TSTP Solution File: SWW622_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW622_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 0.49s
% Output : Proof 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW622_2 : TPTP v8.1.0. Released v6.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.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 20:45:28 EDT 2022
% 0.13/0.35 % 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.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(permut2_type, type, (
% 0.20/0.49 permut2: ( ty * uni * uni * $int * $int ) > $o)).
% 0.20/0.49 tff(tptp_fun_R_11_type, type, (
% 0.20/0.49 tptp_fun_R_11: $int)).
% 0.20/0.49 tff(tptp_fun_L_12_type, type, (
% 0.20/0.49 tptp_fun_L_12: $int)).
% 0.20/0.49 tff(t2tb6_type, type, (
% 0.20/0.49 t2tb6: map_int_elt1 > uni)).
% 0.20/0.49 tff(tptp_fun_A4_18_type, type, (
% 0.20/0.49 tptp_fun_A4_18: map_int_elt1)).
% 0.20/0.49 tff(tptp_fun_A2_16_type, type, (
% 0.20/0.49 tptp_fun_A2_16: map_int_elt1)).
% 0.20/0.49 tff(elt3_type, type, (
% 0.20/0.49 elt3: ty)).
% 0.20/0.49 tff(tptp_fun_A1_14_type, type, (
% 0.20/0.49 tptp_fun_A1_14: map_int_elt1)).
% 0.20/0.49 tff(elts_type, type, (
% 0.20/0.49 elts: ( ty * uni ) > uni)).
% 0.20/0.49 tff(mk_array1_type, type, (
% 0.20/0.49 mk_array1: ( ty * $int * uni ) > uni)).
% 0.20/0.49 tff(tptp_fun_A_15_type, type, (
% 0.20/0.49 tptp_fun_A_15: $int)).
% 0.20/0.49 tff(sort1_type, type, (
% 0.20/0.49 sort1: ( ty * uni ) > $o)).
% 0.20/0.49 tff(map_type, type, (
% 0.20/0.49 map: ( ty * ty ) > ty)).
% 0.20/0.49 tff(int_type, type, (
% 0.20/0.49 int: ty)).
% 0.20/0.49 tff(length1_type, type, (
% 0.20/0.49 length1: ( ty * uni ) > $int)).
% 0.20/0.49 tff(permut3_type, type, (
% 0.20/0.49 permut3: ( ty * uni * uni * $int * $int ) > $o)).
% 0.20/0.49 tff(map_eq_sub1_type, type, (
% 0.20/0.49 map_eq_sub1: ( ty * uni * uni * $int * $int ) > $o)).
% 0.20/0.49 tff(tptp_fun_I_9_type, type, (
% 0.20/0.49 tptp_fun_I_9: ( $int * $int * uni * uni * ty ) > $int)).
% 0.20/0.49 tff(get_type, type, (
% 0.20/0.49 get: ( ty * ty * uni * uni ) > uni)).
% 0.20/0.49 tff(t2tb_type, type, (
% 0.20/0.49 t2tb: $int > uni)).
% 0.20/0.49 tff(tptp_fun_A3_17_type, type, (
% 0.20/0.49 tptp_fun_A3_17: map_int_elt1)).
% 0.20/0.49 tff(t2tb5_type, type, (
% 0.20/0.49 t2tb5: elt2 > uni)).
% 0.20/0.49 tff(tb2t5_type, type, (
% 0.20/0.49 tb2t5: uni > elt2)).
% 0.20/0.49 tff(sorted_sub2_type, type, (
% 0.20/0.49 sorted_sub2: ( array_elt1 * $int * $int ) > $o)).
% 0.20/0.49 tff(div_type, type, (
% 0.20/0.49 div: ( $int * $int ) > $int)).
% 0.20/0.49 tff(tb2t4_type, type, (
% 0.20/0.49 tb2t4: uni > array_elt1)).
% 0.20/0.49 tff(tptp_fun_Tmp_13_type, type, (
% 0.20/0.49 tptp_fun_Tmp_13: $int)).
% 0.20/0.49 tff(permut_sub1_type, type, (
% 0.20/0.49 permut_sub1: ( ty * uni * uni * $int * $int ) > $o)).
% 0.20/0.49 tff(1,plain,
% 0.20/0.49 (^[X: map_int_elt1] : refl(sort1(map(int, elt3), t2tb6(X)) <=> sort1(map(int, elt3), t2tb6(X)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(2,plain,
% 0.20/0.49 (![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X)) <=> ![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 (![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X)) <=> ![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(4,axiom,(![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2tb_sort7')).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.49 tff(6,plain,(
% 0.20/0.49 ![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X))),
% 0.20/0.49 inference(skolemize,[status(sab)],[5])).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 ((~![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X))) | sort1(map(int, elt3), t2tb6(A4!18))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(9,plain,
% 0.20/0.49 (sort1(map(int, elt3), t2tb6(A4!18))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (^[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)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(13,plain,
% 0.20/0.49 (^[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)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (![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))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.50 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')).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.50 tff(17,plain,
% 0.20/0.50 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.50 tff(18,plain,(
% 0.20/0.50 ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.50 inference(skolemize,[status(sab)],[17])).
% 0.20/0.50 tff(19,plain,
% 0.20/0.50 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.50 tff(20,plain,
% 0.20/0.50 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt3), t2tb6(A4!18))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))) = t2tb6(A4!18)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt3), t2tb6(A4!18))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))) = t2tb6(A4!18)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(21,plain,
% 0.20/0.50 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt3), t2tb6(A4!18))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))) = t2tb6(A4!18)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(22,plain,
% 0.20/0.50 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt3), t2tb6(A4!18))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))) = t2tb6(A4!18))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 ((~sort1(map(int, elt3), t2tb6(A4!18))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))) = t2tb6(A4!18))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[22, 19])).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 (elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))) = t2tb6(A4!18)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[23, 9])).
% 0.20/0.50 tff(25,plain,
% 0.20/0.50 (t2tb6(A4!18) = elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18)))),
% 0.20/0.50 inference(symmetry,[status(thm)],[24])).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 ((~![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X))) | sort1(map(int, elt3), t2tb6(A1!14))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 (sort1(map(int, elt3), t2tb6(A1!14))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[26, 7])).
% 0.20/0.50 tff(28,plain,
% 0.20/0.50 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt3), t2tb6(A1!14))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))) = t2tb6(A1!14)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt3), t2tb6(A1!14))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))) = t2tb6(A1!14)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt3), t2tb6(A1!14))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))) = t2tb6(A1!14)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(30,plain,
% 0.20/0.50 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt3), t2tb6(A1!14))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))) = t2tb6(A1!14))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 ((~sort1(map(int, elt3), t2tb6(A1!14))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))) = t2tb6(A1!14))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[30, 19])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))) = t2tb6(A1!14)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[31, 27])).
% 0.20/0.50 tff(33,plain,
% 0.20/0.50 (t2tb6(A1!14) = elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))),
% 0.20/0.50 inference(symmetry,[status(thm)],[32])).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 (permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) <=> permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[33, 25])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) <=> permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11)),
% 0.20/0.50 inference(symmetry,[status(thm)],[34])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 ((~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) <=> (~permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : refl((permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U))))) <=> (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : rewrite((permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : rewrite((permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> (permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int] : rewrite((permut3(A, A1, A2, L, U) <=> ((((((length1(A, A1) = length1(A, A2)) & $lesseq(0, L)) & $lesseq(L, length1(A, A1))) & $lesseq(0, U)) & $lesseq(U, length1(A, A1))) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(45,plain,
% 0.20/0.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((((((length1(A, A1) = length1(A, A2)) & $lesseq(0, L)) & $lesseq(L, length1(A, A1))) & $lesseq(0, U)) & $lesseq(U, length1(A, A1))) & permut2(A, elts(A, A1), elts(A, A2), L, U))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.50 tff(46,axiom,(![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((((((length1(A, A1) = length1(A, A2)) & $lesseq(0, L)) & $lesseq(L, length1(A, A1))) & $lesseq(0, U)) & $lesseq(U, length1(A, A1))) & permut2(A, elts(A, A1), elts(A, A2), L, U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','permut_def1')).
% 0.20/0.50 tff(47,plain,
% 0.20/0.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.50 tff(48,plain,
% 0.20/0.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> ((length1(A, A1) = length1(A, A2)) & $lesseq(0, L) & $lesseq(L, length1(A, A1)) & $lesseq(0, U) & $lesseq(U, length1(A, A1)) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.50 tff(49,plain,
% 0.20/0.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[48, 42])).
% 0.20/0.50 tff(50,plain,(
% 0.20/0.50 ![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, length1(A, A1))), 0) & $greatereq(U, 0) & $lesseq($sum(U, $product(-1, length1(A, A1))), 0) & permut2(A, elts(A, A1), elts(A, A2), L, U)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[49])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.20/0.50 tff(52,plain,
% 0.20/0.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[51, 38])).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(54,plain,
% 0.20/0.50 ((permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11))))) <=> (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[54])).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[55, 53])).
% 0.20/0.51 tff(57,plain,
% 0.20/0.51 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(58,plain,
% 0.20/0.51 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[58, 52])).
% 0.20/0.51 tff(60,plain,
% 0.20/0.51 (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) <=> map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[33, 25])).
% 0.20/0.51 tff(61,plain,
% 0.20/0.51 (map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12) <=> map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)),
% 0.20/0.51 inference(symmetry,[status(thm)],[60])).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 ((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) <=> (~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.51 tff(63,assumption,(~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)), introduced(assumption)).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 (~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.51 tff(65,plain,
% 0.20/0.51 (^[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)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(66,plain,
% 0.20/0.51 (![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))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.51 tff(67,plain,
% 0.20/0.51 (^[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)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(68,plain,
% 0.20/0.51 (![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))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.51 tff(69,plain,
% 0.20/0.51 (![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))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[68, 66])).
% 0.20/0.51 tff(70,plain,
% 0.20/0.51 (^[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))))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(71,plain,
% 0.20/0.51 (![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))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.51 tff(72,plain,
% 0.20/0.51 (^[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))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(73,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.51 tff(74,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(75,plain,
% 0.20/0.51 (^[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))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(76,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.51 tff(77,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')).
% 0.20/0.51 tff(78,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.51 tff(80,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[79, 73])).
% 0.20/0.51 tff(81,plain,(
% 0.20/0.51 ![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))))))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[80])).
% 0.20/0.51 tff(82,plain,
% 0.20/0.51 (![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))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.20/0.51 tff(83,plain,
% 0.20/0.51 (![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))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[82, 69])).
% 0.20/0.51 tff(84,plain,
% 0.20/0.51 (((~![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(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 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(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(85,plain,
% 0.20/0.51 ((~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))))))) <=> (~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(86,plain,
% 0.20/0.51 (((~![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(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 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(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[85])).
% 0.20/0.51 tff(87,plain,
% 0.20/0.51 (((~![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(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 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(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[86, 84])).
% 0.20/0.52 tff(88,plain,
% 0.20/0.52 ((~![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(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(89,plain,
% 0.20/0.52 ((~![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(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.52 tff(90,plain,
% 0.20/0.52 (~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[89, 83])).
% 0.20/0.52 tff(91,plain,
% 0.20/0.52 (((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0))))))) | (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(92,plain,
% 0.20/0.52 (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.20/0.52 tff(93,assumption,(~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)))), introduced(assumption)).
% 0.20/0.52 tff(94,plain,
% 0.20/0.52 (($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0))) | $greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(95,plain,
% 0.20/0.52 ($greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.20/0.52 tff(96,plain,
% 0.20/0.52 (($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0))) | (~$lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(97,plain,
% 0.20/0.52 (~$lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.20/0.52 tff(98,plain,
% 0.20/0.52 (((~![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(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 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(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(99,plain,
% 0.20/0.52 ((~((~((~map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)))))))) <=> (~((~((~map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(100,plain,
% 0.20/0.52 (((~![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(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 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(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.52 tff(101,plain,
% 0.20/0.52 (((~![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(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 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(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[100, 98])).
% 0.20/0.52 tff(102,plain,
% 0.20/0.52 ((~![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(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(103,plain,
% 0.20/0.52 ((~![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(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.52 tff(104,plain,
% 0.20/0.52 (~((~((~map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[103, 83])).
% 0.20/0.53 tff(105,plain,
% 0.20/0.53 (((~((~map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0))))))) | ((~map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(106,plain,
% 0.20/0.53 ((~map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.53 tff(107,plain,
% 0.20/0.53 (((~((~map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0))))))) | (map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(108,plain,
% 0.20/0.53 (map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.20/0.53 tff(109,plain,
% 0.20/0.53 (get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.53 tff(110,plain,
% 0.20/0.53 (get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[109])).
% 0.20/0.53 tff(111,plain,
% 0.20/0.53 (sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) <=> sort1(elt3, get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.53 tff(112,plain,
% 0.20/0.53 (sort1(elt3, get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) <=> sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.20/0.53 inference(symmetry,[status(thm)],[111])).
% 0.20/0.53 tff(113,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(114,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)],[113])).
% 0.20/0.53 tff(115,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(116,axiom,(![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','get_sort4')).
% 0.20/0.53 tff(117,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)],[116, 115])).
% 0.20/0.53 tff(118,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)],[117])).
% 0.20/0.53 tff(119,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)],[118, 114])).
% 0.20/0.53 tff(120,plain,
% 0.20/0.53 ((~![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))) | sort1(elt3, get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(121,plain,
% 0.20/0.53 (sort1(elt3, get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.53 tff(122,plain,
% 0.20/0.53 (sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[121, 112])).
% 0.20/0.53 tff(123,plain,
% 0.20/0.53 ((~![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))) | sort1(elt3, get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(124,plain,
% 0.20/0.53 (sort1(elt3, get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[123, 119])).
