_type, type, (
% 0.20/0.52 elt7: ty)).
% 0.20/0.52 tff(t2tb12_type, type, (
% 0.20/0.52 t2tb12: map_int_elt3 > uni)).
% 0.20/0.52 tff(tptp_fun_A3_21_type, type, (
% 0.20/0.52 tptp_fun_A3_21: map_int_elt3)).
% 0.20/0.52 tff(tptp_fun_A4_22_type, type, (
% 0.20/0.52 tptp_fun_A4_22: map_int_elt3)).
% 0.20/0.52 tff(tptp_fun_Hi_20_type, type, (
% 0.20/0.52 tptp_fun_Hi_20: $int)).
% 0.20/0.52 tff(length1_type, type, (
% 0.20/0.52 length1: ( ty * uni ) > $int)).
% 0.20/0.52 tff(mk_array1_type, type, (
% 0.20/0.52 mk_array1: ( ty * $int * uni ) > uni)).
% 0.20/0.52 tff(tptp_fun_A_14_type, type, (
% 0.20/0.52 tptp_fun_A_14: $int)).
% 0.20/0.52 tff(int_type, type, (
% 0.20/0.52 int: ty)).
% 0.20/0.52 tff(elts_type, type, (
% 0.20/0.52 elts: ( ty * uni ) > uni)).
% 0.20/0.52 tff(sort1_type, type, (
% 0.20/0.52 sort1: ( ty * uni ) > $o)).
% 0.20/0.52 tff(map_type, type, (
% 0.20/0.52 map: ( ty * ty ) > ty)).
% 0.20/0.52 tff(t2tb11_type, type, (
% 0.20/0.52 t2tb11: elt6 > uni)).
% 0.20/0.52 tff(tb2t11_type, type, (
% 0.20/0.52 tb2t11: uni > elt6)).
% 0.20/0.52 tff(tptp_fun_Lo_12_type, type, (
% 0.20/0.52 tptp_fun_Lo_12: $int)).
% 0.20/0.52 tff(map_eq_sub1_type, type, (
% 0.20/0.52 map_eq_sub1: ( ty * uni * uni * $int * $int ) > $o)).
% 0.20/0.52 tff(tptp_fun_A2_18_type, type, (
% 0.20/0.52 tptp_fun_A2_18: map_int_elt3)).
% 0.20/0.52 tff(tptp_fun_Mid_19_type, type, (
% 0.20/0.52 tptp_fun_Mid_19: $int)).
% 0.20/0.52 tff(permut_sub1_type, type, (
% 0.20/0.52 permut_sub1: ( ty * uni * uni * $int * $int ) > $o)).
% 0.20/0.52 tff(tptp_fun_I_17_type, type, (
% 0.20/0.52 tptp_fun_I_17: $int)).
% 0.20/0.52 tff(sorted_sub4_type, type, (
% 0.20/0.52 sorted_sub4: ( array_elt3 * $int * $int ) > $o)).
% 0.20/0.52 tff(tb2t10_type, type, (
% 0.20/0.52 tb2t10: uni > array_elt3)).
% 0.20/0.52 tff(tptp_fun_Tmp_15_type, type, (
% 0.20/0.52 tptp_fun_Tmp_15: $int)).
% 0.20/0.52 tff(tptp_fun_A1_13_type, type, (
% 0.20/0.52 tptp_fun_A1_13: map_int_elt3)).
% 0.20/0.52 tff(permut3_type, type, (
% 0.20/0.52 permut3: ( ty * uni * uni * $int * $int ) > $o)).
% 0.20/0.52 tff(tptp_fun_K_11_type, type, (
% 0.20/0.52 tptp_fun_K_11: $int)).
% 0.20/0.52 tff(tptp_fun_O_16_type, type, (
% 0.20/0.52 tptp_fun_O_16: $int)).
% 0.20/0.52 tff(le4_type, type, (
% 0.20/0.52 le4: ( elt6 * elt6 ) > $o)).
% 0.20/0.52 tff(1,plain,
% 0.20/0.52 (^[X: map_int_elt3] : refl(sort1(map(int, elt7), t2tb12(X)) <=> sort1(map(int, elt7), t2tb12(X)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(2,plain,
% 0.20/0.52 (![X: map_int_elt3] : sort1(map(int, elt7), t2tb12(X)) <=> ![X: map_int_elt3] : sort1(map(int, elt7), t2tb12(X))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.52 tff(3,plain,
% 0.20/0.52 (![X: map_int_elt3] : sort1(map(int, elt7), t2tb12(X)) <=> ![X: map_int_elt3] : sort1(map(int, elt7), t2tb12(X))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(4,axiom,(![X: map_int_elt3] : sort1(map(int, elt7), t2tb12(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2tb_sort15')).
% 0.20/0.52 tff(5,plain,
% 0.20/0.52 (![X: map_int_elt3] : sort1(map(int, elt7), t2tb12(X))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.52 tff(6,plain,(
% 0.20/0.52 ![X: map_int_elt3] : sort1(map(int, elt7), t2tb12(X))),
% 0.20/0.52 inference(skolemize,[status(sab)],[5])).
% 0.20/0.52 tff(7,plain,
% 0.20/0.52 (![X: map_int_elt3] : sort1(map(int, elt7), t2tb12(X))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.52 tff(8,plain,
% 0.20/0.52 ((~![X: map_int_elt3] : sort1(map(int, elt7), t2tb12(X))) | sort1(map(int, elt7), t2tb12(A4!22))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(9,plain,
% 0.20/0.52 (sort1(map(int, elt7), t2tb12(A4!22))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.52 tff(10,plain,
% 0.20/0.52 (^[A: ty, U: $int, U1: uni] : refl(((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(11,plain,
% 0.20/0.52 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.52 tff(12,plain,
% 0.20/0.52 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(13,plain,
% 0.20/0.52 (^[A: ty, U: $int, U1: uni] : rewrite((sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(14,plain,
% 0.20/0.53 (![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.53 tff(15,axiom,(![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','elts_def1')).
% 0.20/0.53 tff(16,plain,
% 0.20/0.53 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.53 tff(17,plain,
% 0.20/0.53 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.53 tff(18,plain,(
% 0.20/0.53 ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.53 inference(skolemize,[status(sab)],[17])).
% 0.20/0.53 tff(19,plain,
% 0.20/0.53 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.53 tff(20,plain,
% 0.20/0.53 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt7), t2tb12(A4!22))) | (elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))) = t2tb12(A4!22)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt7), t2tb12(A4!22))) | (elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))) = t2tb12(A4!22)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(21,plain,
% 0.20/0.53 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt7), t2tb12(A4!22))) | (elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))) = t2tb12(A4!22)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(22,plain,
% 0.20/0.53 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt7), t2tb12(A4!22))) | (elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))) = t2tb12(A4!22))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.53 tff(23,plain,
% 0.20/0.53 ((~sort1(map(int, elt7), t2tb12(A4!22))) | (elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))) = t2tb12(A4!22))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[22, 19])).
% 0.20/0.53 tff(24,plain,
% 0.20/0.53 (elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))) = t2tb12(A4!22)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[23, 9])).
% 0.20/0.53 tff(25,plain,
% 0.20/0.53 (t2tb12(A4!22) = elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[24])).
% 0.20/0.53 tff(26,plain,
% 0.20/0.53 (get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.53 tff(27,plain,
% 0.20/0.53 (get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[26])).
% 0.20/0.53 tff(28,plain,
% 0.20/0.53 (sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) <=> sort1(elt7, get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.53 tff(29,plain,
% 0.20/0.53 (sort1(elt7, get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) <=> sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.20/0.53 inference(symmetry,[status(thm)],[28])).
% 0.20/0.53 tff(30,plain,
% 0.20/0.53 (^[A: ty, B: ty, X: uni, X1: uni] : refl(sort1(B, get(B, A, X, X1)) <=> sort1(B, get(B, A, X, X1)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(31,plain,
% 0.20/0.53 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1)) <=> ![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.53 tff(32,plain,
% 0.20/0.53 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1)) <=> ![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(33,axiom,(![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','get_sort8')).
% 0.20/0.53 tff(34,plain,
% 0.20/0.53 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.53 tff(35,plain,(
% 0.20/0.53 ![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 0.20/0.53 inference(skolemize,[status(sab)],[34])).
% 0.20/0.53 tff(36,plain,
% 0.20/0.53 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.53 tff(37,plain,
% 0.20/0.53 ((~![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))) | sort1(elt7, get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(38,plain,
% 0.20/0.53 (sort1(elt7, get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.53 tff(39,plain,
% 0.20/0.53 (sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[38, 29])).
% 0.20/0.53 tff(40,plain,
% 0.20/0.53 (^[J: uni] : refl(((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J)) <=> ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(41,plain,
% 0.20/0.53 (![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J)) <=> ![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.53 tff(42,plain,
% 0.20/0.53 (![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J)) <=> ![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(43,plain,
% 0.20/0.53 (^[J: uni] : rewrite((sort1(elt7, J) => (t2tb11(tb2t11(J)) = J)) <=> ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(44,plain,
% 0.20/0.53 (![J: uni] : (sort1(elt7, J) => (t2tb11(tb2t11(J)) = J)) <=> ![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.53 tff(45,axiom,(![J: uni] : (sort1(elt7, J) => (t2tb11(tb2t11(J)) = J))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR11')).
% 0.20/0.53 tff(46,plain,
% 0.20/0.53 (![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.53 tff(47,plain,
% 0.20/0.53 (![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.53 tff(48,plain,(
% 0.20/0.53 ![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))),
% 0.20/0.53 inference(skolemize,[status(sab)],[47])).
% 0.20/0.53 tff(49,plain,
% 0.20/0.53 (![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.20/0.53 tff(50,plain,
% 0.20/0.53 (((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | ((~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))) <=> ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | (~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(51,plain,
% 0.20/0.53 ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | ((~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(52,plain,
% 0.20/0.53 ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | (~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.53 tff(53,plain,
% 0.20/0.53 ((~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.20/0.53 tff(54,plain,
% 0.20/0.53 (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[53, 39])).
% 0.20/0.53 tff(55,plain,
% 0.20/0.53 ((~![X: map_int_elt3] : sort1(map(int, elt7), t2tb12(X))) | sort1(map(int, elt7), t2tb12(A3!21))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(56,plain,
% 0.20/0.53 (sort1(map(int, elt7), t2tb12(A3!21))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[55, 7])).
% 0.20/0.53 tff(57,plain,
% 0.20/0.53 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt7), t2tb12(A3!21))) | (elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))) = t2tb12(A3!21)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt7), t2tb12(A3!21))) | (elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))) = t2tb12(A3!21)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(58,plain,
% 0.20/0.53 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt7), t2tb12(A3!21))) | (elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))) = t2tb12(A3!21)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(59,plain,
% 0.20/0.53 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt7), t2tb12(A3!21))) | (elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))) = t2tb12(A3!21))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.53 tff(60,plain,
% 0.20/0.53 ((~sort1(map(int, elt7), t2tb12(A3!21))) | (elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))) = t2tb12(A3!21))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[59, 19])).
% 0.20/0.53 tff(61,plain,
% 0.20/0.53 (elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))) = t2tb12(A3!21)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[60, 56])).
% 0.20/0.53 tff(62,plain,
% 0.20/0.53 (t2tb12(A3!21) = elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[61])).
