TSTP Solution File: SWW607_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW607_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 20:59:26 EDT 2022
% Result : Theorem 1.40s 1.15s
% Output : Proof 1.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW607_2 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.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 20:16:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.40/1.15 % SZS status Theorem
% 1.40/1.15 % SZS output start Proof
% 1.40/1.15 tff(get_type, type, (
% 1.40/1.15 get: ( ty * ty * uni * uni ) > uni)).
% 1.40/1.15 tff(t2tb_type, type, (
% 1.40/1.15 t2tb: $int > uni)).
% 1.40/1.15 tff(tptp_fun_K_17_type, type, (
% 1.40/1.15 tptp_fun_K_17: $int)).
% 1.40/1.15 tff(set_type, type, (
% 1.40/1.15 set: ( ty * ty * uni * uni * uni ) > uni)).
% 1.40/1.15 tff(tptp_fun_I_11_type, type, (
% 1.40/1.15 tptp_fun_I_11: $int)).
% 1.40/1.15 tff(t2tb3_type, type, (
% 1.40/1.15 t2tb3: map_int_elt > uni)).
% 1.40/1.15 tff(tptp_fun_A2_12_type, type, (
% 1.40/1.15 tptp_fun_A2_12: map_int_elt)).
% 1.40/1.15 tff(int_type, type, (
% 1.40/1.15 int: ty)).
% 1.40/1.15 tff(elt_type, type, (
% 1.40/1.15 elt: ty)).
% 1.40/1.15 tff(tptp_fun_J_14_type, type, (
% 1.40/1.15 tptp_fun_J_14: $int)).
% 1.40/1.15 tff(tptp_fun_A4_15_type, type, (
% 1.40/1.15 tptp_fun_A4_15: map_int_elt)).
% 1.40/1.15 tff(tptp_fun_A3_13_type, type, (
% 1.40/1.15 tptp_fun_A3_13: map_int_elt)).
% 1.40/1.15 tff(le1_type, type, (
% 1.40/1.15 le1: ( elt1 * elt1 ) > $o)).
% 1.40/1.15 tff(tb2t4_type, type, (
% 1.40/1.15 tb2t4: uni > elt1)).
% 1.40/1.15 tff(tb2t_type, type, (
% 1.40/1.15 tb2t: uni > $int)).
% 1.40/1.15 tff(tptp_fun_J1_16_type, type, (
% 1.40/1.15 tptp_fun_J1_16: $int)).
% 1.40/1.15 tff(permut_all_type, type, (
% 1.40/1.15 permut_all: ( ty * uni * uni ) > $o)).
% 1.40/1.15 tff(mk_array1_type, type, (
% 1.40/1.15 mk_array1: ( ty * $int * uni ) > uni)).
% 1.40/1.15 tff(tptp_fun_A_10_type, type, (
% 1.40/1.15 tptp_fun_A_10: $int)).
% 1.40/1.15 tff(tptp_fun_A1_9_type, type, (
% 1.40/1.15 tptp_fun_A1_9: map_int_elt)).
% 1.40/1.15 tff(tb2t3_type, type, (
% 1.40/1.15 tb2t3: uni > map_int_elt)).
% 1.40/1.15 tff(exchange3_type, type, (
% 1.40/1.15 exchange3: ( ty * uni * uni * $int * $int ) > $o)).
% 1.40/1.15 tff(sorted_sub6_type, type, (
% 1.40/1.15 sorted_sub6: ( map_int_elt * $int * $int ) > $o)).
% 1.40/1.15 tff(length1_type, type, (
% 1.40/1.15 length1: ( ty * uni ) > $int)).
% 1.40/1.15 tff(exchange2_type, type, (
% 1.40/1.15 exchange2: ( ty * uni * uni * $int * $int * $int * $int ) > $o)).
% 1.40/1.15 tff(tptp_fun_K_6_type, type, (
% 1.40/1.15 tptp_fun_K_6: ( $int * $int * $int * $int * uni * uni * ty ) > $int)).
% 1.40/1.15 tff(elts_type, type, (
% 1.40/1.15 elts: ( ty * uni ) > uni)).
% 1.40/1.15 tff(sort1_type, type, (
% 1.40/1.15 sort1: ( ty * uni ) > $o)).
% 1.40/1.15 tff(map_type, type, (
% 1.40/1.15 map: ( ty * ty ) > ty)).
% 1.40/1.15 tff(1,plain,
% 1.40/1.15 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 1.40/1.15 inference(rewrite,[status(thm)],[])).
% 1.40/1.15 tff(2,plain,
% 1.40/1.15 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 1.40/1.15 inference(rewrite,[status(thm)],[])).
% 1.40/1.15 tff(3,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR')).
% 1.40/1.15 tff(4,plain,
% 1.40/1.15 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 1.40/1.15 inference(modus_ponens,[status(thm)],[3, 2])).
% 1.40/1.15 tff(5,plain,(
% 1.40/1.15 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 1.40/1.15 inference(skolemize,[status(sab)],[4])).
% 1.40/1.15 tff(6,plain,
% 1.40/1.15 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 1.40/1.15 inference(modus_ponens,[status(thm)],[5, 1])).
% 1.40/1.15 tff(7,plain,
% 1.40/1.15 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(t2tb(K!17))) = t2tb(K!17))),
% 1.40/1.15 inference(quant_inst,[status(thm)],[])).
% 1.40/1.15 tff(8,plain,
% 1.40/1.15 (t2tb(tb2t(t2tb(K!17))) = t2tb(K!17)),
% 1.40/1.15 inference(unit_resolution,[status(thm)],[7, 6])).
% 1.40/1.15 tff(9,plain,
% 1.40/1.15 (^[I: $int] : refl(($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0))),
% 1.40/1.15 inference(bind,[status(th)],[])).
% 1.40/1.15 tff(10,plain,
% 1.40/1.15 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 1.40/1.15 inference(quant_intro,[status(thm)],[9])).
% 1.40/1.15 tff(11,plain,
% 1.40/1.15 (^[I: $int] : trans(monotonicity(rewrite($sum(tb2t(t2tb(I)), $product(-1, I)) = $sum($product(-1, I), tb2t(t2tb(I)))), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum($product(-1, I), tb2t(t2tb(I))) = 0))), rewrite(($sum($product(-1, I), tb2t(t2tb(I))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)))),
% 1.40/1.15 inference(bind,[status(th)],[])).
% 1.40/1.15 tff(12,plain,
% 1.40/1.15 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 1.40/1.15 inference(quant_intro,[status(thm)],[11])).
% 1.40/1.15 tff(13,plain,
% 1.40/1.15 (^[I: $int] : rewrite((tb2t(t2tb(I)) = I) <=> ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0))),
% 1.40/1.15 inference(bind,[status(th)],[])).
% 1.40/1.15 tff(14,plain,
% 1.40/1.15 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 1.40/1.15 inference(quant_intro,[status(thm)],[13])).
% 1.40/1.15 tff(15,plain,
% 1.40/1.15 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : (tb2t(t2tb(I)) = I)),
% 1.40/1.15 inference(rewrite,[status(thm)],[])).