% 0.20/0.53 tff(125,plain,
% 0.20/0.53 (^[J: uni] : refl(((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J)) <=> ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(126,plain,
% 0.20/0.53 (![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J)) <=> ![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.53 tff(127,plain,
% 0.20/0.53 (![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J)) <=> ![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(128,plain,
% 0.20/0.53 (^[J: uni] : rewrite((sort1(elt3, J) => (t2tb5(tb2t5(J)) = J)) <=> ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(129,plain,
% 0.20/0.53 (![J: uni] : (sort1(elt3, J) => (t2tb5(tb2t5(J)) = J)) <=> ![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.53 tff(130,axiom,(![J: uni] : (sort1(elt3, J) => (t2tb5(tb2t5(J)) = J))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR5')).
% 0.20/0.53 tff(131,plain,
% 0.20/0.53 (![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.53 tff(132,plain,
% 0.20/0.53 (![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.20/0.53 tff(133,plain,(
% 0.20/0.53 ![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))),
% 0.20/0.53 inference(skolemize,[status(sab)],[132])).
% 0.20/0.53 tff(134,plain,
% 0.20/0.53 (![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.20/0.53 tff(135,plain,
% 0.20/0.53 (((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort1(elt3, get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) | (t2tb5(tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))) <=> ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | (~sort1(elt3, get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) | (t2tb5(tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(136,plain,
% 0.20/0.53 ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort1(elt3, get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) | (t2tb5(tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(137,plain,
% 0.20/0.53 ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | (~sort1(elt3, get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) | (t2tb5(tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.53 tff(138,plain,
% 0.20/0.53 (t2tb5(tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[137, 134, 124])).
% 0.20/0.53 tff(139,assumption,(~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)))), introduced(assumption)).
% 0.20/0.53 tff(140,plain,
% 0.20/0.53 (($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0))) | $greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(141,plain,
% 0.20/0.53 ($greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.20/0.53 tff(142,plain,
% 0.20/0.53 (($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0))) | (~$lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(143,plain,
% 0.20/0.53 (~$lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[142, 139])).
% 0.20/0.53 tff(144,plain,
% 0.20/0.53 ((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(145,plain,
% 0.20/0.53 (~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[144, 143, 141])).
% 0.20/0.53 tff(146,plain,
% 0.20/0.53 (((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(147,plain,
% 0.20/0.53 ((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.53 tff(148,plain,
% 0.20/0.53 (^[I: $int] : refl(((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) <=> ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(149,plain,
% 0.20/0.53 (![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) <=> ![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[148])).
% 0.20/0.53 tff(150,plain,
% 0.20/0.53 (^[I: $int] : rewrite(((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) <=> ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(151,plain,
% 0.20/0.53 (![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) <=> ![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[150])).
% 0.20/0.53 tff(152,plain,
% 0.20/0.53 (((~$lesseq($sum(R!11, $product(-1, L!12)), 1)) & ($greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & (~$lesseq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0))) & ($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum(R!11, $product(-1, L!12)), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)) & (permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) & $greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & $greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & $greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)))) & ($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $greatereq($sum(R!11, $product(-1, L!12)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))) <=> ((~$lesseq($sum(R!11, $product(-1, L!12)), 1)) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & (~$lesseq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0)) & $greatereq(L!12, 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum(R!11, $product(-1, L!12)), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) & $greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & $greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & $greatereq($sum(R!11, $product(-1, L!12)), 0))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(153,plain,
% 0.20/0.54 ((~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $greatereq($sum(R!11, $product(-1, L!12)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) <=> ($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $greatereq($sum(R!11, $product(-1, L!12)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(154,plain,
% 0.20/0.54 ((~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $lesseq($sum(L!12, $product(-1, R!11)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))) <=> (~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $greatereq($sum(R!11, $product(-1, L!12)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(155,plain,
% 0.20/0.54 ((~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $lesseq($sum(L!12, $product(-1, R!11)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) <=> (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $greatereq($sum(R!11, $product(-1, L!12)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.54 tff(156,plain,
% 0.20/0.54 ((~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $lesseq($sum(L!12, $product(-1, R!11)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) <=> ($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $greatereq($sum(R!11, $product(-1, L!12)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))),
% 0.20/0.54 inference(transitivity,[status(thm)],[155, 153])).
% 0.20/0.54 tff(157,plain,
% 0.20/0.54 ((permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) & ($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)))) & ($greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)) & ($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & $greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))))) <=> (permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) & $greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & $greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & $greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(158,plain,
% 0.20/0.54 ((($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & ($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)) & ($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11))) <=> ($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & $greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(159,plain,
% 0.20/0.54 ((~(~($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))) <=> ($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(160,plain,
% 0.20/0.54 ((~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))) <=> ($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(161,plain,
% 0.20/0.54 ((~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11))) <=> permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(162,plain,
% 0.20/0.54 ((($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))) <=> ($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(163,plain,
% 0.20/0.54 (($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) <=> ($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(164,plain,
% 0.20/0.54 ((($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))) <=> (($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[163])).
% 0.20/0.54 tff(165,plain,
% 0.20/0.54 ((($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))) <=> ($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[164, 162])).
% 0.20/0.55 tff(166,plain,
% 0.20/0.55 (((($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))) & (~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))) & (~(~($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11))))) <=> (($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & ($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)) & ($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[165, 161, 160, 159])).
% 0.20/0.55 tff(167,plain,
% 0.20/0.55 (((($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))) & (~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))) & (~(~($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11))))) <=> ($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & $greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[166, 158])).
% 0.20/0.55 tff(168,plain,
% 0.20/0.55 ((~(~($greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) <=> ($greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(169,plain,
% 0.20/0.55 ((~($greatereq($sum(L!12, div($sum($product(-1, L!12), R!11), 2)), 0) & $lesseq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))) <=> (~($greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(170,plain,
% 0.20/0.55 ((~(~($greatereq($sum(L!12, div($sum($product(-1, L!12), R!11), 2)), 0) & $lesseq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) <=> (~(~($greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[169])).
% 0.20/0.55 tff(171,plain,
% 0.20/0.55 ((~(~($greatereq($sum(L!12, div($sum($product(-1, L!12), R!11), 2)), 0) & $lesseq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) <=> ($greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))),
% 0.20/0.55 inference(transitivity,[status(thm)],[170, 168])).
% 0.20/0.55 tff(172,plain,
% 0.20/0.55 ((~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)))))) <=> ($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(173,plain,
% 0.20/0.55 ((~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2))))) <=> (~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(174,plain,
% 0.20/0.55 ((~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2)))))) <=> (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.55 tff(175,plain,
% 0.20/0.55 ((~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2)))))) <=> ($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[174, 172])).
% 0.20/0.55 tff(176,plain,
% 0.20/0.55 ((~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11))) <=> permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(177,plain,
% 0.20/0.55 (((~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2)))))) & (~(~($greatereq($sum(L!12, div($sum($product(-1, L!12), R!11), 2)), 0) & $lesseq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) & ((($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))) & (~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))) & (~(~($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))))) <=> (permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) & ($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)))) & ($greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)) & ($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & $greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[176, 175, 171, 167])).
% 0.20/0.55 tff(178,plain,
% 0.20/0.55 (((~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2)))))) & (~(~($greatereq($sum(L!12, div($sum($product(-1, L!12), R!11), 2)), 0) & $lesseq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) & ((($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))) & (~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))) & (~(~($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))))) <=> (permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) & $greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & $greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & $greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[177, 157])).
% 0.20/0.56 tff(179,plain,
% 0.20/0.56 ((~(~($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum(R!11, $product(-1, L!12)), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) <=> ($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum(R!11, $product(-1, L!12)), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(180,plain,
% 0.20/0.56 ((~($greatereq(L!12, 0) & $greatereq(div($sum($product(-1, L!12), R!11), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum($product(-1, L!12), R!11), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))) <=> (~($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum(R!11, $product(-1, L!12)), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(181,plain,
% 0.20/0.56 ((~(~($greatereq(L!12, 0) & $greatereq(div($sum($product(-1, L!12), R!11), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum($product(-1, L!12), R!11), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) <=> (~(~($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum(R!11, $product(-1, L!12)), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[180])).
% 0.20/0.56 tff(182,plain,
% 0.20/0.56 ((~(~($greatereq(L!12, 0) & $greatereq(div($sum($product(-1, L!12), R!11), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum($product(-1, L!12), R!11), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) <=> ($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum(R!11, $product(-1, L!12)), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))),
% 0.20/0.56 inference(transitivity,[status(thm)],[181, 179])).
% 0.20/0.56 tff(183,plain,
% 0.20/0.56 ((~(~($greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & (~$lesseq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0))))) <=> ($greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & (~$lesseq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(184,plain,
% 0.20/0.56 ((~($greatereq(div($sum($product(-1, L!12), R!11), 2), 0) & (~$greatereq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0)))) <=> (~($greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & (~$lesseq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(185,plain,
% 0.20/0.56 ((~(~($greatereq(div($sum($product(-1, L!12), R!11), 2), 0) & (~$greatereq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0))))) <=> (~(~($greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & (~$lesseq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[184])).
% 0.20/0.56 tff(186,plain,
% 0.20/0.56 ((~(~($greatereq(div($sum($product(-1, L!12), R!11), 2), 0) & (~$greatereq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0))))) <=> ($greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & (~$lesseq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[185, 183])).
% 0.20/0.56 tff(187,plain,
% 0.20/0.56 ((~$greatereq($sum(L!12, $product(-1, R!11)), -1)) <=> (~$lesseq($sum(R!11, $product(-1, L!12)), 1))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(188,plain,
% 0.20/0.56 (((~$greatereq($sum(L!12, $product(-1, R!11)), -1)) & (~(~($greatereq(div($sum($product(-1, L!12), R!11), 2), 0) & (~$greatereq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0))))) & (~(~($greatereq(L!12, 0) & $greatereq(div($sum($product(-1, L!12), R!11), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum($product(-1, L!12), R!11), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) & ((~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2)))))) & (~(~($greatereq($sum(L!12, div($sum($product(-1, L!12), R!11), 2)), 0) & $lesseq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) & ((($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))) & (~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))) & (~(~($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $lesseq($sum(L!12, $product(-1, R!11)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))))) <=> ((~$lesseq($sum(R!11, $product(-1, L!12)), 1)) & ($greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & (~$lesseq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0))) & ($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum(R!11, $product(-1, L!12)), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)) & (permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) & $greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & $greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & $greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)))) & ($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $greatereq($sum(R!11, $product(-1, L!12)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[187, 186, 182, 178, 156])).
% 0.20/0.56 tff(189,plain,
% 0.20/0.56 (((~$greatereq($sum(L!12, $product(-1, R!11)), -1)) & (~(~($greatereq(div($sum($product(-1, L!12), R!11), 2), 0) & (~$greatereq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0))))) & (~(~($greatereq(L!12, 0) & $greatereq(div($sum($product(-1, L!12), R!11), 2), 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum($product(-1, L!12), R!11), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) & ((~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum($product(-1, L!12), R!11), 2)))))) & (~(~($greatereq($sum(L!12, div($sum($product(-1, L!12), R!11), 2)), 0) & $lesseq($sum(L!12, $sum($product(-1, R!11), div($sum($product(-1, L!12), R!11), 2))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0)))) & ((($greatereq(Tmp!13, 0) & $greatereq(A!15, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))) & (~(~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))) & (~(~($greatereq(L!12, 0) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11)))))) & (~(~($greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & $greatereq(L!12, 0) & $lesseq($sum(L!12, $product(-1, R!11)), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0))))) <=> ((~$lesseq($sum(R!11, $product(-1, L!12)), 1)) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & (~$lesseq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0)) & $greatereq(L!12, 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum(R!11, $product(-1, L!12)), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) & $greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & $greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & $greatereq($sum(R!11, $product(-1, L!12)), 0))),
% 0.20/0.57 inference(transitivity,[status(thm)],[188, 152])).