% 0.20/0.53 tff(63,plain,
% 0.20/0.53 (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.53 tff(64,plain,
% 0.20/0.53 (get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[63])).
% 0.20/0.53 tff(65,plain,
% 0.20/0.53 (tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.53 tff(66,plain,
% 0.20/0.53 (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.20/0.53 inference(symmetry,[status(thm)],[65])).
% 0.20/0.53 tff(67,plain,
% 0.20/0.53 (^[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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(68,plain,
% 0.20/0.53 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.53 tff(69,plain,
% 0.20/0.53 (^[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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(70,plain,
% 0.20/0.53 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.53 tff(71,plain,
% 0.20/0.53 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.53 tff(72,plain,
% 0.20/0.53 (^[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, t2tb(I)) = get(A, int, A2, t2tb(I))))) <=> ((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))))) <=> (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A))))))) <=> (map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0)))) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A))))))) <=> (map_eq_sub1(A, A1, A2, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(I))))) & (map_eq_sub1(A, A1, A2, L, U) | (~((~($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, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))))))) <=> (((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$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, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(I))))) & (map_eq_sub1(A, A1, A2, L, U) | (~((~($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, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))))))) <=> (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(73,plain,
% 0.20/0.54 (![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, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(I))))) & (map_eq_sub1(A, A1, A2, L, U) | (~((~($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, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.54 tff(74,plain,
% 0.20/0.54 (^[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, t2tb(I)) = get(A, int, A2, t2tb(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, t2tb(I)) = get(A, int, A2, t2tb(I))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(75,plain,
% 0.20/0.54 (![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, t2tb(I)) = get(A, int, A2, t2tb(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, t2tb(I)) = get(A, int, A2, t2tb(I)))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.54 tff(76,plain,
% 0.20/0.54 (![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, t2tb(I)) = get(A, int, A2, t2tb(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, t2tb(I)) = get(A, int, A2, t2tb(I)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(77,plain,
% 0.20/0.54 (^[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, t2tb(I)) = get(A, int, A2, t2tb(I))))) <=> (map_eq_sub1(A, A1, A2, L, U) <=> ![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(I))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(78,plain,
% 0.20/0.54 (![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, t2tb(I)) = get(A, int, A2, t2tb(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, t2tb(I)) = get(A, int, A2, t2tb(I)))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.54 tff(79,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, t2tb(I)) = get(A, int, A2, t2tb(I)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','map_eq_sub_def')).
% 0.20/0.54 tff(80,plain,
% 0.20/0.54 (![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, t2tb(I)) = get(A, int, A2, t2tb(I)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.54 tff(81,plain,
% 0.20/0.54 (![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, t2tb(I)) = get(A, int, A2, t2tb(I)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.54 tff(82,plain,
% 0.20/0.54 (![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, t2tb(I)) = get(A, int, A2, t2tb(I)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[81, 75])).
% 0.20/0.54 tff(83,plain,(
% 0.20/0.54 ![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, $product(-1, I)), 0)))) | (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(I))))) & (map_eq_sub1(A, A1, A2, L, U) | (~((~($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, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A))))))))),
% 0.20/0.54 inference(skolemize,[status(sab)],[82])).
% 0.20/0.54 tff(84,plain,
% 0.20/0.54 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.20/0.54 tff(85,plain,
% 0.20/0.54 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[84, 71])).
% 0.20/0.55 tff(86,plain,
% 0.20/0.55 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, Hi!20)), 0)) | $greatereq($sum(I, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, Hi!20)), 0)) | $greatereq($sum(I, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(87,plain,
% 0.20/0.55 ((~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I))) | $lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, I)), 0) | (~$lesseq($sum(Hi!20, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))))))) <=> (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, Hi!20)), 0)) | $greatereq($sum(I, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))))))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(88,plain,
% 0.46/0.55 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I))) | $lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, I)), 0) | (~$lesseq($sum(Hi!20, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, Hi!20)), 0)) | $greatereq($sum(I, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))))))))),
% 0.46/0.55 inference(monotonicity,[status(thm)],[87])).
% 0.46/0.55 tff(89,plain,
% 0.46/0.55 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I))) | $lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, I)), 0) | (~$lesseq($sum(Hi!20, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, Hi!20)), 0)) | $greatereq($sum(I, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))))))))),
% 0.46/0.55 inference(transitivity,[status(thm)],[88, 86])).
% 0.46/0.55 tff(90,plain,
% 0.46/0.55 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I))) | $lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, I)), 0) | (~$lesseq($sum(Hi!20, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))))))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(91,plain,
% 0.46/0.55 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, Hi!20)), 0)) | $greatereq($sum(I, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))))))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.46/0.55 tff(92,plain,
% 0.46/0.55 (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, Hi!20)), 0)) | $greatereq($sum(I, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))))))),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[91, 85])).
% 0.46/0.56 tff(93,plain,
% 0.46/0.56 (((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, Hi!20)), 0)) | $greatereq($sum(I, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))))) | (map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))))),
% 0.46/0.56 inference(tautology,[status(thm)],[])).
% 0.46/0.56 tff(94,plain,
% 0.46/0.56 (map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.46/0.56 tff(95,plain,
% 0.46/0.56 (map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) <=> map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))),
% 0.46/0.56 inference(monotonicity,[status(thm)],[62, 25])).
% 0.46/0.56 tff(96,plain,
% 0.46/0.56 (map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) <=> map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))),
% 0.46/0.56 inference(symmetry,[status(thm)],[95])).
% 0.46/0.56 tff(97,plain,
% 0.46/0.56 ((~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) <=> (~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))))),
% 0.46/0.56 inference(monotonicity,[status(thm)],[96])).
% 0.46/0.56 tff(98,plain,
% 0.46/0.56 (map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) <=> map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)),
% 0.46/0.56 inference(monotonicity,[status(thm)],[62, 25])).
% 0.46/0.56 tff(99,plain,
% 0.46/0.56 (map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12) <=> map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)),
% 0.46/0.56 inference(symmetry,[status(thm)],[98])).
% 0.46/0.56 tff(100,plain,
% 0.46/0.56 ((~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) <=> (~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12))),
% 0.46/0.56 inference(monotonicity,[status(thm)],[99])).
% 0.46/0.56 tff(101,assumption,(~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)), introduced(assumption)).
% 0.46/0.56 tff(102,plain,
% 0.46/0.56 (~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.46/0.56 tff(103,plain,
% 0.46/0.56 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Lo!12)), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Lo!12)), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)))))))))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(104,plain,
% 0.46/0.56 ((~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I))) | $lesseq($sum(Lo!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))))))) <=> (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Lo!12)), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0))))))))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(105,plain,
% 0.46/0.56 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I))) | $lesseq($sum(Lo!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Lo!12)), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)))))))))),
% 0.46/0.56 inference(monotonicity,[status(thm)],[104])).
% 0.46/0.56 tff(106,plain,
% 0.46/0.56 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I))) | $lesseq($sum(Lo!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 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, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Lo!12)), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)))))))))),
% 0.46/0.56 inference(transitivity,[status(thm)],[105, 103])).
% 0.46/0.56 tff(107,plain,
% 0.46/0.56 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I))) | $lesseq($sum(Lo!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))))))),
% 0.46/0.56 inference(quant_inst,[status(thm)],[])).
% 0.46/0.56 tff(108,plain,
% 0.46/0.56 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (~((~((~map_eq_sub1(A, A1, A2, L, U)) | ![I: $int] : ((get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(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, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0) | (get(A, int, A1, t2tb(tptp_fun_I_9(U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_I_9(U, L, A2, A1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_9(U, L, A2, A1, A))), 0))))))))) | (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Lo!12)), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0))))))))),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.46/0.56 tff(109,plain,
% 0.46/0.56 (~((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Lo!12)), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)))))))),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[108, 85])).
% 0.46/0.56 tff(110,plain,
% 0.46/0.56 (((~((~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, Lo!12)), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(I)) = get(elt7, int, t2tb12(A4!22), t2tb(I)))))) | (~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0))))))) | (map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)))))),
% 0.46/0.56 inference(tautology,[status(thm)],[])).
% 0.46/0.56 tff(111,plain,
% 0.46/0.56 (map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0))))),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.46/0.56 tff(112,plain,
% 0.46/0.56 (get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))),
% 0.46/0.56 inference(monotonicity,[status(thm)],[25])).
% 0.46/0.56 tff(113,plain,
% 0.46/0.56 (get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))),
% 0.47/0.57 inference(symmetry,[status(thm)],[112])).
% 0.47/0.57 tff(114,plain,
% 0.47/0.57 (sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) <=> sort1(elt7, get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[113])).
% 0.47/0.57 tff(115,plain,
% 0.47/0.57 (sort1(elt7, get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) <=> sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.57 inference(symmetry,[status(thm)],[114])).
% 0.47/0.57 tff(116,plain,
% 0.47/0.57 ((~![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))) | sort1(elt7, get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(117,plain,
% 0.47/0.57 (sort1(elt7, get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[116, 36])).
% 0.47/0.57 tff(118,plain,
% 0.47/0.57 (sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[117, 115])).
% 0.47/0.57 tff(119,plain,
% 0.47/0.57 ((~![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))) | sort1(elt7, get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(120,plain,
% 0.47/0.57 (sort1(elt7, get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[119, 36])).
% 0.47/0.57 tff(121,plain,
% 0.47/0.57 (((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | ((~sort1(elt7, get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))) <=> ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | (~sort1(elt7, get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(122,plain,
% 0.47/0.57 ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | ((~sort1(elt7, get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(123,plain,
% 0.47/0.57 ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | (~sort1(elt7, get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.47/0.57 tff(124,plain,
% 0.47/0.57 (t2tb11(tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[123, 49, 120])).
% 0.47/0.57 tff(125,assumption,(~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)))), introduced(assumption)).
% 0.47/0.57 tff(126,plain,
% 0.47/0.57 (($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0))) | $greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)),
% 0.47/0.57 inference(tautology,[status(thm)],[])).
% 0.47/0.57 tff(127,plain,
% 0.47/0.57 ($greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.47/0.57 tff(128,plain,
% 0.47/0.57 (($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0))) | (~$lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))),
% 0.47/0.57 inference(tautology,[status(thm)],[])).
% 0.47/0.57 tff(129,plain,
% 0.47/0.57 (~$lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[128, 125])).
% 0.47/0.57 tff(130,plain,
% 0.47/0.57 ((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)),
% 0.47/0.57 inference(tautology,[status(thm)],[])).
% 0.47/0.57 tff(131,plain,
% 0.47/0.57 (~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[130, 129, 127])).
% 0.47/0.57 tff(132,plain,
% 0.47/0.57 (((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))) | ((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))),
% 0.47/0.57 inference(tautology,[status(thm)],[])).
% 0.47/0.57 tff(133,plain,
% 0.47/0.57 ((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.47/0.57 tff(134,plain,
% 0.47/0.57 (^[I1: $int] : refl(((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) <=> ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))))),
% 0.47/0.57 inference(bind,[status(th)],[])).
% 0.47/0.57 tff(135,plain,
% 0.47/0.57 (![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) <=> ![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))),
% 0.47/0.57 inference(quant_intro,[status(thm)],[134])).
% 0.47/0.57 tff(136,plain,
% 0.47/0.57 (^[I1: $int] : rewrite(((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) <=> ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))))),
% 0.47/0.57 inference(bind,[status(th)],[])).