% 1.40/1.15 tff(16,axiom,(![I: $int] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeL')).
% 1.40/1.15 tff(17,plain,
% 1.40/1.15 (![I: $int] : (tb2t(t2tb(I)) = I)),
% 1.40/1.15 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.40/1.15 tff(18,plain,
% 1.40/1.15 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 1.40/1.15 inference(modus_ponens,[status(thm)],[17, 14])).
% 1.40/1.15 tff(19,plain,
% 1.40/1.15 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 1.40/1.15 inference(modus_ponens,[status(thm)],[18, 12])).
% 1.40/1.15 tff(20,plain,(
% 1.40/1.15 ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 1.40/1.15 inference(skolemize,[status(sab)],[19])).
% 1.40/1.15 tff(21,plain,
% 1.40/1.15 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 1.40/1.15 inference(modus_ponens,[status(thm)],[20, 10])).
% 1.40/1.15 tff(22,plain,
% 1.40/1.15 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(K!17, $product(-1, tb2t(t2tb(K!17)))) = 0)),
% 1.40/1.15 inference(quant_inst,[status(thm)],[])).
% 1.40/1.15 tff(23,plain,
% 1.40/1.15 ($sum(K!17, $product(-1, tb2t(t2tb(K!17)))) = 0),
% 1.40/1.15 inference(unit_resolution,[status(thm)],[22, 21])).
% 1.40/1.15 tff(24,plain,
% 1.40/1.15 ((~($sum(K!17, $product(-1, tb2t(t2tb(K!17)))) = 0)) | $lesseq($sum(K!17, $product(-1, tb2t(t2tb(K!17)))), 0)),
% 1.40/1.15 inference(theory_lemma,[status(thm)],[])).
% 1.40/1.15 tff(25,plain,
% 1.40/1.15 ($lesseq($sum(K!17, $product(-1, tb2t(t2tb(K!17)))), 0)),
% 1.40/1.15 inference(unit_resolution,[status(thm)],[24, 23])).
% 1.40/1.15 tff(26,plain,
% 1.40/1.15 ((~($sum(K!17, $product(-1, tb2t(t2tb(K!17)))) = 0)) | $greatereq($sum(K!17, $product(-1, tb2t(t2tb(K!17)))), 0)),
% 1.40/1.15 inference(theory_lemma,[status(thm)],[])).
% 1.40/1.15 tff(27,plain,
% 1.40/1.15 ($greatereq($sum(K!17, $product(-1, tb2t(t2tb(K!17)))), 0)),
% 1.40/1.15 inference(unit_resolution,[status(thm)],[26, 23])).
% 1.40/1.15 tff(28,plain,
% 1.40/1.15 (K!17 = tb2t(t2tb(K!17))),
% 1.40/1.15 inference(theory_lemma,[status(thm)],[27, 25])).
% 1.40/1.15 tff(29,plain,
% 1.40/1.15 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 1)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 1))),
% 1.40/1.15 inference(rewrite,[status(thm)],[])).
% 1.40/1.15 tff(30,plain,
% 1.40/1.15 (($sum(-1, $sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14)))))) = 0) <=> ($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 1)),
% 1.40/1.15 inference(rewrite,[status(thm)],[])).
% 1.40/1.15 tff(31,plain,
% 1.40/1.15 ($sum($sum(-1, J!14), $product(-1, tb2t(t2tb($sum(-1, J!14))))) = $sum(-1, $sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))))),
% 1.40/1.15 inference(rewrite,[status(thm)],[])).
% 1.40/1.15 tff(32,plain,
% 1.40/1.15 (($sum($sum(-1, J!14), $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 0) <=> ($sum(-1, $sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14)))))) = 0)),
% 1.40/1.15 inference(monotonicity,[status(thm)],[31])).
% 1.40/1.15 tff(33,plain,
% 1.40/1.15 (($sum($sum(-1, J!14), $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 0) <=> ($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 1)),
% 1.40/1.15 inference(transitivity,[status(thm)],[32, 30])).
% 1.40/1.15 tff(34,plain,
% 1.40/1.15 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(-1, J!14), $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 1))),
% 1.40/1.15 inference(monotonicity,[status(thm)],[33])).
% 1.40/1.15 tff(35,plain,
% 1.40/1.15 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(-1, J!14), $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 1))),
% 1.40/1.15 inference(transitivity,[status(thm)],[34, 29])).
% 1.40/1.15 tff(36,plain,
% 1.40/1.15 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(-1, J!14), $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 0)),
% 1.40/1.15 inference(quant_inst,[status(thm)],[])).
% 1.40/1.15 tff(37,plain,
% 1.40/1.15 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 1)),
% 1.40/1.15 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.40/1.15 tff(38,plain,
% 1.40/1.15 ($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 1),
% 1.40/1.15 inference(unit_resolution,[status(thm)],[37, 21])).
% 1.40/1.15 tff(39,plain,
% 1.40/1.15 ((~($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 1)) | $lesseq($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))), 1)),
% 1.40/1.15 inference(theory_lemma,[status(thm)],[])).
% 1.40/1.15 tff(40,plain,
% 1.40/1.15 ($lesseq($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))), 1)),
% 1.40/1.15 inference(unit_resolution,[status(thm)],[39, 38])).
% 1.40/1.15 tff(41,plain,
% 1.40/1.15 ((~($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))) = 1)) | $greatereq($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))), 1)),
% 1.40/1.15 inference(theory_lemma,[status(thm)],[])).
% 1.40/1.15 tff(42,plain,
% 1.40/1.15 ($greatereq($sum(J!14, $product(-1, tb2t(t2tb($sum(-1, J!14))))), 1)),
% 1.40/1.15 inference(unit_resolution,[status(thm)],[41, 38])).
% 1.40/1.15 tff(43,plain,
% 1.40/1.15 (($greatereq(A!10, 0) & $greatereq(A!10, 2) & ($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0)) & sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12))) & $greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1) & (~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & $greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)) & ($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))) <=> ($greatereq(A!10, 0) & $greatereq(A!10, 2) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0)) & sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12))) & $greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1) & (~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & $greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)) & ($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))),
% 1.40/1.15 inference(rewrite,[status(thm)],[])).
% 1.40/1.15 tff(44,plain,
% 1.40/1.15 ((($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0))) & (sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12)))) & ($greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1)) & ((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & $greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)) & ($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & $greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))) <=> ($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0)) & sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12))) & $greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1) & (~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & $greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)) & ($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(45,plain,
% 1.40/1.16 (((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ($greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0))) & ($greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1))) & (($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & $greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))) & ($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1))) & ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))) <=> ((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & $greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)) & ($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & $greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(46,plain,
% 1.40/1.16 (($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($lesseq($sum(J!14, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))))) <=> ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(47,plain,
% 1.40/1.16 ((~(~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1))))) <=> ($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(48,plain,
% 1.40/1.16 ((~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1)))) <=> (~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1))))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(49,plain,
% 1.40/1.16 ((~(~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) <=> (~(~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)))))),
% 1.40/1.16 inference(monotonicity,[status(thm)],[48])).