% 0.20/0.57 tff(190,plain,
% 0.20/0.57 ((~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($greatereq($sum(L, $product(-1, R)), -1) | (~($greatereq(div($sum($product(-1, L), R), 2), 0) & (~$greatereq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0)))) | (~($greatereq(L, 0) & $greatereq(div($sum($product(-1, L), R), 2), 0) & $lesseq($sum(L, $sum($product(-1, A), div($sum($product(-1, L), R), 2))), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum($product(-1, L), R), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum($product(-1, L), R), 2))))) | (~($greatereq($sum(L, div($sum($product(-1, L), R), 2)), 0) & $lesseq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A3: map_int_elt1] : (![A4: map_int_elt1] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L)), 0))) | ($greatereq($sum(I, $product(-1, R)), 0) & (~$greatereq($sum(I, $product(-1, A)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $greatereq($sum(R, $sum($product(-1, L), $product(-1, div($sum(R, $product(-1, L)), 2)))), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0))))) <=> (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($greatereq($sum(L, $product(-1, R)), -1) | (~($greatereq(div($sum($product(-1, L), R), 2), 0) & (~$greatereq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0)))) | (~($greatereq(L, 0) & $greatereq(div($sum($product(-1, L), R), 2), 0) & $lesseq($sum(L, $sum($product(-1, A), div($sum($product(-1, L), R), 2))), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum($product(-1, L), R), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum($product(-1, L), R), 2))))) | (~($greatereq($sum(L, div($sum($product(-1, L), R), 2)), 0) & $lesseq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A3: map_int_elt1] : (![A4: map_int_elt1] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L)), 0))) | ($greatereq($sum(I, $product(-1, R)), 0) & (~$greatereq($sum(I, $product(-1, A)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $greatereq($sum(R, $sum($product(-1, L), $product(-1, div($sum(R, $product(-1, L)), 2)))), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(191,plain,
% 0.20/0.57 ((~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($lesseq($sum(R, $product(-1, L)), 1) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $lesseq($sum(L, $sum(div($sum(R, $product(-1, L)), 2), $product(-1, A))), 0) & ($sum(A, $product(-1, Tmp)) = 0))) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | (~($greatereq($sum(L, div($sum(R, $product(-1, L)), 2)), 0) & $lesseq($sum(L, $sum(div($sum(R, $product(-1, L)), 2), $product(-1, R))), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0))) | ![A3: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | ![A4: map_int_elt1] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($greatereq(I, 0) & (~$lesseq($sum(L, $product(-1, I)), 0))) | ($lesseq($sum(R, $product(-1, I)), 0) & (~$lesseq($sum(A, $product(-1, I)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $lesseq($sum(L, $sum(div($sum(R, $product(-1, L)), 2), $product(-1, R))), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R)))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($greatereq(div($sum(R, $product(-1, L)), 2), 0) & (~$lesseq($sum(R, $sum($product(-1, L), $product(-1, div($sum(R, $product(-1, L)), 2)))), 0)))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0))))) <=> (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($greatereq($sum(L, $product(-1, R)), -1) | (~($greatereq(div($sum($product(-1, L), R), 2), 0) & (~$greatereq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0)))) | (~($greatereq(L, 0) & $greatereq(div($sum($product(-1, L), R), 2), 0) & $lesseq($sum(L, $sum($product(-1, A), div($sum($product(-1, L), R), 2))), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum($product(-1, L), R), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum($product(-1, L), R), 2))))) | (~($greatereq($sum(L, div($sum($product(-1, L), R), 2)), 0) & $lesseq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A3: map_int_elt1] : (![A4: map_int_elt1] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L)), 0))) | ($greatereq($sum(I, $product(-1, R)), 0) & (~$greatereq($sum(I, $product(-1, A)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $greatereq($sum(R, $sum($product(-1, L), $product(-1, div($sum(R, $product(-1, L)), 2)))), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(192,plain,
% 0.20/0.57 ((~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($lesseq(R, $sum(1, L)) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | ![A3: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | ![A4: map_int_elt1] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($lesseq(0, I) & (~$lesseq(L, I))) | ($lesseq(R, I) & (~$lesseq(A, I))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R)))) | (~($lesseq(0, $sum(L, div($sum(R, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, A) & (A = Tmp))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), A) & (A = Tmp))) | (~($lesseq(0, div($sum(R, $product(-1, L)), 2)) & (~$lesseq(R, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & $lesseq(0, L) & $lesseq(L, R) & $lesseq(R, A) & (A = Tmp))))) <=> (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($lesseq($sum(R, $product(-1, L)), 1) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $lesseq($sum(L, $sum(div($sum(R, $product(-1, L)), 2), $product(-1, A))), 0) & ($sum(A, $product(-1, Tmp)) = 0))) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | (~($greatereq($sum(L, div($sum(R, $product(-1, L)), 2)), 0) & $lesseq($sum(L, $sum(div($sum(R, $product(-1, L)), 2), $product(-1, R))), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0))) | ![A3: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | ![A4: map_int_elt1] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($greatereq(I, 0) & (~$lesseq($sum(L, $product(-1, I)), 0))) | ($lesseq($sum(R, $product(-1, I)), 0) & (~$lesseq($sum(A, $product(-1, I)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $lesseq($sum(L, $sum(div($sum(R, $product(-1, L)), 2), $product(-1, R))), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R)))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($greatereq(div($sum(R, $product(-1, L)), 2), 0) & (~$lesseq($sum(R, $sum($product(-1, L), $product(-1, div($sum(R, $product(-1, L)), 2)))), 0)))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(193,plain,
% 0.20/0.57 ((~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($lesseq(R, $sum(1, L)) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | ![A3: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | ![A4: map_int_elt1] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($lesseq(0, I) & (~$lesseq(L, I))) | ($lesseq(R, I) & (~$lesseq(A, I))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R)))) | (~($lesseq(0, $sum(L, div($sum(R, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, A) & (A = Tmp))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), A) & (A = Tmp))) | (~($lesseq(0, div($sum(R, $product(-1, L)), 2)) & (~$lesseq(R, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & $lesseq(0, L) & $lesseq(L, R) & $lesseq(R, A) & (A = Tmp))))) <=> (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($lesseq(R, $sum(1, L)) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | ![A3: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | ![A4: map_int_elt1] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($lesseq(0, I) & (~$lesseq(L, I))) | ($lesseq(R, I) & (~$lesseq(A, I))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R)))) | (~($lesseq(0, $sum(L, div($sum(R, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, A) & (A = Tmp))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), A) & (A = Tmp))) | (~($lesseq(0, div($sum(R, $product(-1, L)), 2)) & (~$lesseq(R, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & $lesseq(0, L) & $lesseq(L, R) & $lesseq(R, A) & (A = Tmp)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(194,plain,
% 0.20/0.57 ((~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : (((((($lesseq(0, A) & $lesseq(0, Tmp)) & $lesseq(0, L)) & $lesseq(L, R)) & $lesseq(R, A)) & (A = Tmp)) => ($less(L, $difference(R, 1)) => ((~(2 = 0)) => (($lesseq(L, $sum(L, div($difference(R, L), 2))) & $less($sum(L, div($difference(R, L), 2)), R)) => (((($lesseq(0, L) & $lesseq(L, $sum(L, div($difference(R, L), 2)))) & $lesseq($sum(L, div($difference(R, L), 2)), A)) & (A = Tmp)) => ![A2: map_int_elt1] : (((($lesseq(0, A) & $lesseq(0, Tmp)) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($difference(R, L), 2)))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($difference(R, L), 2)))) => (permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R) => (((($lesseq(0, $sum(L, div($difference(R, L), 2))) & $lesseq($sum(L, div($difference(R, L), 2)), R)) & $lesseq(R, A)) & (A = Tmp)) => ![A3: map_int_elt1] : (((($lesseq(0, A) & $lesseq(0, Tmp)) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($difference(R, L), 2)), R)) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($difference(R, L), 2)), R)) => (permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R) => ((((((($lesseq(0, L) & $lesseq(L, $sum(L, div($difference(R, L), 2)))) & $lesseq($sum(L, div($difference(R, L), 2)), R)) & $lesseq(R, Tmp)) & (Tmp = A)) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($difference(R, L), 2)))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($difference(R, L), 2)), R)) => ![A4: map_int_elt1] : ((((($lesseq(0, Tmp) & $lesseq(0, A)) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R)) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R)) & ![I: $int] : ((($lesseq(0, I) & $less(I, L)) | ($lesseq(R, I) & $less(I, A))) => (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I)))))) => permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)))))))))))))) <=> (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($lesseq(R, $sum(1, L)) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | ![A3: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | ![A4: map_int_elt1] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($lesseq(0, I) & (~$lesseq(L, I))) | ($lesseq(R, I) & (~$lesseq(A, I))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R)))) | (~($lesseq(0, $sum(L, div($sum(R, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, A) & (A = Tmp))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), A) & (A = Tmp))) | (~($lesseq(0, div($sum(R, $product(-1, L)), 2)) & (~$lesseq(R, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & $lesseq(0, L) & $lesseq(L, R) & $lesseq(R, A) & (A = Tmp)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(195,axiom,(~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : (((((($lesseq(0, A) & $lesseq(0, Tmp)) & $lesseq(0, L)) & $lesseq(L, R)) & $lesseq(R, A)) & (A = Tmp)) => ($less(L, $difference(R, 1)) => ((~(2 = 0)) => (($lesseq(L, $sum(L, div($difference(R, L), 2))) & $less($sum(L, div($difference(R, L), 2)), R)) => (((($lesseq(0, L) & $lesseq(L, $sum(L, div($difference(R, L), 2)))) & $lesseq($sum(L, div($difference(R, L), 2)), A)) & (A = Tmp)) => ![A2: map_int_elt1] : (((($lesseq(0, A) & $lesseq(0, Tmp)) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($difference(R, L), 2)))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($difference(R, L), 2)))) => (permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R) => (((($lesseq(0, $sum(L, div($difference(R, L), 2))) & $lesseq($sum(L, div($difference(R, L), 2)), R)) & $lesseq(R, A)) & (A = Tmp)) => ![A3: map_int_elt1] : (((($lesseq(0, A) & $lesseq(0, Tmp)) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($difference(R, L), 2)), R)) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($difference(R, L), 2)), R)) => (permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R) => ((((((($lesseq(0, L) & $lesseq(L, $sum(L, div($difference(R, L), 2)))) & $lesseq($sum(L, div($difference(R, L), 2)), R)) & $lesseq(R, Tmp)) & (Tmp = A)) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($difference(R, L), 2)))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($difference(R, L), 2)), R)) => ![A4: map_int_elt1] : ((((($lesseq(0, Tmp) & $lesseq(0, A)) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R)) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R)) & ![I: $int] : ((($lesseq(0, I) & $less(I, L)) | ($lesseq(R, I) & $less(I, A))) => (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I)))))) => permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_mergesort_rec')).
% 0.20/0.57 tff(196,plain,
% 0.20/0.57 (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($lesseq(R, $sum(1, L)) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | ![A3: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | ![A4: map_int_elt1] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($lesseq(0, I) & (~$lesseq(L, I))) | ($lesseq(R, I) & (~$lesseq(A, I))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R)))) | (~($lesseq(0, $sum(L, div($sum(R, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, A) & (A = Tmp))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), A) & (A = Tmp))) | (~($lesseq(0, div($sum(R, $product(-1, L)), 2)) & (~$lesseq(R, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & $lesseq(0, L) & $lesseq(L, R) & $lesseq(R, A) & (A = Tmp))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.57 tff(197,plain,
% 0.20/0.57 (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($lesseq(R, $sum(1, L)) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | ![A3: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | ![A4: map_int_elt1] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($lesseq(0, I) & (~$lesseq(L, I))) | ($lesseq(R, I) & (~$lesseq(A, I))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R)))) | (~($lesseq(0, $sum(L, div($sum(R, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, A) & (A = Tmp))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), A) & (A = Tmp))) | (~($lesseq(0, div($sum(R, $product(-1, L)), 2)) & (~$lesseq(R, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & $lesseq(0, L) & $lesseq(L, R) & $lesseq(R, A) & (A = Tmp))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[196, 193])).
% 0.20/0.57 tff(198,plain,
% 0.20/0.57 (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($lesseq(R, $sum(1, L)) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | ![A3: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | ![A4: map_int_elt1] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($lesseq(0, I) & (~$lesseq(L, I))) | ($lesseq(R, I) & (~$lesseq(A, I))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R)))) | (~($lesseq(0, $sum(L, div($sum(R, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, A) & (A = Tmp))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), A) & (A = Tmp))) | (~($lesseq(0, div($sum(R, $product(-1, L)), 2)) & (~$lesseq(R, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & $lesseq(0, L) & $lesseq(L, R) & $lesseq(R, A) & (A = Tmp))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.20/0.57 tff(199,plain,
% 0.20/0.57 (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($lesseq(R, $sum(1, L)) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | ![A3: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | ![A4: map_int_elt1] : ((~($lesseq(0, Tmp) & $lesseq(0, A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($lesseq(0, I) & (~$lesseq(L, I))) | ($lesseq(R, I) & (~$lesseq(A, I))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R)))) | (~($lesseq(0, $sum(L, div($sum(R, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), R) & $lesseq(R, A) & (A = Tmp))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, L) & $lesseq(0, div($sum(R, $product(-1, L)), 2)) & $lesseq($sum(L, div($sum(R, $product(-1, L)), 2)), A) & (A = Tmp))) | (~($lesseq(0, div($sum(R, $product(-1, L)), 2)) & (~$lesseq(R, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($lesseq(0, A) & $lesseq(0, Tmp) & $lesseq(0, L) & $lesseq(L, R) & $lesseq(R, A) & (A = Tmp))))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[198, 193])).
% 0.47/0.58 tff(200,plain,
% 0.47/0.58 (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($lesseq($sum(R, $product(-1, L)), 1) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $lesseq($sum(L, $sum(div($sum(R, $product(-1, L)), 2), $product(-1, A))), 0) & ($sum(A, $product(-1, Tmp)) = 0))) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | (~($greatereq($sum(L, div($sum(R, $product(-1, L)), 2)), 0) & $lesseq($sum(L, $sum(div($sum(R, $product(-1, L)), 2), $product(-1, R))), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0))) | ![A3: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | ![A4: map_int_elt1] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($greatereq(I, 0) & (~$lesseq($sum(L, $product(-1, I)), 0))) | ($lesseq($sum(R, $product(-1, I)), 0) & (~$lesseq($sum(A, $product(-1, I)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $lesseq($sum(L, $sum(div($sum(R, $product(-1, L)), 2), $product(-1, R))), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R)))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum(R, $product(-1, L)), 2)))))) | (~($greatereq(div($sum(R, $product(-1, L)), 2), 0) & (~$lesseq($sum(R, $sum($product(-1, L), $product(-1, div($sum(R, $product(-1, L)), 2)))), 0)))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(A, $product(-1, Tmp)) = 0))))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[199, 192])).
% 0.47/0.58 tff(201,plain,
% 0.47/0.58 (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($greatereq($sum(L, $product(-1, R)), -1) | (~($greatereq(div($sum($product(-1, L), R), 2), 0) & (~$greatereq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0)))) | (~($greatereq(L, 0) & $greatereq(div($sum($product(-1, L), R), 2), 0) & $lesseq($sum(L, $sum($product(-1, A), div($sum($product(-1, L), R), 2))), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum($product(-1, L), R), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum($product(-1, L), R), 2))))) | (~($greatereq($sum(L, div($sum($product(-1, L), R), 2)), 0) & $lesseq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A3: map_int_elt1] : (![A4: map_int_elt1] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L)), 0))) | ($greatereq($sum(I, $product(-1, R)), 0) & (~$greatereq($sum(I, $product(-1, A)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $greatereq($sum(R, $sum($product(-1, L), $product(-1, div($sum(R, $product(-1, L)), 2)))), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0))))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[200, 191])).