% 0.47/0.57 tff(137,plain,
% 0.47/0.57 (![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) <=> ![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))),
% 0.47/0.57 inference(quant_intro,[status(thm)],[136])).
% 0.47/0.57 tff(138,plain,
% 0.47/0.57 (((~$greatereq($sum(Lo!12, $product(-1, A!14)), -1)) & ($greatereq(Lo!12, 0) & (~$greatereq($sum(Lo!12, $product(-1, A!14)), 0))) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, A!14)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(K!11, 0)) & ($greatereq(K!11, 1) & (~($sum(A!14, $product(-1, O!16)) = 0)) & (~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0)) & (~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))) & $greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1) & $greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))) <=> ((~$greatereq($sum(Lo!12, $product(-1, A!14)), -1)) & $greatereq(Lo!12, 0) & (~$greatereq($sum(Lo!12, $product(-1, A!14)), 0)) & $greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $lesseq($sum(Lo!12, $product(-1, A!14)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(K!11, 0) & $greatereq(K!11, 1) & (~($sum(A!14, $product(-1, O!16)) = 0)) & (~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0)) & (~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))) & $greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(139,plain,
% 0.47/0.57 (($greatereq(K!11, 1) & (~($sum(A!14, $product(-1, O!16)) = 0)) & ((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0))) & ((~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))) & $greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1) & $greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))) <=> ($greatereq(K!11, 1) & (~($sum(A!14, $product(-1, O!16)) = 0)) & (~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0)) & (~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))) & $greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1) & $greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(140,plain,
% 0.47/0.57 ((((~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J)))))) & ($greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1)) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(I!17, 0)) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))) <=> ((~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))) & $greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1) & $greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(141,plain,
% 0.47/0.58 ((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & ($greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))) <=> ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(142,plain,
% 0.47/0.58 (($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(Hi!20, $product(-1, A!14)) = 0) | ((~$greatereq($sum(I!17, $sum($product(-1, Hi!20), Mid!19)), 0)) & (~$greatereq($sum(Hi!20, $product(-1, A!14)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J)))))) <=> ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(143,plain,
% 0.47/0.58 ((~(~($greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))) <=> ($greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(144,plain,
% 0.47/0.58 ((~($greatereq(Lo!12, 0) & $greatereq($sum(Mid!19, $product(-1, Lo!12)), 0) & $greatereq($sum(Hi!20, $product(-1, Mid!19)), 0) & $lesseq($sum(Hi!20, $product(-1, Tmp!15)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20))) <=> (~($greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(145,plain,
% 0.47/0.58 ((~(~($greatereq(Lo!12, 0) & $greatereq($sum(Mid!19, $product(-1, Lo!12)), 0) & $greatereq($sum(Hi!20, $product(-1, Mid!19)), 0) & $lesseq($sum(Hi!20, $product(-1, Tmp!15)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))) <=> (~(~($greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[144])).
% 0.47/0.58 tff(146,plain,
% 0.47/0.58 ((~(~($greatereq(Lo!12, 0) & $greatereq($sum(Mid!19, $product(-1, Lo!12)), 0) & $greatereq($sum(Hi!20, $product(-1, Mid!19)), 0) & $lesseq($sum(Hi!20, $product(-1, Tmp!15)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))) <=> ($greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20))),
% 0.47/0.58 inference(transitivity,[status(thm)],[145, 143])).
% 0.47/0.58 tff(147,plain,
% 0.47/0.58 ((~(~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14))) <=> permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14)),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(148,plain,
% 0.47/0.58 ((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) <=> ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(149,plain,
% 0.47/0.58 (($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($lesseq($sum(Hi!20, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) <=> ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(150,plain,
% 0.47/0.58 ((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($lesseq($sum(Hi!20, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) <=> (($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[149])).
% 0.47/0.58 tff(151,plain,
% 0.47/0.58 ((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($lesseq($sum(Hi!20, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) <=> ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)))),
% 0.47/0.58 inference(transitivity,[status(thm)],[150, 148])).
% 0.47/0.58 tff(152,plain,
% 0.47/0.58 (((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($lesseq($sum(Hi!20, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) & (~(~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14))) & (~(~($greatereq(Lo!12, 0) & $greatereq($sum(Mid!19, $product(-1, Lo!12)), 0) & $greatereq($sum(Hi!20, $product(-1, Mid!19)), 0) & $lesseq($sum(Hi!20, $product(-1, Tmp!15)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(Hi!20, $product(-1, A!14)) = 0) | ((~$greatereq($sum(I!17, $sum($product(-1, Hi!20), Mid!19)), 0)) & (~$greatereq($sum(Hi!20, $product(-1, A!14)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))) <=> (($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & ($greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J)))))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[151, 147, 146, 142])).
% 0.47/0.58 tff(153,plain,
% 0.47/0.58 (((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($lesseq($sum(Hi!20, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) & (~(~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14))) & (~(~($greatereq(Lo!12, 0) & $greatereq($sum(Mid!19, $product(-1, Lo!12)), 0) & $greatereq($sum(Hi!20, $product(-1, Mid!19)), 0) & $lesseq($sum(Hi!20, $product(-1, Tmp!15)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(Hi!20, $product(-1, A!14)) = 0) | ((~$greatereq($sum(I!17, $sum($product(-1, Hi!20), Mid!19)), 0)) & (~$greatereq($sum(Hi!20, $product(-1, A!14)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))) <=> ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))),
% 0.47/0.58 inference(transitivity,[status(thm)],[152, 141])).
% 0.47/0.58 tff(154,plain,
% 0.47/0.58 ((~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(I!17, 0)))) <=> ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(I!17, 0))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(155,plain,
% 0.47/0.58 ((~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $lesseq($sum(Mid!19, $product(-1, A!14)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & $greatereq(I!17, 0))) <=> (~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(I!17, 0)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(156,plain,
% 0.47/0.58 ((~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $lesseq($sum(Mid!19, $product(-1, A!14)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & $greatereq(I!17, 0)))) <=> (~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(I!17, 0))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[155])).
% 0.47/0.58 tff(157,plain,
% 0.47/0.58 ((~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $lesseq($sum(Mid!19, $product(-1, A!14)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & $greatereq(I!17, 0)))) <=> ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(I!17, 0))),
% 0.47/0.58 inference(transitivity,[status(thm)],[156, 154])).
% 0.47/0.58 tff(158,plain,
% 0.47/0.58 ((~(~($greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1)))) <=> ($greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(159,plain,
% 0.47/0.58 ((~($greatereq(I!17, 0) & $lesseq($sum(I!17, $product(-1, K!11)), -1))) <=> (~($greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(160,plain,
% 0.47/0.58 ((~(~($greatereq(I!17, 0) & $lesseq($sum(I!17, $product(-1, K!11)), -1)))) <=> (~(~($greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[159])).
% 0.47/0.58 tff(161,plain,
% 0.47/0.58 ((~(~($greatereq(I!17, 0) & $lesseq($sum(I!17, $product(-1, K!11)), -1)))) <=> ($greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1))),
% 0.47/0.58 inference(transitivity,[status(thm)],[160, 158])).
% 0.47/0.58 tff(162,plain,
% 0.47/0.58 (((~$lesseq($sum(Mid!19, $sum($product(-1, I!17), $product(-1, Lo!12))), 0)) & (~$greatereq($sum(Mid!19, $product(-1, A!14)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J)))))) <=> ((~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(163,plain,
% 0.47/0.59 ((((~$lesseq($sum(Mid!19, $sum($product(-1, I!17), $product(-1, Lo!12))), 0)) & (~$greatereq($sum(Mid!19, $product(-1, A!14)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J)))))) & (~(~($greatereq(I!17, 0) & $lesseq($sum(I!17, $product(-1, K!11)), -1)))) & (~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $lesseq($sum(Mid!19, $product(-1, A!14)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & $greatereq(I!17, 0)))) & ((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($lesseq($sum(Hi!20, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) & (~(~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14))) & (~(~($greatereq(Lo!12, 0) & $greatereq($sum(Mid!19, $product(-1, Lo!12)), 0) & $greatereq($sum(Hi!20, $product(-1, Mid!19)), 0) & $lesseq($sum(Hi!20, $product(-1, Tmp!15)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(Hi!20, $product(-1, A!14)) = 0) | ((~$greatereq($sum(I!17, $sum($product(-1, Hi!20), Mid!19)), 0)) & (~$greatereq($sum(Hi!20, $product(-1, A!14)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J)))))))) <=> (((~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J)))))) & ($greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1)) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(I!17, 0)) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J)))))))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[162, 161, 157, 153])).
% 0.47/0.59 tff(164,plain,
% 0.47/0.59 ((((~$lesseq($sum(Mid!19, $sum($product(-1, I!17), $product(-1, Lo!12))), 0)) & (~$greatereq($sum(Mid!19, $product(-1, A!14)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J)))))) & (~(~($greatereq(I!17, 0) & $lesseq($sum(I!17, $product(-1, K!11)), -1)))) & (~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $lesseq($sum(Mid!19, $product(-1, A!14)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & $greatereq(I!17, 0)))) & ((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($lesseq($sum(Hi!20, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) & (~(~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14))) & (~(~($greatereq(Lo!12, 0) & $greatereq($sum(Mid!19, $product(-1, Lo!12)), 0) & $greatereq($sum(Hi!20, $product(-1, Mid!19)), 0) & $lesseq($sum(Hi!20, $product(-1, Tmp!15)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(Hi!20, $product(-1, A!14)) = 0) | ((~$greatereq($sum(I!17, $sum($product(-1, Hi!20), Mid!19)), 0)) & (~$greatereq($sum(Hi!20, $product(-1, A!14)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J)))))))) <=> ((~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))) & $greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1) & $greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))),
% 0.47/0.59 inference(transitivity,[status(thm)],[163, 140])).
% 0.47/0.59 tff(165,plain,
% 0.47/0.59 ((~(~((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0))))) <=> ((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0)))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(166,plain,
% 0.47/0.59 ((~((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $lesseq($sum(O!16, $product(-1, A!14)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $greatereq($sum(O!16, $product(-1, A!14)), 0)))) <=> (~((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0))))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(167,plain,
% 0.47/0.59 ((~(~((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $lesseq($sum(O!16, $product(-1, A!14)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $greatereq($sum(O!16, $product(-1, A!14)), 0))))) <=> (~(~((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0)))))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[166])).
% 0.47/0.59 tff(168,plain,
% 0.47/0.59 ((~(~((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $lesseq($sum(O!16, $product(-1, A!14)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $greatereq($sum(O!16, $product(-1, A!14)), 0))))) <=> ((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0)))),
% 0.47/0.59 inference(transitivity,[status(thm)],[167, 165])).