% 1.40/1.16 tff(50,plain,
% 1.40/1.16 ((~(~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) <=> ($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)))),
% 1.40/1.16 inference(transitivity,[status(thm)],[49, 47])).
% 1.40/1.16 tff(51,plain,
% 1.40/1.16 (((($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & ($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))) <=> (($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & $greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(52,plain,
% 1.40/1.16 ((~(~($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))))) <=> ($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(53,plain,
% 1.40/1.16 ((~(~exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14))) <=> exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14)),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(54,plain,
% 1.40/1.16 (((~(~($sum(J1!16, $product(-1, J!14)) = -1))) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $lesseq($sum(K!17, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))))) <=> (($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(55,plain,
% 1.40/1.16 ((((~(~($sum(J1!16, $product(-1, J!14)) = -1))) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $lesseq($sum(K!17, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))))) & (~(~exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14))) & (~(~($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))))) <=> ((($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & ($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))))),
% 1.40/1.16 inference(monotonicity,[status(thm)],[54, 53, 52])).
% 1.40/1.16 tff(56,plain,
% 1.40/1.16 ((((~(~($sum(J1!16, $product(-1, J!14)) = -1))) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $lesseq($sum(K!17, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))))) & (~(~exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14))) & (~(~($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))))) <=> (($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & $greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))),
% 1.40/1.16 inference(transitivity,[status(thm)],[55, 51])).
% 1.40/1.16 tff(57,plain,
% 1.40/1.16 ((~(~($greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1))))) <=> ($greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(58,plain,
% 1.40/1.16 ((~($greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1)))) <=> (~($greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1))))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(59,plain,
% 1.44/1.16 ((~(~($greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) <=> (~(~($greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)))))),
% 1.44/1.16 inference(monotonicity,[status(thm)],[58])).
% 1.44/1.16 tff(60,plain,
% 1.44/1.16 ((~(~($greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) <=> ($greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)))),
% 1.44/1.16 inference(transitivity,[status(thm)],[59, 57])).
% 1.44/1.16 tff(61,plain,
% 1.44/1.16 ((~(~($greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0))))) <=> ($greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(62,plain,
% 1.44/1.16 ((~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, A!10)), 0)))) <=> (~($greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0))))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(63,plain,
% 1.44/1.16 ((~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, A!10)), 0))))) <=> (~(~($greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)))))),
% 1.44/1.16 inference(monotonicity,[status(thm)],[62])).
% 1.44/1.16 tff(64,plain,
% 1.44/1.16 ((~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, A!10)), 0))))) <=> ($greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)))),
% 1.44/1.16 inference(transitivity,[status(thm)],[63, 61])).
% 1.44/1.16 tff(65,plain,
% 1.44/1.16 (((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & (((~(~($sum(J1!16, $product(-1, J!14)) = -1))) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $lesseq($sum(K!17, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))))) & (~(~exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14))) & (~(~($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($lesseq($sum(J!14, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))) <=> ((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ($greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0))) & ($greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1))) & (($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & $greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))) & ($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1))) & ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))))))),
% 1.44/1.16 inference(monotonicity,[status(thm)],[64, 60, 56, 50, 46])).
% 1.44/1.16 tff(66,plain,
% 1.44/1.16 (((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & (((~(~($sum(J1!16, $product(-1, J!14)) = -1))) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $lesseq($sum(K!17, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))))) & (~(~exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14))) & (~(~($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($lesseq($sum(J!14, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))) <=> ((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & $greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)) & ($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & $greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))),
% 1.44/1.16 inference(transitivity,[status(thm)],[65, 45])).
% 1.44/1.16 tff(67,plain,
% 1.44/1.16 ((~(~($greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1)))) <=> ($greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(68,plain,
% 1.44/1.16 ((~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, A!10)), -1))) <=> (~($greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1)))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(69,plain,
% 1.44/1.16 ((~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, A!10)), -1)))) <=> (~(~($greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1))))),
% 1.44/1.16 inference(monotonicity,[status(thm)],[68])).
% 1.44/1.16 tff(70,plain,
% 1.44/1.16 ((~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, A!10)), -1)))) <=> ($greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1))),
% 1.44/1.16 inference(transitivity,[status(thm)],[69, 67])).
% 1.44/1.16 tff(71,plain,
% 1.44/1.16 ((~(~(sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12)))))) <=> (sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12))))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(72,plain,
% 1.44/1.16 ((~(~($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0))))) <=> ($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0)))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(73,plain,
% 1.44/1.16 ((~($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, A!10)), 0)))) <=> (~($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0))))),
% 1.44/1.16 inference(rewrite,[status(thm)],[])).
% 1.44/1.16 tff(74,plain,
% 1.44/1.16 ((~(~($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, A!10)), 0))))) <=> (~(~($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0)))))),
% 1.44/1.16 inference(monotonicity,[status(thm)],[73])).
% 1.44/1.16 tff(75,plain,
% 1.44/1.16 ((~(~($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, A!10)), 0))))) <=> ($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0)))),
% 1.44/1.16 inference(transitivity,[status(thm)],[74, 72])).
% 1.44/1.16 tff(76,plain,
% 1.44/1.16 (((~(~($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, A!10)), 0))))) & (~(~(sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12)))))) & (~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, A!10)), -1)))) & ((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & (((~(~($sum(J1!16, $product(-1, J!14)) = -1))) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $lesseq($sum(K!17, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))))) & (~(~exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14))) & (~(~($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($lesseq($sum(J!14, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))))))) <=> (($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0))) & (sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12)))) & ($greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1)) & ((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & $greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)) & ($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & $greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))))))),
% 1.44/1.17 inference(monotonicity,[status(thm)],[75, 71, 70, 66])).
% 1.44/1.17 tff(77,plain,
% 1.44/1.17 (((~(~($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, A!10)), 0))))) & (~(~(sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12)))))) & (~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, A!10)), -1)))) & ((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & (((~(~($sum(J1!16, $product(-1, J!14)) = -1))) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $lesseq($sum(K!17, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))))) & (~(~exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14))) & (~(~($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($lesseq($sum(J!14, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))))))) <=> ($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0)) & sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12))) & $greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1) & (~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & $greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)) & ($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))),
% 1.44/1.17 inference(transitivity,[status(thm)],[76, 44])).
% 1.44/1.17 tff(78,plain,
% 1.44/1.17 ((~(~$greatereq(A!10, 2))) <=> $greatereq(A!10, 2)),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(79,plain,
% 1.44/1.17 ((~(~$greatereq(A!10, 0))) <=> $greatereq(A!10, 0)),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(80,plain,
% 1.44/1.17 (((~(~$greatereq(A!10, 0))) & (~(~$greatereq(A!10, 2))) & ((~(~($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, A!10)), 0))))) & (~(~(sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12)))))) & (~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, A!10)), -1)))) & ((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & (((~(~($sum(J1!16, $product(-1, J!14)) = -1))) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $lesseq($sum(K!17, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))))) & (~(~exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14))) & (~(~($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($lesseq($sum(J!14, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))))) <=> ($greatereq(A!10, 0) & $greatereq(A!10, 2) & ($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0)) & sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12))) & $greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1) & (~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & $greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)) & ($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))))))),
% 1.44/1.17 inference(monotonicity,[status(thm)],[79, 78, 77])).