% 0.47/0.58 tff(202,plain,
% 0.47/0.58 (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($greatereq($sum(L, $product(-1, R)), -1) | (~($greatereq(div($sum($product(-1, L), R), 2), 0) & (~$greatereq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0)))) | (~($greatereq(L, 0) & $greatereq(div($sum($product(-1, L), R), 2), 0) & $lesseq($sum(L, $sum($product(-1, A), div($sum($product(-1, L), R), 2))), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum($product(-1, L), R), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum($product(-1, L), R), 2))))) | (~($greatereq($sum(L, div($sum($product(-1, L), R), 2)), 0) & $lesseq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A3: map_int_elt1] : (![A4: map_int_elt1] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L)), 0))) | ($greatereq($sum(I, $product(-1, R)), 0) & (~$greatereq($sum(I, $product(-1, A)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $greatereq($sum(R, $sum($product(-1, L), $product(-1, div($sum(R, $product(-1, L)), 2)))), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0))))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[201, 190])).
% 0.47/0.58 tff(203,plain,
% 0.47/0.58 (~![A: $int, A1: map_int_elt1, Tmp: $int, L: $int, R: $int] : ($greatereq($sum(L, $product(-1, R)), -1) | (~($greatereq(div($sum($product(-1, L), R), 2), 0) & (~$greatereq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0)))) | (~($greatereq(L, 0) & $greatereq(div($sum($product(-1, L), R), 2), 0) & $lesseq($sum(L, $sum($product(-1, A), div($sum($product(-1, L), R), 2))), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A2: map_int_elt1] : ((~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A2))), L, $sum(L, div($sum($product(-1, L), R), 2))) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A2)), L, $sum(L, div($sum($product(-1, L), R), 2))))) | (~($greatereq($sum(L, div($sum($product(-1, L), R), 2)), 0) & $lesseq($sum(L, $sum($product(-1, R), div($sum($product(-1, L), R), 2))), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0))) | ![A3: map_int_elt1] : (![A4: map_int_elt1] : ((~($greatereq(Tmp, 0) & $greatereq(A, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A4))), L, R) & permut3(elt3, mk_array1(elt3, A, t2tb6(A3)), mk_array1(elt3, A, t2tb6(A4)), L, R) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L)), 0))) | ($greatereq($sum(I, $product(-1, R)), 0) & (~$greatereq($sum(I, $product(-1, A)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3), t2tb(I))))))) | permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A1)), mk_array1(elt3, A, t2tb6(A4)), L, R)) | (~permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), L, R)) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R) & permut_sub1(elt3, mk_array1(elt3, A, t2tb6(A2)), mk_array1(elt3, A, t2tb6(A3)), $sum(L, div($sum(R, $product(-1, L)), 2)), R))) | (~($greatereq(L, 0) & $greatereq(div($sum(R, $product(-1, L)), 2), 0) & $greatereq($sum(R, $sum($product(-1, L), $product(-1, div($sum(R, $product(-1, L)), 2)))), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), L, $sum(L, div($sum(R, $product(-1, L)), 2))) & sorted_sub2(tb2t4(mk_array1(elt3, A, t2tb6(A3))), $sum(L, div($sum(R, $product(-1, L)), 2)), R))))) | (~($greatereq(A, 0) & $greatereq(Tmp, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & ($sum(Tmp, $product(-1, A)) = 0))))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[202, 190])).
% 0.47/0.58 tff(204,plain,
% 0.47/0.58 ((~$lesseq($sum(R!11, $product(-1, L!12)), 1)) & $greatereq(div($sum(R!11, $product(-1, L!12)), 2), 0) & (~$lesseq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0)) & $greatereq(L!12, 0) & $lesseq($sum(L!12, $sum($product(-1, A!15), div($sum(R!11, $product(-1, L!12)), 2))), 0) & ($sum(Tmp!13, $product(-1, A!15)) = 0) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) & $greatereq(A!15, 0) & $greatereq(Tmp!13, 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & $greatereq($sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), 0) & $greatereq($sum(R!11, $sum($product(-1, L!12), $product(-1, div($sum(R!11, $product(-1, L!12)), 2)))), 0) & $lesseq($sum(R!11, $product(-1, A!15)), 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) & permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) & ![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I))))) & (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2)), R!11) & $lesseq($sum(R!11, $product(-1, Tmp!13)), 0) & sorted_sub2(tb2t4(mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, $sum(L!12, div($sum(R!11, $product(-1, L!12)), 2))) & $greatereq($sum(R!11, $product(-1, L!12)), 0)),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[203, 189])).
% 0.47/0.58 tff(205,plain,
% 0.47/0.58 (![I: $int] : ((~(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, L!12)), 0))) | ($greatereq($sum(I, $product(-1, R!11)), 0) & (~$greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))),
% 0.47/0.58 inference(and_elim,[status(thm)],[204])).
% 0.47/0.58 tff(206,plain,
% 0.47/0.58 (![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[205, 151])).
% 0.47/0.58 tff(207,plain,
% 0.47/0.58 (![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[206, 149])).
% 0.47/0.58 tff(208,plain,
% 0.47/0.58 (((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | ((~((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))))) <=> ((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(209,plain,
% 0.47/0.58 (((~((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, L!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, R!11)), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))) <=> ((~((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(210,plain,
% 0.47/0.58 (((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | ((~((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, L!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, R!11)), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))))) <=> ((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | ((~((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[209])).
% 0.47/0.58 tff(211,plain,
% 0.47/0.58 (((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | ((~((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, L!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, R!11)), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))))) <=> ((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))))),
% 0.47/0.58 inference(transitivity,[status(thm)],[210, 208])).
% 0.47/0.58 tff(212,plain,
% 0.47/0.58 ((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | ((~((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, L!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, R!11)), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))))),
% 0.47/0.58 inference(quant_inst,[status(thm)],[])).
% 0.47/0.58 tff(213,plain,
% 0.47/0.58 ((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~((~((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.47/0.58 tff(214,plain,
% 0.47/0.58 (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[213, 207, 147])).
% 0.47/0.58 tff(215,plain,
% 0.47/0.58 (tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[110])).
% 0.47/0.59 tff(216,plain,
% 0.47/0.59 (tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.47/0.59 inference(transitivity,[status(thm)],[215, 214])).
% 0.47/0.59 tff(217,plain,
% 0.47/0.59 (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = t2tb5(tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[216])).
% 0.47/0.59 tff(218,plain,
% 0.47/0.59 (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))),
% 0.47/0.59 inference(transitivity,[status(thm)],[217, 138])).
% 0.47/0.59 tff(219,plain,
% 0.47/0.59 ((t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) <=> (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[218, 110])).
% 0.47/0.59 tff(220,plain,
% 0.47/0.59 ((get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) <=> (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.47/0.59 inference(symmetry,[status(thm)],[219])).
% 0.47/0.59 tff(221,plain,
% 0.47/0.59 ((~(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) <=> (~(t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[220])).
% 0.47/0.59 tff(222,plain,
% 0.47/0.59 (($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0))) | (~(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))),
% 0.47/0.59 inference(tautology,[status(thm)],[])).
% 0.47/0.59 tff(223,plain,
% 0.47/0.59 (~(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[222, 139])).
% 0.47/0.59 tff(224,plain,
% 0.47/0.59 (~(t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.47/0.59 inference(modus_ponens,[status(thm)],[223, 221])).
% 0.47/0.59 tff(225,plain,
% 0.47/0.59 (((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) | (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))) <=> ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | (~sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) | (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(226,plain,
% 0.47/0.59 ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) | (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))))),
% 0.47/0.59 inference(quant_inst,[status(thm)],[])).
% 0.47/0.59 tff(227,plain,
% 0.47/0.59 ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | (~sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) | (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.47/0.59 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.47/0.59 tff(228,plain,
% 0.47/0.59 ((~sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) | (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))))),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[227, 134])).
% 0.47/0.59 tff(229,plain,
% 0.47/0.59 ($false),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[228, 224, 122])).
% 0.47/0.59 tff(230,plain,($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.59 tff(231,plain,
% 0.47/0.59 ((~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)))))) | map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0))))),
% 0.47/0.59 inference(tautology,[status(thm)],[])).
% 0.47/0.59 tff(232,plain,
% 0.47/0.59 ((~(map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A3!17), elt3), 0)))))) | map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.47/0.59 tff(233,plain,
% 0.47/0.59 (map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[232, 108])).
% 0.47/0.59 tff(234,plain,
% 0.47/0.59 ((~((~map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~map_eq_sub1(elt3, t2tb6(A3!17), t2tb6(A4!18), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))))),
% 0.47/0.59 inference(tautology,[status(thm)],[])).
% 0.47/0.59 tff(235,plain,
% 0.49/0.59 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))))),
% 0.49/0.59 inference(unit_resolution,[status(thm)],[234, 233, 106])).
% 0.49/0.59 tff(236,plain,
% 0.49/0.59 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.49/0.59 inference(rewrite,[status(thm)],[])).
% 0.49/0.59 tff(237,plain,
% 0.49/0.59 (((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))))) <=> ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.49/0.59 inference(rewrite,[status(thm)],[])).
% 0.49/0.59 tff(238,plain,
% 0.49/0.59 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))))))),
% 0.49/0.59 inference(monotonicity,[status(thm)],[237])).
% 0.49/0.59 tff(239,plain,
% 0.49/0.59 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.49/0.59 inference(transitivity,[status(thm)],[238, 236])).
% 0.49/0.59 tff(240,plain,
% 0.49/0.59 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.49/0.59 inference(quant_inst,[status(thm)],[])).
% 0.49/0.59 tff(241,plain,
% 0.49/0.59 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.49/0.59 tff(242,plain,
% 0.49/0.59 (get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.49/0.59 inference(unit_resolution,[status(thm)],[241, 235, 97, 95])).
% 0.49/0.59 tff(243,plain,
% 0.49/0.59 (((~![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(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3), 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(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3), 0)))))))))),
% 0.49/0.60 inference(rewrite,[status(thm)],[])).
% 0.49/0.60 tff(244,plain,
% 0.49/0.60 ((~((~((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0)))))))) <=> (~((~((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3), 0))))))))),
% 0.49/0.60 inference(rewrite,[status(thm)],[])).
% 0.49/0.60 tff(245,plain,
% 0.49/0.60 (((~![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(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 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(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3), 0)))))))))),
% 0.49/0.60 inference(monotonicity,[status(thm)],[244])).
% 0.49/0.60 tff(246,plain,
% 0.49/0.60 (((~![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(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 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(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3), 0)))))))))),
% 0.49/0.60 inference(transitivity,[status(thm)],[245, 243])).
% 0.49/0.60 tff(247,plain,
% 0.49/0.60 ((~![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(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0))))))))),
% 0.49/0.60 inference(quant_inst,[status(thm)],[])).
% 0.49/0.60 tff(248,plain,
% 0.49/0.60 ((~![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(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3), 0))))))))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.49/0.60 tff(249,plain,
% 0.49/0.60 (~((~((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3), 0)))))))),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[248, 83])).
% 0.49/0.60 tff(250,plain,
% 0.49/0.60 (((~((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A3!17), t2tb6(A2!16), elt3), 0))))))) | ((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I)))))),
% 0.49/0.60 inference(tautology,[status(thm)],[])).
% 0.49/0.60 tff(251,plain,
% 0.49/0.60 ((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))))),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[250, 249])).
% 0.49/0.60 tff(252,plain,
% 0.49/0.60 ((~![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X))) | sort1(map(int, elt3), t2tb6(A3!17))),
% 0.49/0.60 inference(quant_inst,[status(thm)],[])).
% 0.49/0.60 tff(253,plain,
% 0.49/0.60 (sort1(map(int, elt3), t2tb6(A3!17))),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[252, 7])).
% 0.49/0.60 tff(254,plain,
% 0.49/0.60 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt3), t2tb6(A3!17))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))) = t2tb6(A3!17)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt3), t2tb6(A3!17))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))) = t2tb6(A3!17)))),
% 0.49/0.60 inference(rewrite,[status(thm)],[])).
% 0.49/0.60 tff(255,plain,
% 0.49/0.60 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt3), t2tb6(A3!17))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))) = t2tb6(A3!17)))),
% 0.49/0.60 inference(quant_inst,[status(thm)],[])).
% 0.49/0.60 tff(256,plain,
% 0.49/0.60 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt3), t2tb6(A3!17))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))) = t2tb6(A3!17))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.49/0.60 tff(257,plain,
% 0.49/0.60 ((~sort1(map(int, elt3), t2tb6(A3!17))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))) = t2tb6(A3!17))),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[256, 19])).
% 0.49/0.60 tff(258,plain,
% 0.49/0.60 (elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))) = t2tb6(A3!17)),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[257, 253])).
% 0.49/0.60 tff(259,plain,
% 0.49/0.60 (t2tb6(A3!17) = elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)))),
% 0.49/0.60 inference(symmetry,[status(thm)],[258])).
% 0.49/0.60 tff(260,plain,
% 0.49/0.60 ((~![X: map_int_elt1] : sort1(map(int, elt3), t2tb6(X))) | sort1(map(int, elt3), t2tb6(A2!16))),
% 0.49/0.60 inference(quant_inst,[status(thm)],[])).
% 0.49/0.60 tff(261,plain,
% 0.49/0.60 (sort1(map(int, elt3), t2tb6(A2!16))),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[260, 7])).
% 0.49/0.60 tff(262,plain,
% 0.49/0.60 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt3), t2tb6(A2!16))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))) = t2tb6(A2!16)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt3), t2tb6(A2!16))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))) = t2tb6(A2!16)))),
% 0.49/0.60 inference(rewrite,[status(thm)],[])).
% 0.49/0.60 tff(263,plain,
% 0.49/0.60 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt3), t2tb6(A2!16))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))) = t2tb6(A2!16)))),
% 0.49/0.60 inference(quant_inst,[status(thm)],[])).
% 0.49/0.60 tff(264,plain,
% 0.49/0.60 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt3), t2tb6(A2!16))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))) = t2tb6(A2!16))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.49/0.60 tff(265,plain,
% 0.49/0.60 ((~sort1(map(int, elt3), t2tb6(A2!16))) | (elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))) = t2tb6(A2!16))),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[264, 19])).
% 0.49/0.60 tff(266,plain,
% 0.49/0.60 (elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))) = t2tb6(A2!16)),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[265, 261])).