% 0.47/0.59 tff(169,plain,
% 0.47/0.59 ((~($sum(O!16, $product(-1, A!14)) = 0)) <=> (~($sum(A!14, $product(-1, O!16)) = 0))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(170,plain,
% 0.47/0.59 ((~(~$greatereq(K!11, 1))) <=> $greatereq(K!11, 1)),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(171,plain,
% 0.47/0.59 (((~(~$greatereq(K!11, 1))) & (~($sum(O!16, $product(-1, A!14)) = 0)) & (~(~((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $lesseq($sum(O!16, $product(-1, A!14)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $greatereq($sum(O!16, $product(-1, A!14)), 0))))) & (((~$lesseq($sum(Mid!19, $sum($product(-1, I!17), $product(-1, Lo!12))), 0)) & (~$greatereq($sum(Mid!19, $product(-1, A!14)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J)))))) & (~(~($greatereq(I!17, 0) & $lesseq($sum(I!17, $product(-1, K!11)), -1)))) & (~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $lesseq($sum(Mid!19, $product(-1, A!14)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & $greatereq(I!17, 0)))) & ((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($lesseq($sum(Hi!20, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) & (~(~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14))) & (~(~($greatereq(Lo!12, 0) & $greatereq($sum(Mid!19, $product(-1, Lo!12)), 0) & $greatereq($sum(Hi!20, $product(-1, Mid!19)), 0) & $lesseq($sum(Hi!20, $product(-1, Tmp!15)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(Hi!20, $product(-1, A!14)) = 0) | ((~$greatereq($sum(I!17, $sum($product(-1, Hi!20), Mid!19)), 0)) & (~$greatereq($sum(Hi!20, $product(-1, A!14)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))))) <=> ($greatereq(K!11, 1) & (~($sum(A!14, $product(-1, O!16)) = 0)) & ((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0))) & ((~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))) & $greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1) & $greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J)))))))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[170, 169, 168, 164])).
% 0.47/0.59 tff(172,plain,
% 0.47/0.59 (((~(~$greatereq(K!11, 1))) & (~($sum(O!16, $product(-1, A!14)) = 0)) & (~(~((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $lesseq($sum(O!16, $product(-1, A!14)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $greatereq($sum(O!16, $product(-1, A!14)), 0))))) & (((~$lesseq($sum(Mid!19, $sum($product(-1, I!17), $product(-1, Lo!12))), 0)) & (~$greatereq($sum(Mid!19, $product(-1, A!14)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J)))))) & (~(~($greatereq(I!17, 0) & $lesseq($sum(I!17, $product(-1, K!11)), -1)))) & (~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $lesseq($sum(Mid!19, $product(-1, A!14)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & $greatereq(I!17, 0)))) & ((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($lesseq($sum(Hi!20, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) & (~(~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14))) & (~(~($greatereq(Lo!12, 0) & $greatereq($sum(Mid!19, $product(-1, Lo!12)), 0) & $greatereq($sum(Hi!20, $product(-1, Mid!19)), 0) & $lesseq($sum(Hi!20, $product(-1, Tmp!15)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(Hi!20, $product(-1, A!14)) = 0) | ((~$greatereq($sum(I!17, $sum($product(-1, Hi!20), Mid!19)), 0)) & (~$greatereq($sum(Hi!20, $product(-1, A!14)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))))) <=> ($greatereq(K!11, 1) & (~($sum(A!14, $product(-1, O!16)) = 0)) & (~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0)) & (~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))) & $greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1) & $greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))),
% 0.47/0.59 inference(transitivity,[status(thm)],[171, 139])).
% 0.47/0.59 tff(173,plain,
% 0.47/0.59 ((~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, A!14)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(K!11, 0)))) <=> ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, A!14)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(K!11, 0))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(174,plain,
% 0.47/0.60 ((~(~($greatereq(Lo!12, 0) & (~$greatereq($sum(Lo!12, $product(-1, A!14)), 0))))) <=> ($greatereq(Lo!12, 0) & (~$greatereq($sum(Lo!12, $product(-1, A!14)), 0)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(175,plain,
% 0.47/0.60 (((~$greatereq($sum(Lo!12, $product(-1, A!14)), -1)) & (~(~($greatereq(Lo!12, 0) & (~$greatereq($sum(Lo!12, $product(-1, A!14)), 0))))) & (~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, A!14)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(K!11, 0)))) & ((~(~$greatereq(K!11, 1))) & (~($sum(O!16, $product(-1, A!14)) = 0)) & (~(~((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $lesseq($sum(O!16, $product(-1, A!14)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $greatereq($sum(O!16, $product(-1, A!14)), 0))))) & (((~$lesseq($sum(Mid!19, $sum($product(-1, I!17), $product(-1, Lo!12))), 0)) & (~$greatereq($sum(Mid!19, $product(-1, A!14)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J)))))) & (~(~($greatereq(I!17, 0) & $lesseq($sum(I!17, $product(-1, K!11)), -1)))) & (~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $lesseq($sum(Mid!19, $product(-1, A!14)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & $greatereq(I!17, 0)))) & ((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($lesseq($sum(Hi!20, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) & (~(~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14))) & (~(~($greatereq(Lo!12, 0) & $greatereq($sum(Mid!19, $product(-1, Lo!12)), 0) & $greatereq($sum(Hi!20, $product(-1, Mid!19)), 0) & $lesseq($sum(Hi!20, $product(-1, Tmp!15)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(Hi!20, $product(-1, A!14)) = 0) | ((~$greatereq($sum(I!17, $sum($product(-1, Hi!20), Mid!19)), 0)) & (~$greatereq($sum(Hi!20, $product(-1, A!14)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J)))))))))) <=> ((~$greatereq($sum(Lo!12, $product(-1, A!14)), -1)) & ($greatereq(Lo!12, 0) & (~$greatereq($sum(Lo!12, $product(-1, A!14)), 0))) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, A!14)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(K!11, 0)) & ($greatereq(K!11, 1) & (~($sum(A!14, $product(-1, O!16)) = 0)) & (~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0)) & (~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))) & $greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1) & $greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J)))))))),
% 0.47/0.60 inference(monotonicity,[status(thm)],[174, 173, 172])).
% 0.47/0.60 tff(176,plain,
% 0.47/0.60 (((~$greatereq($sum(Lo!12, $product(-1, A!14)), -1)) & (~(~($greatereq(Lo!12, 0) & (~$greatereq($sum(Lo!12, $product(-1, A!14)), 0))))) & (~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Lo!12, 0) & $lesseq($sum(Lo!12, $product(-1, A!14)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(K!11, 0)))) & ((~(~$greatereq(K!11, 1))) & (~($sum(O!16, $product(-1, A!14)) = 0)) & (~(~((~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $lesseq($sum(O!16, $product(-1, A!14)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $greatereq($sum(O!16, $product(-1, A!14)), 0))))) & (((~$lesseq($sum(Mid!19, $sum($product(-1, I!17), $product(-1, Lo!12))), 0)) & (~$greatereq($sum(Mid!19, $product(-1, A!14)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J)))))) & (~(~($greatereq(I!17, 0) & $lesseq($sum(I!17, $product(-1, K!11)), -1)))) & (~(~($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $greatereq(Mid!19, 0) & $lesseq($sum(Mid!19, $product(-1, A!14)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & $greatereq(I!17, 0)))) & ((($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($lesseq($sum(Hi!20, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20))) & (~(~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14))) & (~(~($greatereq(Lo!12, 0) & $greatereq($sum(Mid!19, $product(-1, Lo!12)), 0) & $greatereq($sum(Hi!20, $product(-1, Mid!19)), 0) & $lesseq($sum(Hi!20, $product(-1, Tmp!15)), 0) & ($sum(Tmp!15, $product(-1, A!14)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20)))) & ($greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & (($sum(Hi!20, $product(-1, A!14)) = 0) | ((~$greatereq($sum(I!17, $sum($product(-1, Hi!20), Mid!19)), 0)) & (~$greatereq($sum(Hi!20, $product(-1, A!14)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J)))))))))) <=> ((~$greatereq($sum(Lo!12, $product(-1, A!14)), -1)) & $greatereq(Lo!12, 0) & (~$greatereq($sum(Lo!12, $product(-1, A!14)), 0)) & $greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $lesseq($sum(Lo!12, $product(-1, A!14)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(K!11, 0) & $greatereq(K!11, 1) & (~($sum(A!14, $product(-1, O!16)) = 0)) & (~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0)) & (~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))) & $greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))))))),
% 0.47/0.60 inference(transitivity,[status(thm)],[175, 138])).