% 1.44/1.17 tff(81,plain,
% 1.44/1.17 (((~(~$greatereq(A!10, 0))) & (~(~$greatereq(A!10, 2))) & ((~(~($greatereq(A!10, 0) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, A!10)), 0))))) & (~(~(sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12)))))) & (~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, A!10)), -1)))) & ((~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & (((~(~($sum(J1!16, $product(-1, J!14)) = -1))) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $lesseq($sum(K!17, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))))) & (~(~exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14))) & (~(~($greatereq(A!10, 0) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!14, 1) & (~$greatereq($sum(J!14, $product(-1, A!10)), 1))))) & ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($lesseq($sum(J!14, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))))) <=> ($greatereq(A!10, 0) & $greatereq(A!10, 2) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0)) & sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12))) & $greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1) & (~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & $greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)) & ($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))),
% 1.44/1.17 inference(transitivity,[status(thm)],[80, 43])).
% 1.44/1.17 tff(82,plain,
% 1.44/1.17 ((~![A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 2)) | ![A2: map_int_elt, I: $int] : ((~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, A)), -1))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | ![K: $int] : ((~($lesseq($sum(J1, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I)), 0))) | ($sum(K2, $product(-1, J)) = 0) | ($sum(K1, $product(-1, J)) = 0)) & ![K: $int] : ((~($lesseq($sum(J, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K))))))))))) <=> (~![A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 2)) | ![A2: map_int_elt, I: $int] : ((~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, A)), -1))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | ![K: $int] : ((~($lesseq($sum(J1, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I)), 0))) | ($sum(K2, $product(-1, J)) = 0) | ($sum(K1, $product(-1, J)) = 0)) & ![K: $int] : ((~($lesseq($sum(J, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))))))))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(83,plain,
% 1.44/1.17 ((~![A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 2)) | ![A2: map_int_elt, I: $int] : ((~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, A)), -1))) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | ![A4: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | ![K: $int] : ((~($lesseq($sum(J1, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(J, 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1)))) | (~($greatereq(A, 0) & $greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), 0) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I)), 0))) | ($sum(K2, $product(-1, J)) = 0) | ($sum(K1, $product(-1, J)) = 0)) & ![K: $int] : ((~($lesseq($sum(J, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K))))))))))) <=> (~![A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 2)) | ![A2: map_int_elt, I: $int] : ((~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, A)), -1))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | ![K: $int] : ((~($lesseq($sum(J1, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I)), 0))) | ($sum(K2, $product(-1, J)) = 0) | ($sum(K1, $product(-1, J)) = 0)) & ![K: $int] : ((~($lesseq($sum(J, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))))))))),
% 1.44/1.17 inference(rewrite,[status(thm)],[])).
% 1.44/1.17 tff(84,plain,
% 1.44/1.17 ((~![A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(2, A)) | ![A2: map_int_elt, I: $int] : ((~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | ![A4: map_int_elt] : ((~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | ![K: $int] : ((~($lesseq(J1, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~($lesseq(0, A) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(0, A) & $lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (K2 = J) | (K1 = J) | (~($lesseq(0, K1) & $lesseq(K1, K2) & $lesseq(K2, I)))) & ![K: $int] : ((~($lesseq(J, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))))) | (~($lesseq(1, I) & $lesseq(I, $sum(-1, A))))))) <=> (~![A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 2)) | ![A2: map_int_elt, I: $int] : ((~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, A)), -1))) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | ![A4: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | ![K: $int] : ((~($lesseq($sum(J1, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(J, 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1)))) | (~($greatereq(A, 0) & $greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), 0) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I)), 0))) | ($sum(K2, $product(-1, J)) = 0) | ($sum(K1, $product(-1, J)) = 0)) & ![K: $int] : ((~($lesseq($sum(J, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))))))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(85,plain,
% 1.44/1.18 ((~![A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(2, A)) | ![A2: map_int_elt, I: $int] : ((~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | ![A4: map_int_elt] : ((~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | ![K: $int] : ((~($lesseq(J1, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~($lesseq(0, A) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(0, A) & $lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (K2 = J) | (K1 = J) | (~($lesseq(0, K1) & $lesseq(K1, K2) & $lesseq(K2, I)))) & ![K: $int] : ((~($lesseq(J, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))))) | (~($lesseq(1, I) & $lesseq(I, $sum(-1, A))))))) <=> (~![A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(2, A)) | ![A2: map_int_elt, I: $int] : ((~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | ![A4: map_int_elt] : ((~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | ![K: $int] : ((~($lesseq(J1, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~($lesseq(0, A) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(0, A) & $lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (K2 = J) | (K1 = J) | (~($lesseq(0, K1) & $lesseq(K1, K2) & $lesseq(K2, I)))) & ![K: $int] : ((~($lesseq(J, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))))) | (~($lesseq(1, I) & $lesseq(I, $sum(-1, A)))))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(86,plain,
% 1.44/1.18 ((~![A: $int, A1: map_int_elt] : ($lesseq(0, A) => ($lesseq(1, $difference(A, 1)) => ![A2: map_int_elt, I: $int] : (($lesseq(1, I) & $lesseq(I, $difference(A, 1))) => ((sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2)))) => ((($lesseq(0, A) & $lesseq(0, I)) & $less(I, A)) => ![J: $int, A3: map_int_elt] : ((((($lesseq(0, J) & $lesseq(J, I)) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))))) & ![K1: $int, K2: $int] : ((($lesseq(0, K1) & $lesseq(K1, K2)) & $lesseq(K2, I)) => ((~(K1 = J)) => ((~(K2 = J)) => le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))))))) & ![K: $int] : (($lesseq($sum(J, 1), K) & $lesseq(K, I)) => le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))) => ($less(0, J) => ((($lesseq(0, A) & $lesseq(0, $difference(J, 1))) & $less($difference(J, 1), A)) => ((~le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($difference(J, 1)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I))))) => (($lesseq(0, $difference(J, 1)) & $less($difference(J, 1), A)) => (($lesseq(0, J) & $less(J, A)) => ![A4: map_int_elt] : (($lesseq(0, A) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($difference(J, 1))))))) => (exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($difference(J, 1)), get(elt, int, t2tb3(A2), t2tb(I)))), $difference(J, 1), J) => ![J1: $int] : ((J1 = $difference(J, 1)) => ![K: $int] : (($lesseq($sum(J1, 1), K) & $lesseq(K, I)) => le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))))))))))))))))) <=> (~![A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(2, A)) | ![A2: map_int_elt, I: $int] : ((~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | ![A4: map_int_elt] : ((~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | ![K: $int] : ((~($lesseq(J1, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~($lesseq(0, A) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(0, A) & $lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (K2 = J) | (K1 = J) | (~($lesseq(0, K1) & $lesseq(K1, K2) & $lesseq(K2, I)))) & ![K: $int] : ((~($lesseq(J, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))))) | (~($lesseq(1, I) & $lesseq(I, $sum(-1, A)))))))),
% 1.44/1.18 inference(rewrite,[status(thm)],[])).