% 0.49/0.60 tff(267,plain,
% 0.49/0.60 (t2tb6(A2!16) = elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))),
% 0.49/0.60 inference(symmetry,[status(thm)],[266])).
% 0.49/0.60 tff(268,plain,
% 0.49/0.60 (map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12) <=> map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)),
% 0.49/0.60 inference(monotonicity,[status(thm)],[267, 259])).
% 0.49/0.60 tff(269,plain,
% 0.49/0.60 (map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12) <=> map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)),
% 0.49/0.60 inference(symmetry,[status(thm)],[268])).
% 0.49/0.60 tff(270,plain,
% 0.49/0.60 (^[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)))))))),
% 0.49/0.60 inference(bind,[status(th)],[])).
% 0.49/0.60 tff(271,plain,
% 0.49/0.60 (![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))))))),
% 0.49/0.60 inference(quant_intro,[status(thm)],[270])).
% 0.49/0.60 tff(272,plain,
% 0.49/0.60 (^[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)))))))),
% 0.49/0.60 inference(bind,[status(th)],[])).
% 0.49/0.60 tff(273,plain,
% 0.49/0.60 (![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))))))),
% 0.49/0.60 inference(quant_intro,[status(thm)],[272])).
% 0.49/0.60 tff(274,plain,
% 0.49/0.60 (![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))))),
% 0.49/0.60 inference(rewrite,[status(thm)],[])).
% 0.49/0.60 tff(275,plain,
% 0.49/0.60 (^[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)))))),
% 0.49/0.60 inference(bind,[status(th)],[])).
% 0.49/0.60 tff(276,plain,
% 0.49/0.60 (![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))))),
% 0.49/0.60 inference(quant_intro,[status(thm)],[275])).
% 0.49/0.60 tff(277,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')).
% 0.49/0.60 tff(278,plain,
% 0.49/0.60 (![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))))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.49/0.60 tff(279,plain,
% 0.49/0.60 (![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))))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[278, 274])).
% 0.49/0.60 tff(280,plain,(
% 0.49/0.60 ![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))))),
% 0.49/0.60 inference(skolemize,[status(sab)],[279])).
% 0.49/0.60 tff(281,plain,
% 0.49/0.60 (![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))))))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[280, 273])).
% 0.49/0.60 tff(282,plain,
% 0.49/0.60 (![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))))))),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[281, 271])).
% 0.49/0.61 tff(283,plain,
% 0.49/0.61 (((~![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(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))))))) <=> ((~![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(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))))))))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(284,plain,
% 0.49/0.61 ((permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))))))) <=> (permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))))))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(285,plain,
% 0.49/0.61 (((~![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(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))))))) <=> ((~![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(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))))))))),
% 0.49/0.61 inference(monotonicity,[status(thm)],[284])).
% 0.49/0.61 tff(286,plain,
% 0.49/0.61 (((~![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(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))))))) <=> ((~![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(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))))))))),
% 0.49/0.61 inference(transitivity,[status(thm)],[285, 283])).
% 0.49/0.61 tff(287,plain,
% 0.49/0.61 ((~![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(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))))))),
% 0.49/0.61 inference(quant_inst,[status(thm)],[])).
% 0.49/0.61 tff(288,plain,
% 0.49/0.61 ((~![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(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))))))),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.49/0.61 tff(289,plain,
% 0.49/0.61 (permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))))))),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[288, 282])).
% 0.49/0.61 tff(290,plain,
% 0.49/0.61 (permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)),
% 0.49/0.61 inference(and_elim,[status(thm)],[204])).
% 0.49/0.61 tff(291,plain,
% 0.49/0.61 ((~(permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))))))) | (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))))))),
% 0.49/0.61 inference(tautology,[status(thm)],[])).
% 0.49/0.61 tff(292,plain,
% 0.49/0.61 ((~(permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))))))) | (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))))))),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.49/0.61 tff(293,plain,
% 0.49/0.61 (~((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))))),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[292, 289])).
% 0.49/0.61 tff(294,plain,
% 0.49/0.61 (((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))))) | map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)),
% 0.49/0.61 inference(tautology,[status(thm)],[])).
% 0.49/0.61 tff(295,plain,
% 0.49/0.61 (map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[294, 293])).
% 0.49/0.61 tff(296,plain,
% 0.49/0.61 (map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[295, 269])).
% 0.49/0.61 tff(297,plain,
% 0.49/0.61 ((~((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))))),
% 0.49/0.61 inference(tautology,[status(thm)],[])).
% 0.49/0.61 tff(298,plain,
% 0.49/0.61 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))))),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[297, 296, 251])).
% 0.49/0.61 tff(299,plain,
% 0.49/0.61 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(300,plain,
% 0.49/0.61 (((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))))) <=> ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(301,plain,
% 0.49/0.61 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))))))),
% 0.49/0.61 inference(monotonicity,[status(thm)],[300])).
% 0.49/0.61 tff(302,plain,
% 0.49/0.61 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.49/0.62 inference(transitivity,[status(thm)],[301, 299])).
% 0.49/0.62 tff(303,plain,
% 0.49/0.62 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.49/0.62 inference(quant_inst,[status(thm)],[])).
% 0.49/0.62 tff(304,plain,
% 0.49/0.62 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.49/0.62 tff(305,plain,
% 0.49/0.62 (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[304, 298, 97, 95])).
% 0.49/0.62 tff(306,plain,
% 0.49/0.62 (((~![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(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3), 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(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3), 0)))))))))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(307,plain,
% 0.49/0.62 ((~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0)))))))) <=> (~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3), 0))))))))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(308,plain,
% 0.49/0.62 (((~![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(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 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(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3), 0)))))))))),
% 0.49/0.62 inference(monotonicity,[status(thm)],[307])).
% 0.49/0.62 tff(309,plain,
% 0.49/0.62 (((~![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(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 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(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3), 0)))))))))),
% 0.49/0.62 inference(transitivity,[status(thm)],[308, 306])).
% 0.49/0.62 tff(310,plain,
% 0.49/0.62 ((~![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(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $lesseq($sum(L!12, $product(-1, I)), 0) | (~$lesseq($sum(0, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0))))))))),
% 0.49/0.62 inference(quant_inst,[status(thm)],[])).
% 0.49/0.62 tff(311,plain,
% 0.49/0.62 ((~![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(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3), 0))))))))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.49/0.62 tff(312,plain,
% 0.49/0.62 (~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3), 0)))))))),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[311, 83])).
% 0.49/0.62 tff(313,plain,
% 0.49/0.62 (((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A2!16), t2tb6(A1!14), elt3), 0))))))) | ((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I)))))),
% 0.49/0.62 inference(tautology,[status(thm)],[])).
% 0.49/0.62 tff(314,plain,
% 0.49/0.62 ((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))))),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[313, 312])).
% 0.49/0.62 tff(315,plain,
% 0.49/0.62 (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12) <=> map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)),
% 0.49/0.62 inference(monotonicity,[status(thm)],[33, 267])).
% 0.49/0.62 tff(316,plain,
% 0.49/0.62 (map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12) <=> map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)),
% 0.49/0.62 inference(symmetry,[status(thm)],[315])).
% 0.49/0.62 tff(317,plain,
% 0.49/0.62 ((~![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(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))))))),
% 0.49/0.63 inference(quant_inst,[status(thm)],[])).
% 0.49/0.63 tff(318,plain,
% 0.49/0.63 (permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))))))),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[317, 282])).
% 0.49/0.63 tff(319,plain,
% 0.49/0.63 (permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)),
% 0.49/0.63 inference(and_elim,[status(thm)],[204])).
% 0.49/0.63 tff(320,plain,
% 0.49/0.63 ((~(permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))))))) | (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))))))),
% 0.49/0.63 inference(tautology,[status(thm)],[])).
% 0.49/0.63 tff(321,plain,
% 0.49/0.63 ((~(permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))))))) | (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))))))),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[320, 319])).
% 0.49/0.63 tff(322,plain,
% 0.49/0.63 (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))))),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[321, 318])).
% 0.49/0.63 tff(323,plain,
% 0.49/0.63 (((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))))) | map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)),
% 0.49/0.63 inference(tautology,[status(thm)],[])).
% 0.49/0.63 tff(324,plain,
% 0.49/0.63 (map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[323, 322])).
% 0.49/0.63 tff(325,plain,
% 0.49/0.63 (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[324, 316])).
% 0.49/0.63 tff(326,plain,
% 0.49/0.63 ((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I)))))) | (~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), 0, L!12)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))))),
% 0.49/0.63 inference(tautology,[status(thm)],[])).
% 0.49/0.63 tff(327,plain,
% 0.49/0.63 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))))),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[326, 325, 314])).
% 0.49/0.63 tff(328,plain,
% 0.49/0.63 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(329,plain,
% 0.49/0.63 (((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))))) <=> ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(330,plain,
% 0.49/0.63 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[329])).
% 0.53/0.63 tff(331,plain,
% 0.53/0.63 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[330, 328])).
% 0.53/0.63 tff(332,plain,
% 0.53/0.63 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))))) | ((~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(333,plain,
% 0.53/0.63 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.53/0.63 tff(334,plain,
% 0.53/0.63 (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[333, 327, 97, 95])).
% 0.53/0.63 tff(335,plain,
% 0.53/0.63 (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.53/0.63 inference(transitivity,[status(thm)],[334, 305, 242])).
% 0.53/0.63 tff(336,plain,
% 0.53/0.63 (($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0))) | (~(get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(337,plain,
% 0.53/0.63 (~(get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[336, 93])).
% 0.53/0.63 tff(338,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[337, 335])).
% 0.53/0.63 tff(339,plain,($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.63 tff(340,plain,
% 0.53/0.63 ((~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)))))) | map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0))))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(341,plain,
% 0.53/0.63 ((~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12) | (~($lesseq($sum(L!12, $product(-1, tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$greatereq(tptp_fun_I_9(L!12, 0, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)))))) | map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[340, 339])).
% 0.53/0.63 tff(342,plain,
% 0.53/0.63 (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), 0, L!12)),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[341, 92])).
% 0.53/0.63 tff(343,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[342, 64])).
% 0.53/0.63 tff(344,plain,(map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.63 tff(345,plain,
% 0.53/0.63 (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) <=> map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[33, 25])).
% 0.53/0.63 tff(346,plain,
% 0.53/0.63 (map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) <=> map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))),
% 0.53/0.63 inference(symmetry,[status(thm)],[345])).
% 0.53/0.63 tff(347,plain,
% 0.53/0.63 ((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) <=> (~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[346])).
% 0.53/0.63 tff(348,assumption,(~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), introduced(assumption)).
% 0.53/0.63 tff(349,plain,
% 0.53/0.63 (~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))),
% 0.53/0.64 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.53/0.64 tff(350,plain,
% 0.53/0.64 (((~![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(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 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(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))))))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(351,plain,
% 0.53/0.64 ((~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))))))) <=> (~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(352,plain,
% 0.53/0.64 (((~![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(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 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(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))))))))),
% 0.53/0.64 inference(monotonicity,[status(thm)],[351])).
% 0.53/0.64 tff(353,plain,
% 0.53/0.64 (((~![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(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 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(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))))))))),
% 0.53/0.64 inference(transitivity,[status(thm)],[352, 350])).
% 0.53/0.64 tff(354,plain,
% 0.53/0.64 ((~![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(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))))))),
% 0.53/0.64 inference(quant_inst,[status(thm)],[])).
% 0.53/0.64 tff(355,plain,
% 0.53/0.64 ((~![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(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))))))),
% 0.53/0.64 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.53/0.64 tff(356,plain,
% 0.53/0.64 (~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[355, 83])).
% 0.53/0.65 tff(357,plain,
% 0.53/0.65 (((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A4!18), t2tb(I)))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))))) | (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))))),
% 0.53/0.65 inference(tautology,[status(thm)],[])).
% 0.53/0.65 tff(358,plain,
% 0.53/0.65 (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[357, 356])).
% 0.53/0.65 tff(359,plain,
% 0.53/0.65 (get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.53/0.65 inference(monotonicity,[status(thm)],[25])).
% 0.53/0.65 tff(360,plain,
% 0.53/0.65 (get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.53/0.65 inference(symmetry,[status(thm)],[359])).
% 0.53/0.65 tff(361,plain,
% 0.53/0.65 (sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) <=> sort1(elt3, get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.65 inference(monotonicity,[status(thm)],[360])).
% 0.53/0.65 tff(362,plain,
% 0.53/0.65 (sort1(elt3, get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) <=> sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.65 inference(symmetry,[status(thm)],[361])).
% 0.53/0.65 tff(363,plain,
% 0.53/0.65 ((~![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))) | sort1(elt3, get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.65 inference(quant_inst,[status(thm)],[])).
% 0.53/0.65 tff(364,plain,
% 0.53/0.65 (sort1(elt3, get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[363, 119])).
% 0.53/0.65 tff(365,plain,
% 0.53/0.65 (sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[364, 362])).
% 0.53/0.65 tff(366,plain,
% 0.53/0.65 (((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) | (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | (~sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) | (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(367,plain,
% 0.53/0.65 ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) | (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.53/0.65 inference(quant_inst,[status(thm)],[])).
% 0.53/0.65 tff(368,plain,
% 0.53/0.65 ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | (~sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) | (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.53/0.65 tff(369,plain,
% 0.53/0.65 ((~sort1(elt3, get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) | (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[368, 134])).
% 0.53/0.65 tff(370,plain,
% 0.53/0.65 (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[369, 365])).
% 0.53/0.65 tff(371,plain,
% 0.53/0.65 (^[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))),
% 0.53/0.65 inference(bind,[status(th)],[])).
% 0.53/0.65 tff(372,plain,
% 0.53/0.65 (![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)),
% 0.53/0.65 inference(quant_intro,[status(thm)],[371])).
% 0.53/0.65 tff(373,plain,
% 0.53/0.65 (^[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)))),
% 0.53/0.65 inference(bind,[status(th)],[])).
% 0.53/0.65 tff(374,plain,
% 0.53/0.65 (![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)),
% 0.53/0.65 inference(quant_intro,[status(thm)],[373])).