% 0.47/0.60 tff(177,plain,
% 0.47/0.60 ((~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ($greatereq($sum(Lo, $product(-1, A)), -1) | (~($greatereq(Lo, 0) & (~$greatereq($sum(Lo, $product(-1, A)), 0)))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(K, 0))) | ![O: $int] : ((~$greatereq(K, 1)) | ($sum(O, $product(-1, A)) = 0) | (~((~$greatereq($sum(Lo, $product(-1, O)), 0)) & $lesseq($sum(O, $product(-1, A)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))) | $greatereq($sum(O, $product(-1, A)), 0)))) | ![Mid: $int, A2: map_int_elt3, I: $int] : ((~((~$lesseq($sum(Mid, $sum($product(-1, I), $product(-1, Lo))), 0)) & (~$greatereq($sum(Mid, $product(-1, A)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, K)), -1))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Mid, 0) & $lesseq($sum(Mid, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & $greatereq(I, 0))) | ![A3: map_int_elt3, Hi: $int] : (![A4: map_int_elt3] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo)), 0))) | ($lesseq($sum(Hi, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | (~($greatereq(Lo, 0) & $greatereq($sum(Mid, $product(-1, Lo)), 0) & $greatereq($sum(Hi, $product(-1, Mid)), 0) & $lesseq($sum(Hi, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & (($sum(Hi, $product(-1, A)) = 0) | ((~$greatereq($sum(I, $sum($product(-1, Hi), Mid)), 0)) & (~$greatereq($sum(Hi, $product(-1, A)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))))))) <=> (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ($greatereq($sum(Lo, $product(-1, A)), -1) | (~($greatereq(Lo, 0) & (~$greatereq($sum(Lo, $product(-1, A)), 0)))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(K, 0))) | ![O: $int] : ((~$greatereq(K, 1)) | ($sum(O, $product(-1, A)) = 0) | (~((~$greatereq($sum(Lo, $product(-1, O)), 0)) & $lesseq($sum(O, $product(-1, A)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))) | $greatereq($sum(O, $product(-1, A)), 0)))) | ![Mid: $int, A2: map_int_elt3, I: $int] : ((~((~$lesseq($sum(Mid, $sum($product(-1, I), $product(-1, Lo))), 0)) & (~$greatereq($sum(Mid, $product(-1, A)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, K)), -1))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Mid, 0) & $lesseq($sum(Mid, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & $greatereq(I, 0))) | ![A3: map_int_elt3, Hi: $int] : (![A4: map_int_elt3] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo)), 0))) | ($lesseq($sum(Hi, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | (~($greatereq(Lo, 0) & $greatereq($sum(Mid, $product(-1, Lo)), 0) & $greatereq($sum(Hi, $product(-1, Mid)), 0) & $lesseq($sum(Hi, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & (($sum(Hi, $product(-1, A)) = 0) | ((~$greatereq($sum(I, $sum($product(-1, Hi), Mid)), 0)) & (~$greatereq($sum(Hi, $product(-1, A)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))))))))))))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(178,plain,
% 0.47/0.60 ((~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ((~($greatereq(Lo, 0) & (~$lesseq($sum(A, $product(-1, Lo)), 0)))) | $lesseq($sum(A, $product(-1, Lo)), 1) | ![O: $int] : ((~$greatereq(K, 1)) | ($sum(O, $product(-1, A)) = 0) | (~((~$lesseq($sum(O, $product(-1, Lo)), 0)) & $lesseq($sum(O, $product(-1, A)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))) | $lesseq($sum(A, $product(-1, O)), 0)))) | ![Mid: $int, A2: map_int_elt3, I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, K)), -1))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Mid, 0) & $lesseq($sum(Mid, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(I, 0))) | ![A3: map_int_elt3, Hi: $int] : ((~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | ![A4: map_int_elt3] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$lesseq($sum(Lo, $product(-1, I1)), 0))) | ($lesseq($sum(Hi, $product(-1, I1)), 0) & (~$lesseq($sum(A, $product(-1, I1)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~($greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, Mid)), 0) & $lesseq($sum(Mid, $product(-1, Hi)), 0) & $lesseq($sum(Hi, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & (($sum(Hi, $product(-1, A)) = 0) | ((~$lesseq($sum(Hi, $sum($product(-1, Mid), $product(-1, I))), 0)) & (~$lesseq($sum(A, $product(-1, Hi)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(Mid, $product(-1, J)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))) | (~((~$lesseq($sum(Mid, $sum($product(-1, Lo), $product(-1, I))), 0)) & (~$lesseq($sum(A, $product(-1, Mid)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(Lo, $product(-1, J)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(K, 0))))) <=> (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ($greatereq($sum(Lo, $product(-1, A)), -1) | (~($greatereq(Lo, 0) & (~$greatereq($sum(Lo, $product(-1, A)), 0)))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(K, 0))) | ![O: $int] : ((~$greatereq(K, 1)) | ($sum(O, $product(-1, A)) = 0) | (~((~$greatereq($sum(Lo, $product(-1, O)), 0)) & $lesseq($sum(O, $product(-1, A)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))) | $greatereq($sum(O, $product(-1, A)), 0)))) | ![Mid: $int, A2: map_int_elt3, I: $int] : ((~((~$lesseq($sum(Mid, $sum($product(-1, I), $product(-1, Lo))), 0)) & (~$greatereq($sum(Mid, $product(-1, A)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, K)), -1))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Mid, 0) & $lesseq($sum(Mid, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & $greatereq(I, 0))) | ![A3: map_int_elt3, Hi: $int] : (![A4: map_int_elt3] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo)), 0))) | ($lesseq($sum(Hi, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | (~($greatereq(Lo, 0) & $greatereq($sum(Mid, $product(-1, Lo)), 0) & $greatereq($sum(Hi, $product(-1, Mid)), 0) & $lesseq($sum(Hi, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & (($sum(Hi, $product(-1, A)) = 0) | ((~$greatereq($sum(I, $sum($product(-1, Hi), Mid)), 0)) & (~$greatereq($sum(Hi, $product(-1, A)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))))))))))))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(179,plain,
% 0.47/0.60 ((~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ((~($lesseq(0, Lo) & (~$lesseq(A, Lo)))) | $lesseq(A, $sum(1, Lo)) | ![O: $int] : ((O = A) | (~$lesseq(1, K)) | ![Mid: $int, A2: map_int_elt3, I: $int] : (![A3: map_int_elt3, Hi: $int] : ((~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | ![A4: map_int_elt3] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(Lo, I1))) | ($lesseq(Hi, I1) & (~$lesseq(A, I1))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~($lesseq(0, Lo) & $lesseq(Lo, Mid) & $lesseq(Mid, Hi) & $lesseq(Hi, Tmp) & (Tmp = A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & ((Hi = A) | ((~$lesseq(Hi, $sum(Mid, I))) & (~$lesseq(A, Hi)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Mid, J)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Mid) & $lesseq(Mid, A) & (A = Tmp) & $lesseq(0, I))) | (~((~$lesseq(Mid, $sum(Lo, I))) & (~$lesseq(A, Mid)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Lo, J)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, K))))) | (~((~$lesseq(O, Lo)) & $lesseq(O, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ($lesseq(A, O) | (~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Lo) & $lesseq(Lo, A) & (A = Tmp) & $lesseq(0, K))))) <=> (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ((~($greatereq(Lo, 0) & (~$lesseq($sum(A, $product(-1, Lo)), 0)))) | $lesseq($sum(A, $product(-1, Lo)), 1) | ![O: $int] : ((~$greatereq(K, 1)) | ($sum(O, $product(-1, A)) = 0) | (~((~$lesseq($sum(O, $product(-1, Lo)), 0)) & $lesseq($sum(O, $product(-1, A)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))) | $lesseq($sum(A, $product(-1, O)), 0)))) | ![Mid: $int, A2: map_int_elt3, I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, K)), -1))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Mid, 0) & $lesseq($sum(Mid, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(I, 0))) | ![A3: map_int_elt3, Hi: $int] : ((~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | ![A4: map_int_elt3] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$lesseq($sum(Lo, $product(-1, I1)), 0))) | ($lesseq($sum(Hi, $product(-1, I1)), 0) & (~$lesseq($sum(A, $product(-1, I1)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~($greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, Mid)), 0) & $lesseq($sum(Mid, $product(-1, Hi)), 0) & $lesseq($sum(Hi, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & (($sum(Hi, $product(-1, A)) = 0) | ((~$lesseq($sum(Hi, $sum($product(-1, Mid), $product(-1, I))), 0)) & (~$lesseq($sum(A, $product(-1, Hi)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(Mid, $product(-1, J)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))) | (~((~$lesseq($sum(Mid, $sum($product(-1, Lo), $product(-1, I))), 0)) & (~$lesseq($sum(A, $product(-1, Mid)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(Lo, $product(-1, J)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(K, 0)))))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(180,plain,
% 0.47/0.60 ((~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ((~($lesseq(0, Lo) & (~$lesseq(A, Lo)))) | $lesseq(A, $sum(1, Lo)) | ![O: $int] : ((O = A) | (~$lesseq(1, K)) | ![Mid: $int, A2: map_int_elt3, I: $int] : (![A3: map_int_elt3, Hi: $int] : ((~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | ![A4: map_int_elt3] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(Lo, I1))) | ($lesseq(Hi, I1) & (~$lesseq(A, I1))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~($lesseq(0, Lo) & $lesseq(Lo, Mid) & $lesseq(Mid, Hi) & $lesseq(Hi, Tmp) & (Tmp = A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & ((Hi = A) | ((~$lesseq(Hi, $sum(Mid, I))) & (~$lesseq(A, Hi)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Mid, J)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Mid) & $lesseq(Mid, A) & (A = Tmp) & $lesseq(0, I))) | (~((~$lesseq(Mid, $sum(Lo, I))) & (~$lesseq(A, Mid)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Lo, J)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, K))))) | (~((~$lesseq(O, Lo)) & $lesseq(O, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ($lesseq(A, O) | (~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Lo) & $lesseq(Lo, A) & (A = Tmp) & $lesseq(0, K))))) <=> (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ((~($lesseq(0, Lo) & (~$lesseq(A, Lo)))) | $lesseq(A, $sum(1, Lo)) | ![O: $int] : ((O = A) | (~$lesseq(1, K)) | ![Mid: $int, A2: map_int_elt3, I: $int] : (![A3: map_int_elt3, Hi: $int] : ((~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | ![A4: map_int_elt3] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(Lo, I1))) | ($lesseq(Hi, I1) & (~$lesseq(A, I1))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~($lesseq(0, Lo) & $lesseq(Lo, Mid) & $lesseq(Mid, Hi) & $lesseq(Hi, Tmp) & (Tmp = A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & ((Hi = A) | ((~$lesseq(Hi, $sum(Mid, I))) & (~$lesseq(A, Hi)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Mid, J)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Mid) & $lesseq(Mid, A) & (A = Tmp) & $lesseq(0, I))) | (~((~$lesseq(Mid, $sum(Lo, I))) & (~$lesseq(A, Mid)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Lo, J)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, K))))) | (~((~$lesseq(O, Lo)) & $lesseq(O, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ($lesseq(A, O) | (~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Lo) & $lesseq(Lo, A) & (A = Tmp) & $lesseq(0, K)))))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(181,plain,
% 0.47/0.60 ((~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : (((((($lesseq(0, Tmp) & $lesseq(0, A)) & $lesseq(0, Lo)) & $lesseq(Lo, A)) & (A = Tmp)) & $lesseq(0, K)) => ((~$lesseq($difference(A, 1), Lo)) => (($lesseq(0, Lo) & $less(Lo, A)) => ![O: $int] : (((($less(Lo, O) & $lesseq(O, A)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O)) & ($less(O, A) => (~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($difference(O, 1)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))))) => ((~(O = A)) => ($lesseq(0, $difference(K, 1)) => ![Mid: $int, A2: map_int_elt3, I: $int] : (($lesseq(0, I) & $lesseq(I, $difference(K, 1))) => ((((($less($sum(Lo, I), Mid) & $less(Mid, A)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid)) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A)) & ![J: $int] : (($lesseq(0, J) & $less(J, Lo)) => (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J)))))) => (((((($lesseq(0, Tmp) & $lesseq(0, A)) & $lesseq(0, Mid)) & $lesseq(Mid, A)) & (A = Tmp)) & $lesseq(0, I)) => ![A3: map_int_elt3, Hi: $int] : (((((($lesseq(0, Tmp) & $lesseq(0, A)) & ((Hi = A) | ($less($sum(Mid, I), Hi) & $less(Hi, A)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi)) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A)) & ![J: $int] : (($lesseq(0, J) & $less(J, Mid)) => (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))) => (permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A) => ((((((($lesseq(0, Lo) & $lesseq(Lo, Mid)) & $lesseq(Mid, Hi)) & $lesseq(Hi, Tmp)) & (Tmp = A)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi)) => ![A4: map_int_elt3] : ((((($lesseq(0, Tmp) & $lesseq(0, A)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi)) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) & ![I1: $int] : ((($lesseq(0, I1) & $less(I1, Lo)) | ($lesseq(Hi, I1) & $less(I1, A))) => (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1)))))) => permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi))))))))))))))) <=> (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ((~($lesseq(0, Lo) & (~$lesseq(A, Lo)))) | $lesseq(A, $sum(1, Lo)) | ![O: $int] : ((O = A) | (~$lesseq(1, K)) | ![Mid: $int, A2: map_int_elt3, I: $int] : (![A3: map_int_elt3, Hi: $int] : ((~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | ![A4: map_int_elt3] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(Lo, I1))) | ($lesseq(Hi, I1) & (~$lesseq(A, I1))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~($lesseq(0, Lo) & $lesseq(Lo, Mid) & $lesseq(Mid, Hi) & $lesseq(Hi, Tmp) & (Tmp = A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & ((Hi = A) | ((~$lesseq(Hi, $sum(Mid, I))) & (~$lesseq(A, Hi)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Mid, J)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Mid) & $lesseq(Mid, A) & (A = Tmp) & $lesseq(0, I))) | (~((~$lesseq(Mid, $sum(Lo, I))) & (~$lesseq(A, Mid)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Lo, J)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, K))))) | (~((~$lesseq(O, Lo)) & $lesseq(O, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ($lesseq(A, O) | (~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Lo) & $lesseq(Lo, A) & (A = Tmp) & $lesseq(0, K)))))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(182,axiom,(~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : (((((($lesseq(0, Tmp) & $lesseq(0, A)) & $lesseq(0, Lo)) & $lesseq(Lo, A)) & (A = Tmp)) & $lesseq(0, K)) => ((~$lesseq($difference(A, 1), Lo)) => (($lesseq(0, Lo) & $less(Lo, A)) => ![O: $int] : (((($less(Lo, O) & $lesseq(O, A)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O)) & ($less(O, A) => (~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($difference(O, 1)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))))) => ((~(O = A)) => ($lesseq(0, $difference(K, 1)) => ![Mid: $int, A2: map_int_elt3, I: $int] : (($lesseq(0, I) & $lesseq(I, $difference(K, 1))) => ((((($less($sum(Lo, I), Mid) & $less(Mid, A)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid)) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A)) & ![J: $int] : (($lesseq(0, J) & $less(J, Lo)) => (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J)))))) => (((((($lesseq(0, Tmp) & $lesseq(0, A)) & $lesseq(0, Mid)) & $lesseq(Mid, A)) & (A = Tmp)) & $lesseq(0, I)) => ![A3: map_int_elt3, Hi: $int] : (((((($lesseq(0, Tmp) & $lesseq(0, A)) & ((Hi = A) | ($less($sum(Mid, I), Hi) & $less(Hi, A)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi)) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A)) & ![J: $int] : (($lesseq(0, J) & $less(J, Mid)) => (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))) => (permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A) => ((((((($lesseq(0, Lo) & $lesseq(Lo, Mid)) & $lesseq(Mid, Hi)) & $lesseq(Hi, Tmp)) & (Tmp = A)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi)) => ![A4: map_int_elt3] : ((((($lesseq(0, Tmp) & $lesseq(0, A)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi)) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) & ![I1: $int] : ((($lesseq(0, I1) & $less(I1, Lo)) | ($lesseq(Hi, I1) & $less(I1, A))) => (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1)))))) => permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_naturalrec')).