% 1.44/1.18 tff(87,axiom,(~![A: $int, A1: map_int_elt] : ($lesseq(0, A) => ($lesseq(1, $difference(A, 1)) => ![A2: map_int_elt, I: $int] : (($lesseq(1, I) & $lesseq(I, $difference(A, 1))) => ((sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2)))) => ((($lesseq(0, A) & $lesseq(0, I)) & $less(I, A)) => ![J: $int, A3: map_int_elt] : ((((($lesseq(0, J) & $lesseq(J, I)) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))))) & ![K1: $int, K2: $int] : ((($lesseq(0, K1) & $lesseq(K1, K2)) & $lesseq(K2, I)) => ((~(K1 = J)) => ((~(K2 = J)) => le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))))))) & ![K: $int] : (($lesseq($sum(J, 1), K) & $lesseq(K, I)) => le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))) => ($less(0, J) => ((($lesseq(0, A) & $lesseq(0, $difference(J, 1))) & $less($difference(J, 1), A)) => ((~le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($difference(J, 1)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I))))) => (($lesseq(0, $difference(J, 1)) & $less($difference(J, 1), A)) => (($lesseq(0, J) & $less(J, A)) => ![A4: map_int_elt] : (($lesseq(0, A) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($difference(J, 1))))))) => (exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($difference(J, 1)), get(elt, int, t2tb3(A2), t2tb(I)))), $difference(J, 1), J) => ![J1: $int] : ((J1 = $difference(J, 1)) => ![K: $int] : (($lesseq($sum(J1, 1), K) & $lesseq(K, I)) => le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_insertion_sort1')).
% 1.44/1.18 tff(88,plain,
% 1.44/1.18 (~![A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(2, A)) | ![A2: map_int_elt, I: $int] : ((~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | ![A4: map_int_elt] : ((~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | ![K: $int] : ((~($lesseq(J1, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~($lesseq(0, A) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(0, A) & $lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (K2 = J) | (K1 = J) | (~($lesseq(0, K1) & $lesseq(K1, K2) & $lesseq(K2, I)))) & ![K: $int] : ((~($lesseq(J, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))))) | (~($lesseq(1, I) & $lesseq(I, $sum(-1, A))))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.44/1.18 tff(89,plain,
% 1.44/1.18 (~![A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(2, A)) | ![A2: map_int_elt, I: $int] : ((~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | ![A4: map_int_elt] : ((~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | ![K: $int] : ((~($lesseq(J1, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~($lesseq(0, A) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(0, A) & $lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (K2 = J) | (K1 = J) | (~($lesseq(0, K1) & $lesseq(K1, K2) & $lesseq(K2, I)))) & ![K: $int] : ((~($lesseq(J, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))))) | (~($lesseq(1, I) & $lesseq(I, $sum(-1, A))))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[88, 85])).
% 1.44/1.18 tff(90,plain,
% 1.44/1.18 (~![A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(2, A)) | ![A2: map_int_elt, I: $int] : ((~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | ![A4: map_int_elt] : ((~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | ![K: $int] : ((~($lesseq(J1, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~($lesseq(0, A) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(0, A) & $lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (K2 = J) | (K1 = J) | (~($lesseq(0, K1) & $lesseq(K1, K2) & $lesseq(K2, I)))) & ![K: $int] : ((~($lesseq(J, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))))) | (~($lesseq(1, I) & $lesseq(I, $sum(-1, A))))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[89, 85])).
% 1.44/1.18 tff(91,plain,
% 1.44/1.18 (~![A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(2, A)) | ![A2: map_int_elt, I: $int] : ((~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | ![A4: map_int_elt] : ((~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | ![K: $int] : ((~($lesseq(J1, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~($lesseq(0, A) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(0, A) & $lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (K2 = J) | (K1 = J) | (~($lesseq(0, K1) & $lesseq(K1, K2) & $lesseq(K2, I)))) & ![K: $int] : ((~($lesseq(J, $sum(-1, K)) & $lesseq(K, I))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K)))))))) | (~($lesseq(1, I) & $lesseq(I, $sum(-1, A))))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[90, 85])).
% 1.44/1.18 tff(92,plain,
% 1.44/1.18 (~![A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 2)) | ![A2: map_int_elt, I: $int] : ((~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, A)), -1))) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | ![A4: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | ![K: $int] : ((~($lesseq($sum(J1, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(J, 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1)))) | (~($greatereq(A, 0) & $greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), 0) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I)), 0))) | ($sum(K2, $product(-1, J)) = 0) | ($sum(K1, $product(-1, J)) = 0)) & ![K: $int] : ((~($lesseq($sum(J, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K))))))))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[91, 84])).
% 1.44/1.18 tff(93,plain,
% 1.44/1.18 (~![A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 2)) | ![A2: map_int_elt, I: $int] : ((~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, A)), -1))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | ![K: $int] : ((~($lesseq($sum(J1, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I)), 0))) | ($sum(K2, $product(-1, J)) = 0) | ($sum(K1, $product(-1, J)) = 0)) & ![K: $int] : ((~($lesseq($sum(J, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K))))))))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[92, 83])).
% 1.44/1.18 tff(94,plain,
% 1.44/1.18 (~![A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 2)) | ![A2: map_int_elt, I: $int] : ((~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, A)), -1))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | ![K: $int] : ((~($lesseq($sum(J1, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I)), 0))) | ($sum(K2, $product(-1, J)) = 0) | ($sum(K1, $product(-1, J)) = 0)) & ![K: $int] : ((~($lesseq($sum(J, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K))))))))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[93, 82])).
% 1.44/1.18 tff(95,plain,
% 1.44/1.18 (~![A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 2)) | ![A2: map_int_elt, I: $int] : ((~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~(sorted_sub6(A2, 0, I) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, t2tb3(A2))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, A)), -1))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le1(tb2t4(get(elt, int, t2tb3(A3), t2tb($sum(-1, J)))), tb2t4(get(elt, int, t2tb3(A2), t2tb(I)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | ![K: $int] : ((~($lesseq($sum(J1, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A4), t2tb(K)))))) | (~exchange3(elt, mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I)))), mk_array1(elt, A, set(elt, int, t2tb3(A4), t2tb($sum(-1, J)), get(elt, int, t2tb3(A2), t2tb(I)))), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A4 = tb2t3(set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt, mk_array1(elt, A, t2tb3(A1)), mk_array1(elt, A, set(elt, int, t2tb3(A3), t2tb(J), get(elt, int, t2tb3(A2), t2tb(I))))) & ![K1: $int, K2: $int] : (le1(tb2t4(get(elt, int, t2tb3(A3), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K2)))) | (~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I)), 0))) | ($sum(K2, $product(-1, J)) = 0) | ($sum(K1, $product(-1, J)) = 0)) & ![K: $int] : ((~($lesseq($sum(J, $product(-1, K)), -1) & $lesseq($sum(K, $product(-1, I)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2), t2tb(I))), tb2t4(get(elt, int, t2tb3(A3), t2tb(K))))))))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[94, 82])).