% 0.53/0.65 tff(375,plain,
% 0.53/0.65 (^[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))),
% 0.53/0.65 inference(bind,[status(th)],[])).
% 0.53/0.65 tff(376,plain,
% 0.53/0.65 (![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)),
% 0.53/0.65 inference(quant_intro,[status(thm)],[375])).
% 0.53/0.65 tff(377,plain,
% 0.53/0.65 (![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)),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(378,axiom,(![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','length_def1')).
% 0.53/0.65 tff(379,plain,
% 0.53/0.65 (![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.53/0.65 tff(380,plain,
% 0.53/0.65 (![A: ty, U: $int, U1: uni] : ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0)),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[379, 376])).
% 0.53/0.65 tff(381,plain,
% 0.53/0.65 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[380, 374])).
% 0.53/0.65 tff(382,plain,(
% 0.53/0.65 ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.53/0.65 inference(skolemize,[status(sab)],[381])).
% 0.53/0.65 tff(383,plain,
% 0.53/0.65 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[382, 372])).
% 0.53/0.65 tff(384,plain,
% 0.53/0.65 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)) | ($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) = 0)),
% 0.53/0.65 inference(quant_inst,[status(thm)],[])).
% 0.53/0.65 tff(385,plain,
% 0.53/0.65 ($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) = 0),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[384, 383])).
% 0.53/0.65 tff(386,plain,
% 0.53/0.65 ((~($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) = 0)) | $greatereq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)),
% 0.53/0.65 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.65 tff(387,plain,
% 0.53/0.65 ($greatereq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[386, 385])).
% 0.53/0.65 tff(388,plain,
% 0.53/0.65 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)) | ($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)),
% 0.53/0.65 inference(quant_inst,[status(thm)],[])).
% 0.53/0.65 tff(389,plain,
% 0.53/0.65 ($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[388, 383])).
% 0.53/0.65 tff(390,plain,
% 0.53/0.65 ((~($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | $lesseq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)),
% 0.53/0.65 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.65 tff(391,plain,
% 0.53/0.65 ($lesseq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[390, 389])).
% 0.53/0.65 tff(392,assumption,(~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))), introduced(assumption)).
% 0.53/0.65 tff(393,plain,
% 0.53/0.65 (($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~$lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))),
% 0.53/0.65 inference(tautology,[status(thm)],[])).
% 0.53/0.65 tff(394,plain,
% 0.53/0.65 (~$lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[393, 392])).
% 0.53/0.65 tff(395,plain,
% 0.53/0.65 ((~$lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (~$lesseq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (~$greatereq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))),
% 0.53/0.65 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.65 tff(396,plain,
% 0.53/0.65 (~$lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[395, 394, 391, 387])).
% 0.53/0.65 tff(397,plain,
% 0.53/0.65 (($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | $lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.53/0.66 inference(tautology,[status(thm)],[])).
% 0.53/0.66 tff(398,plain,
% 0.53/0.66 ($lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[397, 392])).
% 0.53/0.66 tff(399,plain,
% 0.53/0.66 (((~![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(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 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(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0)))))))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(400,plain,
% 0.53/0.66 ((~((~((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0)))))))) <=> (~((~((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0))))))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(401,plain,
% 0.53/0.66 (((~![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(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 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(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0)))))))))),
% 0.53/0.66 inference(monotonicity,[status(thm)],[400])).
% 0.53/0.66 tff(402,plain,
% 0.53/0.66 (((~![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(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 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(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0)))))))))),
% 0.53/0.66 inference(transitivity,[status(thm)],[401, 399])).
% 0.53/0.66 tff(403,plain,
% 0.53/0.66 ((~![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(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0))))))))),
% 0.53/0.66 inference(quant_inst,[status(thm)],[])).
% 0.53/0.66 tff(404,plain,
% 0.53/0.66 ((~![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(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0))))))))),
% 0.53/0.66 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.53/0.66 tff(405,plain,
% 0.53/0.66 (~((~((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0)))))))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[404, 83])).
% 0.53/0.66 tff(406,plain,
% 0.53/0.66 (((~((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, t2tb6(A3!17), t2tb6(A2!16), elt3))), 0))))))) | ((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)))),
% 0.53/0.67 inference(tautology,[status(thm)],[])).
% 0.53/0.67 tff(407,plain,
% 0.53/0.67 ((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[406, 405])).
% 0.53/0.67 tff(408,plain,
% 0.53/0.67 (map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) <=> map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))),
% 0.53/0.67 inference(monotonicity,[status(thm)],[267, 259])).
% 0.53/0.67 tff(409,plain,
% 0.53/0.67 (map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))) <=> map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))),
% 0.53/0.67 inference(symmetry,[status(thm)],[408])).
% 0.53/0.67 tff(410,plain,
% 0.53/0.67 (((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))))) | map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))),
% 0.53/0.67 inference(tautology,[status(thm)],[])).
% 0.53/0.67 tff(411,plain,
% 0.53/0.67 (map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[410, 293])).
% 0.53/0.67 tff(412,plain,
% 0.53/0.67 (map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))),
% 0.53/0.67 inference(modus_ponens,[status(thm)],[411, 409])).
% 0.53/0.67 tff(413,plain,
% 0.53/0.67 ((~((~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)))) | (~map_eq_sub1(elt3, t2tb6(A2!16), t2tb6(A3!17), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))),
% 0.53/0.67 inference(tautology,[status(thm)],[])).
% 0.53/0.67 tff(414,plain,
% 0.53/0.67 (![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[413, 412, 407])).
% 0.53/0.67 tff(415,plain,
% 0.53/0.67 (((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))) | ((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) <=> ((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))),
% 0.53/0.67 inference(rewrite,[status(thm)],[])).
% 0.53/0.67 tff(416,plain,
% 0.53/0.67 (((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) <=> ((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))),
% 0.53/0.67 inference(rewrite,[status(thm)],[])).
% 0.53/0.67 tff(417,plain,
% 0.53/0.67 ($greatereq($sum($product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))), tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)), 0) <=> $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.53/0.67 inference(rewrite,[status(thm)],[])).
% 0.53/0.67 tff(418,plain,
% 0.53/0.67 ($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = $sum($product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))), tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))),
% 0.53/0.67 inference(rewrite,[status(thm)],[])).
% 0.53/0.67 tff(419,plain,
% 0.53/0.67 ($greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0) <=> $greatereq($sum($product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))), tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)), 0)),
% 0.53/0.67 inference(monotonicity,[status(thm)],[418])).
% 0.53/0.67 tff(420,plain,
% 0.53/0.67 ($greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0) <=> $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.53/0.67 inference(transitivity,[status(thm)],[419, 417])).
% 0.53/0.67 tff(421,plain,
% 0.53/0.67 ((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) <=> (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))),
% 0.53/0.67 inference(rewrite,[status(thm)],[])).
% 0.53/0.67 tff(422,plain,
% 0.53/0.67 (((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) <=> ((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))),
% 0.53/0.67 inference(monotonicity,[status(thm)],[421, 420])).
% 0.53/0.67 tff(423,plain,
% 0.53/0.67 (((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) <=> ((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))),
% 0.53/0.67 inference(transitivity,[status(thm)],[422, 416])).
% 0.53/0.67 tff(424,plain,
% 0.53/0.67 (((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))) | ((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))) <=> ((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))) | ((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))),
% 0.53/0.68 inference(monotonicity,[status(thm)],[423])).
% 0.53/0.68 tff(425,plain,
% 0.53/0.68 (((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))) | ((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))) <=> ((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))),
% 0.53/0.68 inference(transitivity,[status(thm)],[424, 415])).
% 0.53/0.68 tff(426,plain,
% 0.53/0.68 ((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))) | ((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))),
% 0.53/0.68 inference(quant_inst,[status(thm)],[])).
% 0.53/0.68 tff(427,plain,
% 0.53/0.68 ((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(I)) = get(elt3, int, t2tb6(A3!17), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.53/0.68 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.53/0.68 tff(428,plain,
% 0.53/0.68 ((get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.53/0.68 inference(unit_resolution,[status(thm)],[427, 414, 398])).
% 0.53/0.68 tff(429,plain,
% 0.53/0.68 (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.53/0.68 inference(unit_resolution,[status(thm)],[428, 396])).
% 0.53/0.68 tff(430,plain,
% 0.53/0.68 (tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.68 inference(monotonicity,[status(thm)],[429])).
% 0.53/0.68 tff(431,plain,
% 0.53/0.68 (tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.68 inference(symmetry,[status(thm)],[430])).
% 0.53/0.68 tff(432,plain,
% 0.53/0.68 ((~$lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (~$greatereq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))),
% 0.53/0.68 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.68 tff(433,plain,
% 0.53/0.68 (~$lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.53/0.68 inference(unit_resolution,[status(thm)],[432, 394, 387])).
% 0.53/0.68 tff(434,plain,
% 0.53/0.68 ((~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.53/0.68 inference(tautology,[status(thm)],[])).
% 0.53/0.68 tff(435,plain,
% 0.53/0.68 ((~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.53/0.68 inference(unit_resolution,[status(thm)],[434, 398])).
% 0.53/0.68 tff(436,plain,
% 0.53/0.68 (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))),
% 0.53/0.68 inference(unit_resolution,[status(thm)],[435, 433])).
% 0.53/0.68 tff(437,plain,
% 0.53/0.68 (((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))) | ((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))),
% 0.53/0.68 inference(tautology,[status(thm)],[])).
% 0.53/0.68 tff(438,plain,
% 0.53/0.68 ((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))),
% 0.53/0.68 inference(unit_resolution,[status(thm)],[437, 436])).
% 0.53/0.68 tff(439,plain,
% 0.53/0.68 (((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | ((~((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))))) <=> ((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))))),
% 0.53/0.68 inference(rewrite,[status(thm)],[])).
% 0.53/0.68 tff(440,plain,
% 0.53/0.68 (((~((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))))),
% 0.53/0.68 inference(rewrite,[status(thm)],[])).
% 0.53/0.68 tff(441,plain,
% 0.53/0.68 (((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | ((~((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))))) <=> ((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | ((~((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))))),
% 0.53/0.68 inference(monotonicity,[status(thm)],[440])).
% 0.53/0.68 tff(442,plain,
% 0.53/0.68 (((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | ((~((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))))) <=> ((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))))),
% 0.53/0.69 inference(transitivity,[status(thm)],[441, 439])).
% 0.53/0.69 tff(443,plain,
% 0.53/0.69 ((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | ((~((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, L!12)), 0))) | (~((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))))),
% 0.53/0.69 inference(quant_inst,[status(thm)],[])).
% 0.53/0.69 tff(444,plain,
% 0.53/0.69 ((~![I: $int] : ((~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, L!12)), 0))) | (~((~$greatereq($sum(I, $product(-1, R!11)), 0)) | $greatereq($sum(I, $product(-1, A!15)), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(I))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(I)))))) | (~((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.53/0.69 tff(445,plain,
% 0.53/0.69 ((~((~((~$greatereq(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), 0)) | $lesseq($sum(L!12, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | $lesseq($sum(A!15, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))) | (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[444, 207])).
% 0.53/0.69 tff(446,plain,
% 0.53/0.69 (tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A3!17), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[445, 438])).
% 0.53/0.69 tff(447,plain,
% 0.53/0.69 (tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.69 inference(monotonicity,[status(thm)],[360])).
% 0.53/0.69 tff(448,plain,
% 0.53/0.69 (tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) = tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.53/0.69 inference(transitivity,[status(thm)],[447, 446, 431])).
% 0.53/0.69 tff(449,plain,
% 0.53/0.69 (t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = t2tb5(tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.53/0.69 inference(monotonicity,[status(thm)],[448])).
% 0.53/0.69 tff(450,plain,
% 0.53/0.69 (t2tb5(tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = t2tb5(tb2t5(get(elt3, int, elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.53/0.69 inference(symmetry,[status(thm)],[449])).
% 0.53/0.69 tff(451,plain,
% 0.53/0.69 (((~![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(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 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(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0)))))))))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(452,plain,
% 0.53/0.69 ((~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0)))))))) <=> (~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0))))))))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(453,plain,
% 0.53/0.69 (((~![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(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 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(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0)))))))))),
% 0.53/0.70 inference(monotonicity,[status(thm)],[452])).
% 0.53/0.70 tff(454,plain,
% 0.53/0.70 (((~![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(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 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(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0)))))))))),
% 0.53/0.70 inference(transitivity,[status(thm)],[453, 451])).
% 0.53/0.70 tff(455,plain,
% 0.53/0.70 ((~![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(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, I)), 0) | (~$lesseq($sum(R!11, $product(-1, I)), 0))))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0))))))))),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(456,plain,
% 0.53/0.70 ((~![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(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0))))))))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[455, 454])).
% 0.53/0.70 tff(457,plain,
% 0.53/0.70 (~((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0)))))))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[456, 83])).
% 0.53/0.70 tff(458,plain,
% 0.53/0.70 (((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)))) | (~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A2!16), t2tb6(A1!14), elt3))), 0))))))) | ((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)))),
% 0.60/0.70 inference(tautology,[status(thm)],[])).
% 0.60/0.70 tff(459,plain,
% 0.60/0.70 ((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))),
% 0.60/0.70 inference(unit_resolution,[status(thm)],[458, 457])).
% 0.60/0.70 tff(460,plain,
% 0.60/0.70 (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) <=> map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))),
% 0.60/0.70 inference(monotonicity,[status(thm)],[33, 267])).
% 0.60/0.70 tff(461,plain,
% 0.60/0.70 (map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) <=> map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))),
% 0.60/0.70 inference(symmetry,[status(thm)],[460])).
% 0.60/0.70 tff(462,plain,
% 0.60/0.70 (((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))))) | map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))),
% 0.60/0.70 inference(tautology,[status(thm)],[])).
% 0.60/0.70 tff(463,plain,
% 0.60/0.70 (map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))),
% 0.60/0.70 inference(unit_resolution,[status(thm)],[462, 322])).