% 0.47/0.61 tff(183,plain,
% 0.47/0.61 (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ((~($lesseq(0, Lo) & (~$lesseq(A, Lo)))) | $lesseq(A, $sum(1, Lo)) | ![O: $int] : ((O = A) | (~$lesseq(1, K)) | ![Mid: $int, A2: map_int_elt3, I: $int] : (![A3: map_int_elt3, Hi: $int] : ((~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | ![A4: map_int_elt3] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(Lo, I1))) | ($lesseq(Hi, I1) & (~$lesseq(A, I1))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~($lesseq(0, Lo) & $lesseq(Lo, Mid) & $lesseq(Mid, Hi) & $lesseq(Hi, Tmp) & (Tmp = A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & ((Hi = A) | ((~$lesseq(Hi, $sum(Mid, I))) & (~$lesseq(A, Hi)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Mid, J)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Mid) & $lesseq(Mid, A) & (A = Tmp) & $lesseq(0, I))) | (~((~$lesseq(Mid, $sum(Lo, I))) & (~$lesseq(A, Mid)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Lo, J)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, K))))) | (~((~$lesseq(O, Lo)) & $lesseq(O, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ($lesseq(A, O) | (~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Lo) & $lesseq(Lo, A) & (A = Tmp) & $lesseq(0, K))))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.47/0.61 tff(184,plain,
% 0.47/0.61 (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ((~($lesseq(0, Lo) & (~$lesseq(A, Lo)))) | $lesseq(A, $sum(1, Lo)) | ![O: $int] : ((O = A) | (~$lesseq(1, K)) | ![Mid: $int, A2: map_int_elt3, I: $int] : (![A3: map_int_elt3, Hi: $int] : ((~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | ![A4: map_int_elt3] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(Lo, I1))) | ($lesseq(Hi, I1) & (~$lesseq(A, I1))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~($lesseq(0, Lo) & $lesseq(Lo, Mid) & $lesseq(Mid, Hi) & $lesseq(Hi, Tmp) & (Tmp = A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & ((Hi = A) | ((~$lesseq(Hi, $sum(Mid, I))) & (~$lesseq(A, Hi)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Mid, J)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Mid) & $lesseq(Mid, A) & (A = Tmp) & $lesseq(0, I))) | (~((~$lesseq(Mid, $sum(Lo, I))) & (~$lesseq(A, Mid)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Lo, J)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, K))))) | (~((~$lesseq(O, Lo)) & $lesseq(O, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ($lesseq(A, O) | (~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Lo) & $lesseq(Lo, A) & (A = Tmp) & $lesseq(0, K))))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[183, 180])).
% 0.47/0.61 tff(185,plain,
% 0.47/0.61 (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ((~($lesseq(0, Lo) & (~$lesseq(A, Lo)))) | $lesseq(A, $sum(1, Lo)) | ![O: $int] : ((O = A) | (~$lesseq(1, K)) | ![Mid: $int, A2: map_int_elt3, I: $int] : (![A3: map_int_elt3, Hi: $int] : ((~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | ![A4: map_int_elt3] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(Lo, I1))) | ($lesseq(Hi, I1) & (~$lesseq(A, I1))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~($lesseq(0, Lo) & $lesseq(Lo, Mid) & $lesseq(Mid, Hi) & $lesseq(Hi, Tmp) & (Tmp = A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & ((Hi = A) | ((~$lesseq(Hi, $sum(Mid, I))) & (~$lesseq(A, Hi)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Mid, J)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Mid) & $lesseq(Mid, A) & (A = Tmp) & $lesseq(0, I))) | (~((~$lesseq(Mid, $sum(Lo, I))) & (~$lesseq(A, Mid)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Lo, J)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, K))))) | (~((~$lesseq(O, Lo)) & $lesseq(O, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ($lesseq(A, O) | (~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Lo) & $lesseq(Lo, A) & (A = Tmp) & $lesseq(0, K))))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.47/0.61 tff(186,plain,
% 0.47/0.61 (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ((~($lesseq(0, Lo) & (~$lesseq(A, Lo)))) | $lesseq(A, $sum(1, Lo)) | ![O: $int] : ((O = A) | (~$lesseq(1, K)) | ![Mid: $int, A2: map_int_elt3, I: $int] : (![A3: map_int_elt3, Hi: $int] : ((~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | ![A4: map_int_elt3] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(Lo, I1))) | ($lesseq(Hi, I1) & (~$lesseq(A, I1))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~($lesseq(0, Lo) & $lesseq(Lo, Mid) & $lesseq(Mid, Hi) & $lesseq(Hi, Tmp) & (Tmp = A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & ((Hi = A) | ((~$lesseq(Hi, $sum(Mid, I))) & (~$lesseq(A, Hi)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Mid, J)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Mid) & $lesseq(Mid, A) & (A = Tmp) & $lesseq(0, I))) | (~((~$lesseq(Mid, $sum(Lo, I))) & (~$lesseq(A, Mid)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(Lo, J)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, K))))) | (~((~$lesseq(O, Lo)) & $lesseq(O, A) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ($lesseq(A, O) | (~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, Lo) & $lesseq(Lo, A) & (A = Tmp) & $lesseq(0, K))))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[185, 180])).
% 0.47/0.61 tff(187,plain,
% 0.47/0.61 (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ((~($greatereq(Lo, 0) & (~$lesseq($sum(A, $product(-1, Lo)), 0)))) | $lesseq($sum(A, $product(-1, Lo)), 1) | ![O: $int] : ((~$greatereq(K, 1)) | ($sum(O, $product(-1, A)) = 0) | (~((~$lesseq($sum(O, $product(-1, Lo)), 0)) & $lesseq($sum(O, $product(-1, A)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))) | $lesseq($sum(A, $product(-1, O)), 0)))) | ![Mid: $int, A2: map_int_elt3, I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, K)), -1))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Mid, 0) & $lesseq($sum(Mid, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(I, 0))) | ![A3: map_int_elt3, Hi: $int] : ((~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | ![A4: map_int_elt3] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$lesseq($sum(Lo, $product(-1, I1)), 0))) | ($lesseq($sum(Hi, $product(-1, I1)), 0) & (~$lesseq($sum(A, $product(-1, I1)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~($greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, Mid)), 0) & $lesseq($sum(Mid, $product(-1, Hi)), 0) & $lesseq($sum(Hi, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & (($sum(Hi, $product(-1, A)) = 0) | ((~$lesseq($sum(Hi, $sum($product(-1, Mid), $product(-1, I))), 0)) & (~$lesseq($sum(A, $product(-1, Hi)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(Mid, $product(-1, J)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))) | (~((~$lesseq($sum(Mid, $sum($product(-1, Lo), $product(-1, I))), 0)) & (~$lesseq($sum(A, $product(-1, Mid)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(Lo, $product(-1, J)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(K, 0))))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.47/0.61 tff(188,plain,
% 0.47/0.61 (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ($greatereq($sum(Lo, $product(-1, A)), -1) | (~($greatereq(Lo, 0) & (~$greatereq($sum(Lo, $product(-1, A)), 0)))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(K, 0))) | ![O: $int] : ((~$greatereq(K, 1)) | ($sum(O, $product(-1, A)) = 0) | (~((~$greatereq($sum(Lo, $product(-1, O)), 0)) & $lesseq($sum(O, $product(-1, A)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))) | $greatereq($sum(O, $product(-1, A)), 0)))) | ![Mid: $int, A2: map_int_elt3, I: $int] : ((~((~$lesseq($sum(Mid, $sum($product(-1, I), $product(-1, Lo))), 0)) & (~$greatereq($sum(Mid, $product(-1, A)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, K)), -1))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Mid, 0) & $lesseq($sum(Mid, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & $greatereq(I, 0))) | ![A3: map_int_elt3, Hi: $int] : (![A4: map_int_elt3] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo)), 0))) | ($lesseq($sum(Hi, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | (~($greatereq(Lo, 0) & $greatereq($sum(Mid, $product(-1, Lo)), 0) & $greatereq($sum(Hi, $product(-1, Mid)), 0) & $lesseq($sum(Hi, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & (($sum(Hi, $product(-1, A)) = 0) | ((~$greatereq($sum(I, $sum($product(-1, Hi), Mid)), 0)) & (~$greatereq($sum(Hi, $product(-1, A)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))))))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[187, 178])).
% 0.47/0.61 tff(189,plain,
% 0.47/0.61 (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ($greatereq($sum(Lo, $product(-1, A)), -1) | (~($greatereq(Lo, 0) & (~$greatereq($sum(Lo, $product(-1, A)), 0)))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(K, 0))) | ![O: $int] : ((~$greatereq(K, 1)) | ($sum(O, $product(-1, A)) = 0) | (~((~$greatereq($sum(Lo, $product(-1, O)), 0)) & $lesseq($sum(O, $product(-1, A)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))) | $greatereq($sum(O, $product(-1, A)), 0)))) | ![Mid: $int, A2: map_int_elt3, I: $int] : ((~((~$lesseq($sum(Mid, $sum($product(-1, I), $product(-1, Lo))), 0)) & (~$greatereq($sum(Mid, $product(-1, A)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, K)), -1))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Mid, 0) & $lesseq($sum(Mid, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & $greatereq(I, 0))) | ![A3: map_int_elt3, Hi: $int] : (![A4: map_int_elt3] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo)), 0))) | ($lesseq($sum(Hi, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | (~($greatereq(Lo, 0) & $greatereq($sum(Mid, $product(-1, Lo)), 0) & $greatereq($sum(Hi, $product(-1, Mid)), 0) & $lesseq($sum(Hi, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & (($sum(Hi, $product(-1, A)) = 0) | ((~$greatereq($sum(I, $sum($product(-1, Hi), Mid)), 0)) & (~$greatereq($sum(Hi, $product(-1, A)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))))))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[188, 177])).