% 1.44/1.18 tff(96,plain,
% 1.44/1.18 ($greatereq(A!10, 0) & $greatereq(A!10, 2) & $greatereq(I!11, 0) & (~$lesseq($sum(A!10, $product(-1, I!11)), 0)) & sorted_sub6(A2!12, 0, I!11) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, t2tb3(A2!12))) & $greatereq(I!11, 1) & $greatereq($sum(A!10, $product(-1, I!11)), 1) & (~$lesseq(J!14, 0)) & (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & $greatereq(J!14, 0) & (~$lesseq($sum(A!10, $product(-1, J!14)), 0)) & $greatereq(J!14, 1) & (~$lesseq($sum(A!10, $product(-1, J!14)), -1)) & ($sum(J!14, $product(-1, J1!16)) = 1) & (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))) & exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) & (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) & $greatereq($sum(I!11, $product(-1, J!14)), 0) & permut_all(elt, mk_array1(elt, A!10, t2tb3(A1!9)), mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & $lesseq($sum(K1, $product(-1, K2)), 0) & $lesseq($sum(K2, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K1))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K2)))) | ($sum(K2, $product(-1, J!14)) = 0) | ($sum(K1, $product(-1, J!14)) = 0)) & ![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))))),
% 1.44/1.18 inference(modus_ponens,[status(thm)],[95, 81])).
% 1.44/1.18 tff(97,plain,
% 1.44/1.18 ($sum(J!14, $product(-1, J1!16)) = 1),
% 1.44/1.18 inference(and_elim,[status(thm)],[96])).
% 1.44/1.18 tff(98,plain,
% 1.44/1.18 ((~($sum(J!14, $product(-1, J1!16)) = 1)) | $lesseq($sum(J!14, $product(-1, J1!16)), 1)),
% 1.44/1.18 inference(theory_lemma,[status(thm)],[])).
% 1.44/1.18 tff(99,plain,
% 1.44/1.18 ($lesseq($sum(J!14, $product(-1, J1!16)), 1)),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[98, 97])).
% 1.44/1.18 tff(100,plain,
% 1.44/1.18 (~((~($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))))),
% 1.44/1.18 inference(and_elim,[status(thm)],[96])).
% 1.44/1.18 tff(101,plain,
% 1.44/1.18 ($lesseq($sum(J1!16, $product(-1, K!17)), -1) & $greatereq($sum(I!11, $product(-1, K!17)), 0)),
% 1.44/1.18 inference(or_elim,[status(thm)],[100])).
% 1.44/1.18 tff(102,plain,
% 1.44/1.18 ($lesseq($sum(J1!16, $product(-1, K!17)), -1)),
% 1.44/1.18 inference(and_elim,[status(thm)],[101])).
% 1.44/1.18 tff(103,plain,
% 1.44/1.18 ($lesseq($sum(J!14, $product(-1, K!17)), 0) | (~$lesseq($sum(J1!16, $product(-1, K!17)), -1)) | (~$lesseq($sum(J!14, $product(-1, J1!16)), 1))),
% 1.44/1.18 inference(theory_lemma,[status(thm)],[])).
% 1.44/1.18 tff(104,plain,
% 1.44/1.18 ($lesseq($sum(J!14, $product(-1, K!17)), 0)),
% 1.44/1.18 inference(unit_resolution,[status(thm)],[103, 102, 99])).
% 1.44/1.18 tff(105,assumption,(~$lesseq($sum(J!14, $product(-1, K!17)), -1)), introduced(assumption)).
% 1.44/1.18 tff(106,plain,
% 1.44/1.18 (J!14 = K!17),
% 1.44/1.18 inference(theory_lemma,[status(thm)],[42, 40, 105, 104, 42, 40])).
% 1.44/1.18 tff(107,plain,
% 1.44/1.18 (J!14 = tb2t(t2tb(K!17))),
% 1.44/1.18 inference(transitivity,[status(thm)],[106, 28])).
% 1.44/1.18 tff(108,plain,
% 1.44/1.18 (t2tb(J!14) = t2tb(tb2t(t2tb(K!17)))),
% 1.44/1.18 inference(monotonicity,[status(thm)],[107])).
% 1.44/1.18 tff(109,plain,
% 1.44/1.18 (t2tb(J!14) = t2tb(K!17)),
% 1.44/1.18 inference(transitivity,[status(thm)],[108, 8])).
% 1.44/1.18 tff(110,plain,
% 1.44/1.18 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> (~((~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))))))),
% 1.44/1.18 inference(bind,[status(th)],[])).
% 1.44/1.18 tff(111,plain,
% 1.44/1.18 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))),
% 1.44/1.18 inference(quant_intro,[status(thm)],[110])).
% 1.44/1.18 tff(112,plain,
% 1.44/1.18 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : refl((~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))))),
% 1.44/1.19 inference(bind,[status(th)],[])).
% 1.44/1.19 tff(113,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 1.44/1.19 inference(quant_intro,[status(thm)],[112])).
% 1.44/1.19 tff(114,plain,
% 1.44/1.19 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))))),
% 1.44/1.19 inference(bind,[status(th)],[])).
% 1.44/1.19 tff(115,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 1.44/1.19 inference(quant_intro,[status(thm)],[114])).
% 1.44/1.19 tff(116,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 1.44/1.19 inference(transitivity,[status(thm)],[115, 113])).
% 1.44/1.19 tff(117,plain,
% 1.44/1.19 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : trans(monotonicity(rewrite(((~exchange2(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) <=> ((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))), trans(monotonicity(rewrite((~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) <=> (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))), ((exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))) <=> (exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))), rewrite((exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))) <=> (exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))), ((exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))) <=> (exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))), ((((~exchange2(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> (((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))) & (exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))), rewrite((((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))) & (exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) <=> (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))), ((((~exchange2(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))))),
% 1.44/1.19 inference(bind,[status(th)],[])).
% 1.44/1.19 tff(118,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (((~exchange2(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 1.44/1.19 inference(quant_intro,[status(thm)],[117])).
% 1.44/1.19 tff(119,plain,
% 1.44/1.19 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((((~exchange2(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange2(A, A1, A2, L, U, I, J) | ((~$greatereq($sum(I, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, I)), 0))) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, J)), 0))) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | (~($greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, L)), 0) & (~$greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, U)), 0)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0)))))) <=> (((~exchange2(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))))),
% 1.44/1.19 inference(bind,[status(th)],[])).
% 1.44/1.19 tff(120,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (((~exchange2(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange2(A, A1, A2, L, U, I, J) | ((~$greatereq($sum(I, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, I)), 0))) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, J)), 0))) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | (~($greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, L)), 0) & (~$greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, U)), 0)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0)))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (((~exchange2(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 1.44/1.19 inference(quant_intro,[status(thm)],[119])).