% 0.60/0.70 tff(464,plain,
% 0.60/0.70 (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))),
% 0.60/0.70 inference(modus_ponens,[status(thm)],[463, 461])).
% 0.60/0.70 tff(465,plain,
% 0.60/0.70 ((~((~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)))) | (~map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A2!16), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))),
% 0.60/0.70 inference(tautology,[status(thm)],[])).
% 0.60/0.70 tff(466,plain,
% 0.60/0.70 (![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))),
% 0.60/0.70 inference(unit_resolution,[status(thm)],[465, 464, 459])).
% 0.60/0.70 tff(467,plain,
% 0.60/0.70 (((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))) | ($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.60/0.70 inference(rewrite,[status(thm)],[])).
% 0.60/0.70 tff(468,plain,
% 0.60/0.70 (((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) <=> ($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.60/0.70 inference(rewrite,[status(thm)],[])).
% 0.60/0.70 tff(469,plain,
% 0.60/0.70 ($greatereq($sum($product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))), tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)), 0) <=> $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.60/0.71 inference(rewrite,[status(thm)],[])).
% 0.60/0.71 tff(470,plain,
% 0.60/0.71 ($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) = $sum($product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))), tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))),
% 0.60/0.71 inference(rewrite,[status(thm)],[])).
% 0.60/0.71 tff(471,plain,
% 0.60/0.71 ($greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0) <=> $greatereq($sum($product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))), tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)), 0)),
% 0.60/0.71 inference(monotonicity,[status(thm)],[470])).
% 0.60/0.71 tff(472,plain,
% 0.60/0.71 ($greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0) <=> $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)),
% 0.60/0.71 inference(transitivity,[status(thm)],[471, 469])).
% 0.60/0.71 tff(473,plain,
% 0.60/0.71 (((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) <=> ((~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))),
% 0.60/0.71 inference(monotonicity,[status(thm)],[421, 472])).
% 0.60/0.71 tff(474,plain,
% 0.60/0.71 (((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) <=> ($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.60/0.71 inference(transitivity,[status(thm)],[473, 468])).
% 0.60/0.71 tff(475,plain,
% 0.60/0.71 (((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))) | ((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))) <=> ((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))) | ($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))))),
% 0.60/0.71 inference(monotonicity,[status(thm)],[474])).
% 0.60/0.71 tff(476,plain,
% 0.60/0.71 (((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))) | ((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))) <=> ((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.60/0.71 inference(transitivity,[status(thm)],[475, 467])).
% 0.60/0.71 tff(477,plain,
% 0.60/0.71 ((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))) | ((~$greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | $greatereq($sum(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))),
% 0.60/0.71 inference(quant_inst,[status(thm)],[])).
% 0.60/0.71 tff(478,plain,
% 0.60/0.71 ((~![I: $int] : ((~$greatereq($sum(I, $product(-1, R!11)), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(I)) = get(elt3, int, t2tb6(A2!16), t2tb(I))) | $greatereq($sum(I, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0))) | $lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.60/0.71 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.60/0.71 tff(479,plain,
% 0.60/0.71 (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.60/0.71 inference(unit_resolution,[status(thm)],[478, 466, 394, 398])).
% 0.60/0.71 tff(480,plain,
% 0.60/0.71 (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.60/0.71 inference(symmetry,[status(thm)],[479])).
% 0.60/0.71 tff(481,plain,
% 0.60/0.71 (sort1(elt3, get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) <=> sort1(elt3, get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.60/0.71 inference(monotonicity,[status(thm)],[480])).
% 0.60/0.71 tff(482,plain,
% 0.60/0.71 (sort1(elt3, get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) <=> sort1(elt3, get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.60/0.71 inference(symmetry,[status(thm)],[481])).
% 0.60/0.71 tff(483,plain,
% 0.60/0.71 ((~![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))) | sort1(elt3, get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.60/0.71 inference(quant_inst,[status(thm)],[])).
% 0.60/0.71 tff(484,plain,
% 0.60/0.71 (sort1(elt3, get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.60/0.71 inference(unit_resolution,[status(thm)],[483, 119])).
% 0.60/0.71 tff(485,plain,
% 0.60/0.71 (sort1(elt3, get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.60/0.71 inference(modus_ponens,[status(thm)],[484, 482])).
% 0.60/0.71 tff(486,plain,
% 0.60/0.71 (((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort1(elt3, get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) | (t2tb5(tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))) <=> ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | (~sort1(elt3, get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) | (t2tb5(tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.60/0.71 inference(rewrite,[status(thm)],[])).
% 0.60/0.71 tff(487,plain,
% 0.60/0.71 ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort1(elt3, get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) | (t2tb5(tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.60/0.71 inference(quant_inst,[status(thm)],[])).
% 0.60/0.71 tff(488,plain,
% 0.60/0.71 ((~![J: uni] : ((~sort1(elt3, J)) | (t2tb5(tb2t5(J)) = J))) | (~sort1(elt3, get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) | (t2tb5(tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.60/0.71 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.60/0.71 tff(489,plain,
% 0.60/0.71 ((~sort1(elt3, get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) | (t2tb5(tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.60/0.71 inference(unit_resolution,[status(thm)],[488, 134])).
% 0.60/0.71 tff(490,plain,
% 0.60/0.71 (t2tb5(tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))) = get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.60/0.71 inference(unit_resolution,[status(thm)],[489, 485])).
% 0.60/0.71 tff(491,plain,
% 0.60/0.71 (get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = t2tb5(tb2t5(get(elt3, int, t2tb6(A2!16), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.60/0.71 inference(symmetry,[status(thm)],[490])).
% 0.60/0.71 tff(492,plain,
% 0.60/0.71 (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))),
% 0.60/0.71 inference(transitivity,[status(thm)],[479, 491, 450, 370, 360])).
% 0.60/0.71 tff(493,plain,
% 0.60/0.71 (($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))) | (~(get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))))),
% 0.60/0.72 inference(tautology,[status(thm)],[])).
% 0.60/0.72 tff(494,plain,
% 0.60/0.72 (~(get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))))),
% 0.60/0.72 inference(unit_resolution,[status(thm)],[493, 392])).
% 0.60/0.72 tff(495,plain,
% 0.60/0.72 ($false),
% 0.60/0.72 inference(unit_resolution,[status(thm)],[494, 492])).
% 0.60/0.72 tff(496,plain,($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.72 tff(497,plain,
% 0.60/0.72 ((~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))))) | map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0))))),
% 0.60/0.72 inference(tautology,[status(thm)],[])).
% 0.60/0.72 tff(498,plain,
% 0.60/0.72 ((~(map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))) | (~($lesseq($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0) | (get(elt3, int, t2tb6(A1!14), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))) = get(elt3, int, t2tb6(A4!18), t2tb(tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3)))) | (~$lesseq($sum(R!11, $product(-1, tptp_fun_I_9(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), R!11, t2tb6(A4!18), t2tb6(A1!14), elt3))), 0)))))) | map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))),
% 0.60/0.72 inference(unit_resolution,[status(thm)],[497, 496])).
% 0.60/0.72 tff(499,plain,
% 0.60/0.72 (map_eq_sub1(elt3, t2tb6(A1!14), t2tb6(A4!18), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))),
% 0.60/0.72 inference(unit_resolution,[status(thm)],[498, 358])).
% 0.60/0.72 tff(500,plain,
% 0.60/0.72 ($false),
% 0.60/0.72 inference(unit_resolution,[status(thm)],[499, 349])).
% 0.60/0.72 tff(501,plain,(map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.72 tff(502,plain,
% 0.60/0.72 ((~![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(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))))))),
% 0.60/0.72 inference(quant_inst,[status(thm)],[])).
% 0.60/0.72 tff(503,plain,
% 0.60/0.72 (permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))))))),
% 0.60/0.72 inference(unit_resolution,[status(thm)],[502, 282])).
% 0.60/0.72 tff(504,plain,
% 0.60/0.72 (~permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)),
% 0.60/0.72 inference(and_elim,[status(thm)],[204])).
% 0.60/0.72 tff(505,plain,
% 0.60/0.72 ((~(permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))))))) | permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) | ((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))))),
% 0.60/0.72 inference(tautology,[status(thm)],[])).
% 0.60/0.72 tff(506,plain,
% 0.60/0.72 ((~(permut_sub1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))))))) | ((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))))),
% 0.60/0.72 inference(unit_resolution,[status(thm)],[505, 504])).
% 0.60/0.72 tff(507,plain,
% 0.60/0.72 ((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))))),
% 0.60/0.72 inference(unit_resolution,[status(thm)],[506, 503])).
% 0.60/0.72 tff(508,plain,
% 0.60/0.72 ((~((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))))) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))))),
% 0.60/0.72 inference(tautology,[status(thm)],[])).
% 0.60/0.72 tff(509,plain,
% 0.60/0.72 ((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))))),
% 0.60/0.72 inference(unit_resolution,[status(thm)],[508, 507])).
% 0.60/0.72 tff(510,plain,
% 0.60/0.72 ((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11))),
% 0.60/0.72 inference(unit_resolution,[status(thm)],[509, 501])).
% 0.60/0.72 tff(511,plain,
% 0.60/0.72 (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)),
% 0.60/0.72 inference(unit_resolution,[status(thm)],[510, 344])).
% 0.60/0.72 tff(512,plain,
% 0.60/0.72 ((~(permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))))) | permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) | ((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))),
% 0.60/0.72 inference(tautology,[status(thm)],[])).
% 0.60/0.72 tff(513,plain,
% 0.60/0.72 ((~(permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))))) | ((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[512, 511])).
% 0.60/0.73 tff(514,plain,
% 0.60/0.73 ((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11))),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[513, 59])).
% 0.60/0.73 tff(515,plain,
% 0.60/0.73 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)) | ($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)),
% 0.60/0.73 inference(quant_inst,[status(thm)],[])).
% 0.60/0.73 tff(516,plain,
% 0.60/0.73 ($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[515, 383])).
% 0.60/0.73 tff(517,plain,
% 0.60/0.73 ((~($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | $lesseq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))), 0)),
% 0.60/0.73 inference(theory_lemma,[status(thm)],[])).
% 0.60/0.73 tff(518,plain,
% 0.60/0.73 ($lesseq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))), 0)),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[517, 516])).
% 0.60/0.73 tff(519,plain,
% 0.60/0.73 ((~($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | $greatereq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))), 0)),
% 0.60/0.73 inference(theory_lemma,[status(thm)],[])).
% 0.60/0.73 tff(520,plain,
% 0.60/0.73 ($greatereq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))), 0)),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[519, 516])).
% 0.60/0.73 tff(521,plain,
% 0.60/0.73 ((~($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))) = 0)) | $lesseq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)),
% 0.60/0.73 inference(theory_lemma,[status(thm)],[])).
% 0.60/0.73 tff(522,plain,
% 0.60/0.73 ($lesseq($sum(A!15, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[521, 385])).
% 0.60/0.73 tff(523,plain,
% 0.60/0.73 ($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0),
% 0.60/0.73 inference(theory_lemma,[status(thm)],[387, 522, 520, 518])).
% 0.60/0.73 tff(524,plain,
% 0.60/0.73 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11))))))),
% 0.60/0.73 inference(rewrite,[status(thm)],[])).
% 0.60/0.73 tff(525,plain,
% 0.60/0.73 ((permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11))))) <=> (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)))))),
% 0.60/0.73 inference(rewrite,[status(thm)],[])).
% 0.60/0.73 tff(526,plain,
% 0.60/0.73 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11))))))),
% 0.60/0.73 inference(monotonicity,[status(thm)],[525])).
% 0.60/0.73 tff(527,plain,
% 0.60/0.73 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11))))))),
% 0.60/0.73 inference(transitivity,[status(thm)],[526, 524])).
% 0.60/0.73 tff(528,plain,
% 0.60/0.73 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)))))),
% 0.60/0.73 inference(quant_inst,[status(thm)],[])).
% 0.60/0.73 tff(529,plain,
% 0.60/0.73 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)))))),
% 0.60/0.73 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.60/0.73 tff(530,plain,
% 0.60/0.73 (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11))))),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[529, 52])).
% 0.60/0.73 tff(531,plain,
% 0.60/0.73 (((~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), 0, L!12)) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)))))) | permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)),
% 0.60/0.73 inference(tautology,[status(thm)],[])).
% 0.60/0.73 tff(532,plain,
% 0.60/0.73 (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[531, 322])).
% 0.60/0.73 tff(533,plain,
% 0.60/0.73 ((~(permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)))))) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11)) | (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11))))),
% 0.60/0.73 inference(tautology,[status(thm)],[])).
% 0.60/0.73 tff(534,plain,
% 0.60/0.73 ((~(permut3(elt3, mk_array1(elt3, A!15, t2tb6(A1!14)), mk_array1(elt3, A!15, t2tb6(A2!16)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)))))) | (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11))))),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[533, 532])).
% 0.60/0.73 tff(535,plain,
% 0.60/0.73 (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)))),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[534, 530])).
% 0.60/0.73 tff(536,plain,
% 0.60/0.73 (((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11))) | $lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)),
% 0.60/0.73 inference(tautology,[status(thm)],[])).
% 0.60/0.73 tff(537,plain,
% 0.60/0.73 ($lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[536, 535])).
% 0.60/0.73 tff(538,plain,
% 0.60/0.73 (((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11))) | $lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)),
% 0.60/0.73 inference(tautology,[status(thm)],[])).
% 0.60/0.73 tff(539,plain,
% 0.60/0.73 ($lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)),
% 0.60/0.73 inference(unit_resolution,[status(thm)],[538, 535])).
% 0.60/0.73 tff(540,plain,
% 0.60/0.73 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0))))))),
% 0.60/0.74 inference(rewrite,[status(thm)],[])).
% 0.60/0.74 tff(541,plain,
% 0.60/0.74 ((permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11))))) <=> (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)))))),
% 0.60/0.74 inference(rewrite,[status(thm)],[])).