% 0.47/0.61 tff(190,plain,
% 0.47/0.61 (~![Tmp: $int, A: $int, A1: map_int_elt3, Lo: $int, K: $int] : ($greatereq($sum(Lo, $product(-1, A)), -1) | (~($greatereq(Lo, 0) & (~$greatereq($sum(Lo, $product(-1, A)), 0)))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Lo, 0) & $lesseq($sum(Lo, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & $greatereq(K, 0))) | ![O: $int] : ((~$greatereq(K, 1)) | ($sum(O, $product(-1, A)) = 0) | (~((~$greatereq($sum(Lo, $product(-1, O)), 0)) & $lesseq($sum(O, $product(-1, A)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A1))), Lo, O) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1), t2tb($sum(-1, O)))), tb2t11(get(elt7, int, t2tb12(A1), t2tb(O))))) | $greatereq($sum(O, $product(-1, A)), 0)))) | ![Mid: $int, A2: map_int_elt3, I: $int] : ((~((~$lesseq($sum(Mid, $sum($product(-1, I), $product(-1, Lo))), 0)) & (~$greatereq($sum(Mid, $product(-1, A)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A2))), Lo, Mid) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A2)), Lo, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1), t2tb(J))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, K)), -1))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(Mid, 0) & $lesseq($sum(Mid, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & $greatereq(I, 0))) | ![A3: map_int_elt3, Hi: $int] : (![A4: map_int_elt3] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A4))), Lo, Hi) & permut3(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo)), 0))) | ($lesseq($sum(Hi, $product(-1, I1)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3), t2tb(I1))))))) | permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A3)), mk_array1(elt7, A, t2tb12(A4)), Lo, Hi)) | (~permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A1)), mk_array1(elt7, A, t2tb12(A3)), Lo, A)) | (~($greatereq(Lo, 0) & $greatereq($sum(Mid, $product(-1, Lo)), 0) & $greatereq($sum(Hi, $product(-1, Mid)), 0) & $lesseq($sum(Hi, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Lo, Mid) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi))) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & (($sum(Hi, $product(-1, A)) = 0) | ((~$greatereq($sum(I, $sum($product(-1, Hi), Mid)), 0)) & (~$greatereq($sum(Hi, $product(-1, A)), 0)))) & sorted_sub4(tb2t10(mk_array1(elt7, A, t2tb12(A3))), Mid, Hi) & permut_sub1(elt7, mk_array1(elt7, A, t2tb12(A2)), mk_array1(elt7, A, t2tb12(A3)), Mid, A) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2), t2tb(J)))))))))))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[189, 177])).
% 0.47/0.61 tff(191,plain,
% 0.47/0.61 ((~$greatereq($sum(Lo!12, $product(-1, A!14)), -1)) & $greatereq(Lo!12, 0) & (~$greatereq($sum(Lo!12, $product(-1, A!14)), 0)) & $greatereq(Tmp!15, 0) & $greatereq(A!14, 0) & $lesseq($sum(Lo!12, $product(-1, A!14)), 0) & ($sum(A!14, $product(-1, Tmp!15)) = 0) & $greatereq(K!11, 0) & $greatereq(K!11, 1) & (~($sum(A!14, $product(-1, O!16)) = 0)) & (~$greatereq($sum(Lo!12, $product(-1, O!16)), 0)) & $greatereq($sum(A!14, $product(-1, O!16)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A1!13))), Lo!12, O!16) & ((~le4(tb2t11(get(elt7, int, t2tb12(A1!13), t2tb($sum(-1, O!16)))), tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(O!16))))) | $lesseq($sum(A!14, $product(-1, O!16)), 0)) & (~$greatereq($sum(Lo!12, $sum(I!17, $product(-1, Mid!19))), 0)) & (~$lesseq($sum(A!14, $product(-1, Mid!19)), 0)) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A2!18))), Lo!12, Mid!19) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A2!18)), Lo!12, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Lo!12)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A1!13), t2tb(J))))) & $greatereq(I!17, 0) & $greatereq($sum(K!11, $product(-1, I!17)), 1) & $greatereq(Mid!19, 0) & $greatereq($sum(A!14, $product(-1, Mid!19)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A4!22))), Lo!12, Hi!20) & permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1))))) & (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A1!13)), mk_array1(elt7, A!14, t2tb12(A3!21)), Lo!12, A!14) & $lesseq($sum(Lo!12, $product(-1, Mid!19)), 0) & $lesseq($sum(Mid!19, $product(-1, Hi!20)), 0) & $greatereq($sum(Tmp!15, $product(-1, Hi!20)), 0) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Lo!12, Mid!19) & sorted_sub4(tb2t10(mk_array1(elt7, A!14, t2tb12(A3!21))), Mid!19, Hi!20) & (($sum(A!14, $product(-1, Hi!20)) = 0) | ((~$greatereq($sum(I!17, $sum(Mid!19, $product(-1, Hi!20))), 0)) & (~$lesseq($sum(A!14, $product(-1, Hi!20)), 0)))) & permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A2!18)), mk_array1(elt7, A!14, t2tb12(A3!21)), Mid!19, A!14) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Mid!19)), 0)))) | (tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(J))) = tb2t11(get(elt7, int, t2tb12(A2!18), t2tb(J)))))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[190, 176])).
% 0.47/0.61 tff(192,plain,
% 0.47/0.61 (![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, Lo!12)), 0))) | ($greatereq($sum(I1, $product(-1, Hi!20)), 0) & (~$greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))),
% 0.47/0.61 inference(and_elim,[status(thm)],[191])).
% 0.47/0.61 tff(193,plain,
% 0.47/0.61 (![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[192, 137])).
% 0.47/0.61 tff(194,plain,
% 0.47/0.61 (![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[193, 135])).
% 0.47/0.61 tff(195,plain,
% 0.47/0.61 (((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | ((~((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))))) <=> ((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | (~((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(196,plain,
% 0.47/0.61 (((~((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Hi!20)), 0)) | $greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))) <=> ((~((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(197,plain,
% 0.47/0.61 (((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | ((~((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Hi!20)), 0)) | $greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))))) <=> ((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | ((~((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))))),
% 0.47/0.61 inference(monotonicity,[status(thm)],[196])).
% 0.47/0.61 tff(198,plain,
% 0.47/0.61 (((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | ((~((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Hi!20)), 0)) | $greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))))) <=> ((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | (~((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))))),
% 0.47/0.62 inference(transitivity,[status(thm)],[197, 195])).
% 0.47/0.62 tff(199,plain,
% 0.47/0.62 ((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | ((~((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Hi!20)), 0)) | $greatereq($sum(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))))),
% 0.47/0.62 inference(quant_inst,[status(thm)],[])).
% 0.47/0.62 tff(200,plain,
% 0.47/0.62 ((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | (~((~((~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.47/0.62 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.47/0.62 tff(201,plain,
% 0.47/0.62 (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[200, 194, 133])).
% 0.47/0.62 tff(202,plain,
% 0.47/0.62 (tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.62 inference(monotonicity,[status(thm)],[113])).
% 0.47/0.62 tff(203,plain,
% 0.47/0.62 (tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.62 inference(transitivity,[status(thm)],[202, 201])).
% 0.47/0.62 tff(204,plain,
% 0.47/0.62 (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = t2tb11(tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.47/0.62 inference(monotonicity,[status(thm)],[203])).
% 0.47/0.62 tff(205,plain,
% 0.47/0.62 (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))),
% 0.47/0.62 inference(transitivity,[status(thm)],[204, 124])).
% 0.47/0.62 tff(206,plain,
% 0.47/0.62 ((t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) <=> (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.62 inference(monotonicity,[status(thm)],[205, 113])).
% 0.47/0.62 tff(207,plain,
% 0.47/0.62 ((get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) <=> (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.62 inference(symmetry,[status(thm)],[206])).
% 0.47/0.62 tff(208,plain,
% 0.47/0.62 ((~(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) <=> (~(t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.47/0.62 inference(monotonicity,[status(thm)],[207])).
% 0.47/0.62 tff(209,plain,
% 0.47/0.62 (($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0))) | (~(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.47/0.62 inference(tautology,[status(thm)],[])).
% 0.47/0.62 tff(210,plain,
% 0.47/0.62 (~(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[209, 125])).
% 0.47/0.62 tff(211,plain,
% 0.47/0.62 (~(t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.62 inference(modus_ponens,[status(thm)],[210, 208])).
% 0.47/0.62 tff(212,plain,
% 0.47/0.62 (((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | ((~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))) <=> ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | (~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.47/0.62 inference(rewrite,[status(thm)],[])).
% 0.47/0.62 tff(213,plain,
% 0.47/0.62 ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | ((~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.47/0.62 inference(quant_inst,[status(thm)],[])).
% 0.47/0.62 tff(214,plain,
% 0.47/0.62 ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | (~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.62 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.47/0.62 tff(215,plain,
% 0.47/0.62 ((~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[214, 49])).
% 0.47/0.62 tff(216,plain,
% 0.47/0.62 ($false),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[215, 211, 118])).
% 0.47/0.62 tff(217,plain,($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.62 tff(218,plain,
% 0.47/0.62 ((~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)))))) | map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0))))),
% 0.47/0.62 inference(tautology,[status(thm)],[])).
% 0.47/0.62 tff(219,plain,
% 0.47/0.62 ((~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12) | (~($lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$greatereq(tptp_fun_I_9(Lo!12, 0, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)))))) | map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.53/0.62 tff(220,plain,
% 0.53/0.62 (map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), 0, Lo!12)),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[219, 111])).
% 0.53/0.62 tff(221,plain,
% 0.53/0.62 ($false),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[220, 102])).
% 0.53/0.62 tff(222,plain,(map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.62 tff(223,plain,
% 0.53/0.62 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : refl((permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1)))))) <=> (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1)))))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(224,plain,
% 0.53/0.62 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1)))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[223])).
% 0.53/0.62 tff(225,plain,
% 0.53/0.62 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : rewrite((permut_sub1(A, A1, A2, L, U) <=> (map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1)))) <=> (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1)))))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(226,plain,
% 0.53/0.62 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1)))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[225])).
% 0.53/0.62 tff(227,plain,
% 0.53/0.62 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1)))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(228,plain,
% 0.53/0.62 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : rewrite((permut_sub1(A, A1, A2, L, U) <=> ((map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U)) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1)))) <=> (permut_sub1(A, A1, A2, L, U) <=> (map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1)))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(229,plain,
% 0.53/0.62 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> ((map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U)) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1)))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[228])).
% 0.53/0.62 tff(230,axiom,(![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> ((map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U)) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','permut_sub_def')).
% 0.53/0.62 tff(231,plain,
% 0.53/0.62 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.53/0.62 tff(232,plain,
% 0.53/0.62 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.53/0.62 tff(233,plain,(
% 0.53/0.62 ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L) & permut3(A, A1, A2, L, U) & map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))),
% 0.53/0.62 inference(skolemize,[status(sab)],[232])).
% 0.53/0.62 tff(234,plain,
% 0.53/0.62 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.53/0.62 tff(235,plain,
% 0.53/0.62 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[234, 224])).