% 1.44/1.19 tff(121,plain,
% 1.44/1.19 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | ($sum(K, $product(-1, J)) = 0) | ($sum(K, $product(-1, I)) = 0) | (~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(U, $product(-1, K)), 0))))))) <=> (exchange2(A, A1, A2, L, U, I, J) <=> ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))))),
% 1.44/1.19 inference(bind,[status(th)],[])).
% 1.44/1.19 tff(122,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | ($sum(K, $product(-1, J)) = 0) | ($sum(K, $product(-1, I)) = 0) | (~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(U, $product(-1, K)), 0))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0))))),
% 1.44/1.19 inference(quant_intro,[status(thm)],[121])).
% 1.44/1.19 tff(123,plain,
% 1.44/1.19 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K))))))) <=> (exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | ($sum(K, $product(-1, J)) = 0) | ($sum(K, $product(-1, I)) = 0) | (~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(U, $product(-1, K)), 0))))))))),
% 1.44/1.19 inference(bind,[status(th)],[])).
% 1.44/1.19 tff(124,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | ($sum(K, $product(-1, J)) = 0) | ($sum(K, $product(-1, I)) = 0) | (~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(U, $product(-1, K)), 0)))))))),
% 1.44/1.19 inference(quant_intro,[status(thm)],[123])).
% 1.44/1.19 tff(125,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K)))))))),
% 1.44/1.19 inference(rewrite,[status(thm)],[])).
% 1.44/1.19 tff(126,plain,
% 1.44/1.19 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((exchange2(A, A1, A2, L, U, I, J) <=> (((((($lesseq(L, I) & $less(I, U)) & $lesseq(L, J)) & $less(J, U)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) & ![K: $int] : (($lesseq(L, K) & $less(K, U)) => ((~(K = I)) => ((~(K = J)) => (get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K)))))))) <=> (exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K))))))))),
% 1.44/1.19 inference(bind,[status(th)],[])).
% 1.44/1.19 tff(127,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> (((((($lesseq(L, I) & $less(I, U)) & $lesseq(L, J)) & $less(J, U)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) & ![K: $int] : (($lesseq(L, K) & $less(K, U)) => ((~(K = I)) => ((~(K = J)) => (get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K)))))))),
% 1.44/1.19 inference(quant_intro,[status(thm)],[126])).
% 1.44/1.19 tff(128,axiom,(![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> (((((($lesseq(L, I) & $less(I, U)) & $lesseq(L, J)) & $less(J, U)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) & ![K: $int] : (($lesseq(L, K) & $less(K, U)) => ((~(K = I)) => ((~(K = J)) => (get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','exchange_def')).
% 1.44/1.19 tff(129,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K)))))))),
% 1.44/1.19 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.44/1.19 tff(130,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K)))))))),
% 1.44/1.19 inference(modus_ponens,[status(thm)],[129, 125])).
% 1.44/1.19 tff(131,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> ($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | ($sum(K, $product(-1, J)) = 0) | ($sum(K, $product(-1, I)) = 0) | (~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(U, $product(-1, K)), 0)))))))),
% 1.44/1.19 inference(modus_ponens,[status(thm)],[130, 124])).
% 1.44/1.19 tff(132,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange2(A, A1, A2, L, U, I, J) <=> ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0))))),
% 1.44/1.19 inference(modus_ponens,[status(thm)],[131, 122])).
% 1.44/1.19 tff(133,plain,(
% 1.44/1.19 ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (((~exchange2(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange2(A, A1, A2, L, U, I, J) | ((~$greatereq($sum(I, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, I)), 0))) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, J)), 0))) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | (~($greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, L)), 0) & (~$greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, U)), 0)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0))))))),
% 1.44/1.19 inference(skolemize,[status(sab)],[132])).
% 1.44/1.19 tff(134,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (((~exchange2(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 1.44/1.19 inference(modus_ponens,[status(thm)],[133, 120])).
% 1.44/1.19 tff(135,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 1.44/1.19 inference(modus_ponens,[status(thm)],[134, 118])).
% 1.44/1.19 tff(136,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 1.44/1.19 inference(modus_ponens,[status(thm)],[135, 116])).
% 1.44/1.19 tff(137,plain,
% 1.44/1.19 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))),
% 1.44/1.20 inference(modus_ponens,[status(thm)],[136, 111])).
% 1.44/1.20 tff(138,plain,
% 1.44/1.20 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~((~$greatereq(J!14, 0)) | exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 1) | (~$greatereq(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~((~$greatereq(J!14, 0)) | exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 1) | (~$greatereq(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))))))))))),
% 1.44/1.20 inference(rewrite,[status(thm)],[])).
% 1.44/1.20 tff(139,plain,
% 1.44/1.20 ((~((~(exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, $sum(-1, J!14))), 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, J!14)), 0) | (~$greatereq($sum(J!14, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!14), $product(-1, 0)), 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | ($sum($sum(-1, J!14), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~($lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, $sum(-1, J!14))), 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, J!14)), 0) | (~$greatereq($sum(J!14, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!14), $product(-1, 0)), 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | (~![K: $int] : ((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K)) = 0) | ($sum($sum(-1, J!14), $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)))))))))) <=> (~((~((~$greatereq(J!14, 0)) | exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 1) | (~$greatereq(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)))))))))),
% 1.44/1.21 inference(rewrite,[status(thm)],[])).
% 1.44/1.21 tff(140,plain,
% 1.44/1.21 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~(exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, $sum(-1, J!14))), 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, J!14)), 0) | (~$greatereq($sum(J!14, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!14), $product(-1, 0)), 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | ($sum($sum(-1, J!14), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~($lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, $sum(-1, J!14))), 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, J!14)), 0) | (~$greatereq($sum(J!14, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!14), $product(-1, 0)), 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | (~![K: $int] : ((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K)) = 0) | ($sum($sum(-1, J!14), $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, 0)), 0))))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~((~$greatereq(J!14, 0)) | exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 1) | (~$greatereq(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))))))))))),
% 1.44/1.22 inference(monotonicity,[status(thm)],[139])).
% 1.44/1.22 tff(141,plain,
% 1.44/1.22 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~(exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, $sum(-1, J!14))), 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, J!14)), 0) | (~$greatereq($sum(J!14, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!14), $product(-1, 0)), 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | ($sum($sum(-1, J!14), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~($lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, $sum(-1, J!14))), 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, J!14)), 0) | (~$greatereq($sum(J!14, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!14), $product(-1, 0)), 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | (~![K: $int] : ((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K)) = 0) | ($sum($sum(-1, J!14), $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, 0)), 0))))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~((~$greatereq(J!14, 0)) | exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 1) | (~$greatereq(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))))))))))),
% 1.44/1.22 inference(transitivity,[status(thm)],[140, 138])).
% 1.44/1.22 tff(142,plain,
% 1.44/1.22 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~(exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, $sum(-1, J!14))), 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, J!14)), 0) | (~$greatereq($sum(J!14, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!14), $product(-1, 0)), 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | ($sum($sum(-1, J!14), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~($lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, $sum(-1, J!14))), 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, J!14)), 0) | (~$greatereq($sum(J!14, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!14), $product(-1, 0)), 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | (~![K: $int] : ((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K)) = 0) | ($sum($sum(-1, J!14), $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, 0)), 0))))))))))),
% 1.51/1.23 inference(quant_inst,[status(thm)],[])).