% 0.60/0.74 tff(542,plain,
% 0.60/0.74 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0))))))),
% 0.60/0.74 inference(monotonicity,[status(thm)],[541])).
% 0.60/0.74 tff(543,plain,
% 0.60/0.74 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0))))))),
% 0.60/0.74 inference(transitivity,[status(thm)],[542, 540])).
% 0.60/0.74 tff(544,plain,
% 0.60/0.74 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))))),
% 0.60/0.74 inference(quant_inst,[status(thm)],[])).
% 0.60/0.74 tff(545,plain,
% 0.60/0.74 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)))))),
% 0.60/0.74 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.60/0.74 tff(546,plain,
% 0.60/0.74 (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0))))),
% 0.60/0.74 inference(unit_resolution,[status(thm)],[545, 52])).
% 0.60/0.74 tff(547,plain,
% 0.60/0.74 (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)),
% 0.60/0.74 inference(and_elim,[status(thm)],[204])).
% 0.60/0.74 tff(548,plain,
% 0.60/0.74 ((~(permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)))))) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11)) | (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0))))),
% 0.60/0.74 inference(tautology,[status(thm)],[])).
% 0.60/0.74 tff(549,plain,
% 0.60/0.74 ((~(permut3(elt3, mk_array1(elt3, A!15, t2tb6(A3!17)), mk_array1(elt3, A!15, t2tb6(A4!18)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)))))) | (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0))))),
% 0.60/0.74 inference(unit_resolution,[status(thm)],[548, 547])).
% 0.60/0.74 tff(550,plain,
% 0.60/0.74 (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)))),
% 0.60/0.74 inference(unit_resolution,[status(thm)],[549, 546])).
% 0.60/0.74 tff(551,plain,
% 0.60/0.74 (((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0))) | $greatereq(R!11, 0)),
% 0.60/0.74 inference(tautology,[status(thm)],[])).
% 0.60/0.74 tff(552,plain,
% 0.60/0.74 ($greatereq(R!11, 0)),
% 0.60/0.74 inference(unit_resolution,[status(thm)],[551, 550])).
% 0.60/0.74 tff(553,plain,
% 0.60/0.74 ($greatereq(L!12, 0)),
% 0.60/0.74 inference(and_elim,[status(thm)],[204])).
% 0.60/0.74 tff(554,plain,
% 0.60/0.74 ((~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))) | (~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11))),
% 0.60/0.74 inference(tautology,[status(thm)],[])).
% 0.60/0.74 tff(555,plain,
% 0.60/0.74 ((~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))))) = 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)))) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11))),
% 0.60/0.74 inference(unit_resolution,[status(thm)],[554, 553, 552, 539, 537, 523])).
% 0.60/0.74 tff(556,plain,
% 0.60/0.74 (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)),
% 0.60/0.74 inference(unit_resolution,[status(thm)],[555, 514])).
% 0.60/0.74 tff(557,plain,
% 0.60/0.74 (~permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11)),
% 0.60/0.74 inference(modus_ponens,[status(thm)],[556, 36])).
% 0.60/0.74 tff(558,plain,
% 0.60/0.74 (permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11) <=> permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)),
% 0.60/0.74 inference(monotonicity,[status(thm)],[33, 267])).
% 0.60/0.74 tff(559,plain,
% 0.60/0.74 (permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11) <=> permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)),
% 0.60/0.74 inference(symmetry,[status(thm)],[558])).
% 0.60/0.74 tff(560,plain,
% 0.60/0.74 (((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11))) | permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)),
% 0.60/0.74 inference(tautology,[status(thm)],[])).
% 0.60/0.74 tff(561,plain,
% 0.60/0.74 (permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A1!14))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), L!12, R!11)),
% 0.60/0.74 inference(unit_resolution,[status(thm)],[560, 535])).
% 0.60/0.74 tff(562,plain,
% 0.60/0.74 (permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)),
% 0.60/0.74 inference(modus_ponens,[status(thm)],[561, 559])).
% 0.60/0.74 tff(563,plain,
% 0.60/0.74 (^[A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : refl((permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U))) <=> (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U))))),
% 0.60/0.74 inference(bind,[status(th)],[])).
% 0.60/0.74 tff(564,plain,
% 0.60/0.74 (![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U))) <=> ![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))),
% 0.60/0.75 inference(quant_intro,[status(thm)],[563])).
% 0.60/0.75 tff(565,plain,
% 0.60/0.75 (![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U))) <=> ![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))),
% 0.60/0.75 inference(rewrite,[status(thm)],[])).
% 0.60/0.75 tff(566,plain,
% 0.60/0.75 (^[A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : trans(monotonicity(rewrite((permut2(A, A2, A3, L, U) => permut2(A, A1, A3, L, U)) <=> ((~permut2(A, A2, A3, L, U)) | permut2(A, A1, A3, L, U))), ((permut2(A, A1, A2, L, U) => (permut2(A, A2, A3, L, U) => permut2(A, A1, A3, L, U))) <=> (permut2(A, A1, A2, L, U) => ((~permut2(A, A2, A3, L, U)) | permut2(A, A1, A3, L, U))))), rewrite((permut2(A, A1, A2, L, U) => ((~permut2(A, A2, A3, L, U)) | permut2(A, A1, A3, L, U))) <=> (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))), ((permut2(A, A1, A2, L, U) => (permut2(A, A2, A3, L, U) => permut2(A, A1, A3, L, U))) <=> (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))))),
% 0.60/0.75 inference(bind,[status(th)],[])).
% 0.60/0.75 tff(567,plain,
% 0.60/0.75 (![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A2, L, U) => (permut2(A, A2, A3, L, U) => permut2(A, A1, A3, L, U))) <=> ![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))),
% 0.60/0.75 inference(quant_intro,[status(thm)],[566])).
% 0.60/0.75 tff(568,axiom,(![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A2, L, U) => (permut2(A, A2, A3, L, U) => permut2(A, A1, A3, L, U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','permut_trans')).
% 0.60/0.75 tff(569,plain,
% 0.60/0.75 (![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))),
% 0.60/0.75 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.60/0.75 tff(570,plain,
% 0.60/0.75 (![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))),
% 0.60/0.75 inference(modus_ponens,[status(thm)],[569, 565])).
% 0.60/0.75 tff(571,plain,(
% 0.60/0.75 ![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))),
% 0.60/0.75 inference(skolemize,[status(sab)],[570])).
% 0.60/0.75 tff(572,plain,
% 0.60/0.75 (![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))),
% 0.60/0.75 inference(modus_ponens,[status(thm)],[571, 564])).
% 0.60/0.75 tff(573,plain,
% 0.60/0.75 (((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | ((~permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)) | permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11)))) <=> ((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (~permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)) | permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11)))),
% 0.60/0.75 inference(rewrite,[status(thm)],[])).
% 0.60/0.75 tff(574,plain,
% 0.60/0.75 ((permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11))) <=> ((~permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)) | permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11)))),
% 0.60/0.75 inference(rewrite,[status(thm)],[])).
% 0.60/0.75 tff(575,plain,
% 0.60/0.75 (((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11)))) <=> ((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | ((~permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)) | permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11))))),
% 0.60/0.75 inference(monotonicity,[status(thm)],[574])).
% 0.60/0.75 tff(576,plain,
% 0.60/0.75 (((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11)))) <=> ((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (~permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)) | permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11)))),
% 0.60/0.75 inference(transitivity,[status(thm)],[575, 573])).
% 0.60/0.75 tff(577,plain,
% 0.60/0.75 ((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11)))),
% 0.60/0.75 inference(quant_inst,[status(thm)],[])).
% 0.60/0.75 tff(578,plain,
% 0.60/0.75 ((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (~permut2(elt3, t2tb6(A1!14), t2tb6(A2!16), L!12, R!11)) | permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11))),
% 0.60/0.75 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.60/0.75 tff(579,plain,
% 0.60/0.75 (permut2(elt3, t2tb6(A1!14), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11))),
% 0.60/0.75 inference(unit_resolution,[status(thm)],[578, 572, 562])).
% 0.60/0.75 tff(580,plain,
% 0.60/0.75 (~permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11)),
% 0.60/0.75 inference(unit_resolution,[status(thm)],[579, 557])).
% 0.60/0.75 tff(581,plain,
% 0.60/0.75 (permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11) <=> permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)),
% 0.60/0.75 inference(monotonicity,[status(thm)],[267, 259])).
% 0.60/0.75 tff(582,plain,
% 0.60/0.75 (permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11) <=> permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)),
% 0.60/0.75 inference(symmetry,[status(thm)],[581])).
% 0.60/0.75 tff(583,plain,
% 0.60/0.75 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11))))))),
% 0.60/0.75 inference(rewrite,[status(thm)],[])).
% 0.60/0.75 tff(584,plain,
% 0.60/0.75 ((permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11))))) <=> (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)))))),
% 0.60/0.75 inference(rewrite,[status(thm)],[])).
% 0.60/0.75 tff(585,plain,
% 0.60/0.75 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11))))))),
% 0.60/0.75 inference(monotonicity,[status(thm)],[584])).
% 0.60/0.75 tff(586,plain,
% 0.60/0.75 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11))))))),
% 0.60/0.75 inference(transitivity,[status(thm)],[585, 583])).
% 0.60/0.75 tff(587,plain,
% 0.60/0.75 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(R!11, 0)) | (~$greatereq(L!12, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)))))),
% 0.60/0.75 inference(quant_inst,[status(thm)],[])).
% 0.60/0.75 tff(588,plain,
% 0.60/0.75 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int] : (permut3(A, A1, A2, L, U) <=> (~((~$greatereq(U, 0)) | (~$greatereq(L, 0)) | (~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~$lesseq($sum(L, $product(-1, length1(A, A1))), 0)) | (~$lesseq($sum(U, $product(-1, length1(A, A1))), 0)) | (~permut2(A, elts(A, A1), elts(A, A2), L, U)))))) | (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.60/0.76 tff(589,plain,
% 0.60/0.76 (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11))))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[588, 52])).
% 0.60/0.76 tff(590,plain,
% 0.60/0.76 (((~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), 0, L!12)) | (~map_eq_sub1(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), R!11, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)))))) | permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(591,plain,
% 0.60/0.76 (permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[590, 293])).
% 0.60/0.76 tff(592,plain,
% 0.60/0.76 ((~(permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)))))) | (~permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11)) | (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11))))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(593,plain,
% 0.60/0.76 ((~(permut3(elt3, mk_array1(elt3, A!15, t2tb6(A2!16)), mk_array1(elt3, A!15, t2tb6(A3!17)), L!12, R!11) <=> (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)))))) | (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11))))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[592, 591])).
% 0.60/0.76 tff(594,plain,
% 0.60/0.76 (~((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[593, 589])).
% 0.60/0.76 tff(595,plain,
% 0.60/0.76 (((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11))) | permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(596,plain,
% 0.60/0.76 (permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A2!16))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), L!12, R!11)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[595, 594])).
% 0.60/0.76 tff(597,plain,
% 0.60/0.76 (permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[596, 582])).
% 0.60/0.76 tff(598,plain,
% 0.60/0.76 (permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11) <=> permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[259, 25])).
% 0.60/0.76 tff(599,plain,
% 0.60/0.76 (permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11) <=> permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11)),
% 0.60/0.76 inference(symmetry,[status(thm)],[598])).
% 0.60/0.76 tff(600,plain,
% 0.60/0.76 (((~$greatereq(L!12, 0)) | (~$greatereq(R!11, 0)) | (~$lesseq($sum(L!12, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~$lesseq($sum(R!11, $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))), 0)) | (~permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)) | (~($sum(length1(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), $product(-1, length1(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))))) = 0))) | permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(601,plain,
% 0.60/0.76 (permut2(elt3, elts(elt3, mk_array1(elt3, A!15, t2tb6(A3!17))), elts(elt3, mk_array1(elt3, A!15, t2tb6(A4!18))), L!12, R!11)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[600, 550])).
% 0.60/0.76 tff(602,plain,
% 0.60/0.76 (permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[601, 599])).
% 0.60/0.76 tff(603,plain,
% 0.60/0.76 (((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | ((~permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11)) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)) | permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11))) <=> ((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (~permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11)) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)) | permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(604,plain,
% 0.60/0.76 ((permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)) | (~permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11))) <=> ((~permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11)) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)) | permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11))),
% 0.66/0.77 inference(rewrite,[status(thm)],[])).
% 0.66/0.77 tff(605,plain,
% 0.66/0.77 (((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)) | (~permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11)))) <=> ((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | ((~permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11)) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)) | permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11)))),
% 0.66/0.77 inference(monotonicity,[status(thm)],[604])).
% 0.66/0.77 tff(606,plain,
% 0.66/0.77 (((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)) | (~permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11)))) <=> ((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (~permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11)) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)) | permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11))),
% 0.66/0.77 inference(transitivity,[status(thm)],[605, 603])).
% 0.66/0.77 tff(607,plain,
% 0.66/0.77 ((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)) | (~permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11)))),
% 0.66/0.77 inference(quant_inst,[status(thm)],[])).
% 0.66/0.77 tff(608,plain,
% 0.66/0.77 ((~![A: ty, A1: uni, A2: uni, A3: uni, L: $int, U: $int] : (permut2(A, A1, A3, L, U) | (~permut2(A, A1, A2, L, U)) | (~permut2(A, A2, A3, L, U)))) | (~permut2(elt3, t2tb6(A3!17), t2tb6(A4!18), L!12, R!11)) | (~permut2(elt3, t2tb6(A2!16), t2tb6(A3!17), L!12, R!11)) | permut2(elt3, t2tb6(A2!16), t2tb6(A4!18), L!12, R!11)),
% 0.66/0.77 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.66/0.77 tff(609,plain,
% 0.66/0.77 ($false),
% 0.66/0.77 inference(unit_resolution,[status(thm)],[608, 572, 602, 597, 580])).
% 0.66/0.77 % SZS output end Proof
%------------------------------------------------------------------------------