% 0.53/0.62 tff(236,plain,
% 0.53/0.62 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))) | (permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))) | (permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))))))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(237,plain,
% 0.53/0.62 ((permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))))))) <=> (permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(238,plain,
% 0.53/0.62 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))) | (permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))) | (permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))))))))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[237])).
% 0.53/0.62 tff(239,plain,
% 0.53/0.62 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))) | (permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))) | (permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))))))))),
% 0.53/0.62 inference(transitivity,[status(thm)],[238, 236])).
% 0.53/0.62 tff(240,plain,
% 0.53/0.62 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))) | (permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(241,plain,
% 0.53/0.63 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut_sub1(A, A1, A2, L, U) <=> (~((~map_eq_sub1(A, elts(A, A1), elts(A, A2), 0, L)) | (~permut3(A, A1, A2, L, U)) | (~map_eq_sub1(A, elts(A, A1), elts(A, A2), U, length1(A, A1))))))) | (permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.53/0.63 tff(242,plain,
% 0.53/0.63 (permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[241, 235])).
% 0.53/0.63 tff(243,plain,
% 0.53/0.63 (~permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)),
% 0.53/0.63 inference(and_elim,[status(thm)],[191])).
% 0.53/0.63 tff(244,plain,
% 0.53/0.63 ((~(permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))))) | permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) | ((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(245,plain,
% 0.53/0.63 ((~(permut_sub1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20) <=> (~((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))))) | ((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.53/0.63 tff(246,plain,
% 0.53/0.63 ((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[245, 242])).
% 0.53/0.63 tff(247,plain,
% 0.53/0.63 (permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)),
% 0.53/0.63 inference(and_elim,[status(thm)],[191])).
% 0.53/0.63 tff(248,plain,
% 0.53/0.63 ((~((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))) | (~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(249,plain,
% 0.53/0.63 ((~((~permut3(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)), mk_array1(elt7, A!14, t2tb12(A4!22)), Lo!12, Hi!20)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))))) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.53/0.63 tff(250,plain,
% 0.53/0.63 ((~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), 0, Lo!12)) | (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[249, 246])).
% 0.53/0.63 tff(251,plain,
% 0.53/0.63 (~map_eq_sub1(elt7, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[250, 222])).
% 0.53/0.63 tff(252,plain,
% 0.53/0.63 (~map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[251, 97])).
% 0.53/0.63 tff(253,plain,
% 0.53/0.63 ((~(map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))))) | map_eq_sub1(elt7, t2tb12(A3!21), t2tb12(A4!22), Hi!20, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21)))) | (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(254,plain,
% 0.53/0.63 (~($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[253, 252, 94])).
% 0.53/0.63 tff(255,plain,
% 0.53/0.63 (($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~$lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(256,plain,
% 0.53/0.63 (~$lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.53/0.63 tff(257,assumption,($lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)), introduced(assumption)).
% 0.53/0.63 tff(258,plain,
% 0.53/0.63 (^[A: ty, U: $int, U1: uni] : refl(($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0) <=> ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0))),
% 0.53/0.63 inference(bind,[status(th)],[])).
% 0.53/0.63 tff(259,plain,
% 0.53/0.63 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.53/0.63 inference(quant_intro,[status(thm)],[258])).
% 0.53/0.63 tff(260,plain,
% 0.53/0.63 (^[A: ty, U: $int, U1: uni] : trans(monotonicity(rewrite($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = $sum($product(-1, U), length1(A, mk_array1(A, U, U1)))), (($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ($sum($product(-1, U), length1(A, mk_array1(A, U, U1))) = 0))), rewrite(($sum($product(-1, U), length1(A, mk_array1(A, U, U1))) = 0) <=> ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)), (($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)))),
% 0.53/0.63 inference(bind,[status(th)],[])).
% 0.53/0.63 tff(261,plain,
% 0.53/0.63 (![A: ty, U: $int, U1: uni] : ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.53/0.63 inference(quant_intro,[status(thm)],[260])).
% 0.53/0.63 tff(262,plain,
% 0.53/0.63 (^[A: ty, U: $int, U1: uni] : rewrite((length1(A, mk_array1(A, U, U1)) = U) <=> ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0))),
% 0.53/0.63 inference(bind,[status(th)],[])).
% 0.53/0.63 tff(263,plain,
% 0.53/0.63 (![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0)),
% 0.53/0.63 inference(quant_intro,[status(thm)],[262])).
% 0.53/0.63 tff(264,plain,
% 0.53/0.63 (![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(265,axiom,(![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','length_def1')).
% 0.53/0.63 tff(266,plain,
% 0.53/0.63 (![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.53/0.63 tff(267,plain,
% 0.53/0.63 (![A: ty, U: $int, U1: uni] : ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0)),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[266, 263])).
% 0.53/0.63 tff(268,plain,
% 0.53/0.63 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[267, 261])).
% 0.53/0.63 tff(269,plain,(
% 0.53/0.63 ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.53/0.63 inference(skolemize,[status(sab)],[268])).
% 0.53/0.63 tff(270,plain,
% 0.53/0.63 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[269, 259])).
% 0.53/0.63 tff(271,plain,
% 0.53/0.63 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)) | ($sum(A!14, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) = 0)),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(272,plain,
% 0.53/0.63 ($sum(A!14, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) = 0),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[271, 270])).
% 0.53/0.63 tff(273,plain,
% 0.53/0.63 ((~($sum(A!14, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))) = 0)) | $greatereq($sum(A!14, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))), 0)),
% 0.53/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.63 tff(274,plain,
% 0.53/0.63 ($greatereq($sum(A!14, $product(-1, length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))))), 0)),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[273, 272])).
% 0.53/0.63 tff(275,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(theory_lemma,[status(thm)],[274, 257, 256])).
% 0.53/0.63 tff(276,plain,(~$lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.63 tff(277,plain,
% 0.53/0.63 (($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | $lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(278,plain,
% 0.53/0.63 ($lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[277, 254])).
% 0.53/0.63 tff(279,plain,
% 0.53/0.63 ((~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(280,plain,
% 0.53/0.63 ((~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[279, 278])).
% 0.53/0.63 tff(281,plain,
% 0.53/0.63 (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[280, 276])).
% 0.53/0.63 tff(282,plain,
% 0.53/0.63 (((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))) | ((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(283,plain,
% 0.53/0.63 ((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.53/0.63 tff(284,plain,
% 0.53/0.63 (((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | ((~((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))))) <=> ((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | (~((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(285,plain,
% 0.53/0.64 (((~((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Hi!20)), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))) <=> ((~((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(286,plain,
% 0.53/0.64 (((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | ((~((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Hi!20)), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))))) <=> ((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | ((~((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))))),
% 0.53/0.64 inference(monotonicity,[status(thm)],[285])).
% 0.53/0.64 tff(287,plain,
% 0.53/0.64 (((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | ((~((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Hi!20)), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))))) <=> ((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | (~((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))))),
% 0.53/0.64 inference(transitivity,[status(thm)],[286, 284])).
% 0.53/0.64 tff(288,plain,
% 0.53/0.64 ((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | ((~((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, Hi!20)), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))))),
% 0.53/0.64 inference(quant_inst,[status(thm)],[])).
% 0.53/0.64 tff(289,plain,
% 0.53/0.64 ((~![I1: $int] : ((~((~((~$greatereq(I1, 0)) | $greatereq($sum(I1, $product(-1, Lo!12)), 0))) | (~((~$greatereq($sum(I1, $product(-1, Hi!20)), 0)) | $greatereq($sum(I1, $product(-1, A!14)), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(I1))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(I1)))))) | (~((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.53/0.64 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.53/0.64 tff(290,plain,
% 0.53/0.64 ((~((~((~$greatereq(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7), 0)) | $lesseq($sum(Lo!12, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~((~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0)) | $lesseq($sum(A!14, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))))) | (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[289, 194])).
% 0.53/0.64 tff(291,plain,
% 0.53/0.64 (tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[290, 283])).
% 0.53/0.64 tff(292,plain,
% 0.53/0.64 (tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.53/0.64 inference(monotonicity,[status(thm)],[27])).
% 0.53/0.64 tff(293,plain,
% 0.53/0.64 (tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) = tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.53/0.64 inference(transitivity,[status(thm)],[292, 291, 66])).
% 0.53/0.64 tff(294,plain,
% 0.53/0.64 (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.53/0.64 inference(monotonicity,[status(thm)],[293])).
% 0.53/0.64 tff(295,plain,
% 0.53/0.64 (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A4!22))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.53/0.64 inference(symmetry,[status(thm)],[294])).
% 0.53/0.64 tff(296,plain,
% 0.53/0.64 (sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) <=> sort1(elt7, get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.53/0.64 inference(monotonicity,[status(thm)],[64])).
% 0.53/0.64 tff(297,plain,
% 0.53/0.64 (sort1(elt7, get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) <=> sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.53/0.64 inference(symmetry,[status(thm)],[296])).
% 0.53/0.64 tff(298,plain,
% 0.53/0.64 ((~![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))) | sort1(elt7, get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.53/0.64 inference(quant_inst,[status(thm)],[])).
% 0.53/0.64 tff(299,plain,
% 0.53/0.64 (sort1(elt7, get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[298, 36])).
% 0.53/0.64 tff(300,plain,
% 0.53/0.64 (sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.53/0.64 inference(modus_ponens,[status(thm)],[299, 297])).
% 0.53/0.64 tff(301,plain,
% 0.53/0.64 (((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | ((~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))) <=> ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | (~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(302,plain,
% 0.53/0.64 ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | ((~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.53/0.64 inference(quant_inst,[status(thm)],[])).
% 0.53/0.64 tff(303,plain,
% 0.53/0.64 ((~![J: uni] : ((~sort1(elt7, J)) | (t2tb11(tb2t11(J)) = J))) | (~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.53/0.64 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.53/0.64 tff(304,plain,
% 0.53/0.64 ((~sort1(elt7, get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) | (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[303, 49])).
% 0.53/0.64 tff(305,plain,
% 0.53/0.64 (t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))) = get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[304, 300])).
% 0.53/0.64 tff(306,plain,
% 0.53/0.64 (get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = t2tb11(tb2t11(get(elt7, int, elts(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.53/0.64 inference(symmetry,[status(thm)],[305])).
% 0.53/0.64 tff(307,plain,
% 0.53/0.64 (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))),
% 0.53/0.65 inference(transitivity,[status(thm)],[63, 306, 295, 54, 27])).
% 0.53/0.65 tff(308,plain,
% 0.53/0.65 (($lesseq($sum(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0) | (get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))) | (~$lesseq($sum(Hi!20, $product(-1, tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))), 0))) | (~(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7)))))),
% 0.53/0.65 inference(tautology,[status(thm)],[])).
% 0.53/0.65 tff(309,plain,
% 0.53/0.65 (~(get(elt7, int, t2tb12(A3!21), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))) = get(elt7, int, t2tb12(A4!22), t2tb(tptp_fun_I_9(length1(elt7, mk_array1(elt7, A!14, t2tb12(A3!21))), Hi!20, t2tb12(A4!22), t2tb12(A3!21), elt7))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[308, 254])).
% 0.53/0.65 tff(310,plain,
% 0.53/0.65 ($false),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[309, 307])).
% 0.53/0.65 % SZS output end Proof
%------------------------------------------------------------------------------