% 1.51/1.23 tff(143,plain,
% 1.51/1.23 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange2(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange2(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~((~$greatereq(J!14, 0)) | exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 1) | (~$greatereq(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)))))))))),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[142, 141])).
% 1.51/1.23 tff(144,plain,
% 1.51/1.23 (~((~((~$greatereq(J!14, 0)) | exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 1) | (~$greatereq(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))))))))),
% 1.51/1.24 inference(unit_resolution,[status(thm)],[143, 137])).
% 1.51/1.24 tff(145,plain,
% 1.51/1.24 (((~((~$greatereq(J!14, 0)) | exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt)))) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 0) | $lesseq($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))), 0) | ($sum(J!14, $product(-1, tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt))) = 1) | (~$greatereq(tptp_fun_K_6(J!14, $sum(-1, J!14), length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), elt), 0)))))) | (~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)))))))) | ((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))))))),
% 1.51/1.24 inference(tautology,[status(thm)],[])).
% 1.51/1.24 tff(146,plain,
% 1.51/1.24 ((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)))))),
% 1.51/1.24 inference(unit_resolution,[status(thm)],[145, 144])).
% 1.51/1.24 tff(147,plain,
% 1.51/1.24 (^[A: ty, B: ty, X: uni, X1: uni, X2: uni] : refl(sort1(map(A, B), set(B, A, X, X1, X2)) <=> sort1(map(A, B), set(B, A, X, X1, X2)))),
% 1.51/1.24 inference(bind,[status(th)],[])).
% 1.51/1.24 tff(148,plain,
% 1.51/1.24 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 1.51/1.24 inference(quant_intro,[status(thm)],[147])).
% 1.51/1.24 tff(149,plain,
% 1.51/1.24 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 1.51/1.24 inference(rewrite,[status(thm)],[])).
% 1.51/1.24 tff(150,axiom,(![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','set_sort4')).
% 1.51/1.24 tff(151,plain,
% 1.51/1.24 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 1.51/1.24 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.51/1.24 tff(152,plain,(
% 1.51/1.24 ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 1.51/1.24 inference(skolemize,[status(sab)],[151])).
% 1.51/1.24 tff(153,plain,
% 1.51/1.24 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 1.51/1.24 inference(modus_ponens,[status(thm)],[152, 148])).
% 1.51/1.24 tff(154,plain,
% 1.51/1.24 ((~![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))) | sort1(map(int, elt), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))),
% 1.51/1.24 inference(quant_inst,[status(thm)],[])).
% 1.51/1.24 tff(155,plain,
% 1.51/1.24 (sort1(map(int, elt), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))),
% 1.51/1.24 inference(unit_resolution,[status(thm)],[154, 153])).
% 1.51/1.24 tff(156,plain,
% 1.51/1.24 (^[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)))),
% 1.51/1.24 inference(bind,[status(th)],[])).
% 1.51/1.24 tff(157,plain,
% 1.51/1.24 (![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))),
% 1.51/1.24 inference(quant_intro,[status(thm)],[156])).
% 1.51/1.24 tff(158,plain,
% 1.51/1.24 (![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))),
% 1.51/1.24 inference(rewrite,[status(thm)],[])).
% 1.51/1.24 tff(159,plain,
% 1.51/1.24 (^[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)))),
% 1.51/1.24 inference(bind,[status(th)],[])).
% 1.51/1.24 tff(160,plain,
% 1.51/1.24 (![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))),
% 1.51/1.24 inference(quant_intro,[status(thm)],[159])).
% 1.51/1.24 tff(161,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')).
% 1.51/1.24 tff(162,plain,
% 1.51/1.24 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 1.51/1.24 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.51/1.24 tff(163,plain,
% 1.51/1.24 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 1.51/1.24 inference(modus_ponens,[status(thm)],[162, 158])).
% 1.51/1.24 tff(164,plain,(
% 1.51/1.24 ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 1.51/1.24 inference(skolemize,[status(sab)],[163])).
% 1.51/1.24 tff(165,plain,
% 1.51/1.24 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 1.51/1.24 inference(modus_ponens,[status(thm)],[164, 157])).
% 1.51/1.24 tff(166,plain,
% 1.51/1.24 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) | (elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) = set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) | (elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) = set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))))),
% 1.51/1.24 inference(rewrite,[status(thm)],[])).
% 1.51/1.24 tff(167,plain,
% 1.51/1.24 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) | (elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) = set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))))),
% 1.51/1.25 inference(quant_inst,[status(thm)],[])).
% 1.51/1.25 tff(168,plain,
% 1.51/1.25 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) | (elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) = set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))),
% 1.51/1.25 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.51/1.25 tff(169,plain,
% 1.51/1.25 (elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) = set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))),
% 1.51/1.25 inference(unit_resolution,[status(thm)],[168, 165, 155])).
% 1.51/1.25 tff(170,plain,
% 1.51/1.25 (set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))) = elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))))),
% 1.51/1.25 inference(symmetry,[status(thm)],[169])).
% 1.51/1.25 tff(171,plain,
% 1.51/1.25 ((~![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))) | sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))),
% 1.51/1.25 inference(quant_inst,[status(thm)],[])).
% 1.51/1.25 tff(172,plain,
% 1.51/1.25 (sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))),
% 1.51/1.25 inference(unit_resolution,[status(thm)],[171, 153])).
% 1.51/1.25 tff(173,plain,
% 1.51/1.25 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) | (elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) = set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) | (elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) = set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))))),
% 1.51/1.25 inference(rewrite,[status(thm)],[])).
% 1.51/1.25 tff(174,plain,
% 1.51/1.25 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) | (elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) = set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))))),
% 1.51/1.25 inference(quant_inst,[status(thm)],[])).
% 1.51/1.25 tff(175,plain,
% 1.51/1.25 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) | (elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) = set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))),
% 1.51/1.25 inference(modus_ponens,[status(thm)],[174, 173])).
% 1.51/1.25 tff(176,plain,
% 1.51/1.25 (elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))) = set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))),
% 1.51/1.25 inference(unit_resolution,[status(thm)],[175, 165, 172])).
% 1.51/1.25 tff(177,plain,
% 1.51/1.25 (set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))) = elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))))),
% 1.51/1.25 inference(symmetry,[status(thm)],[176])).
% 1.51/1.25 tff(178,plain,
% 1.51/1.25 (exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) <=> exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)),
% 1.51/1.25 inference(monotonicity,[status(thm)],[177, 170])).
% 1.51/1.25 tff(179,plain,
% 1.51/1.25 (exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14) <=> exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)),
% 1.51/1.25 inference(symmetry,[status(thm)],[178])).
% 1.51/1.25 tff(180,plain,
% 1.51/1.25 (^[A: ty, A1: uni, A2: uni, I: $int, J: $int] : refl((exchange3(A, A1, A2, I, J) <=> (~((~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J))))) <=> (exchange3(A, A1, A2, I, J) <=> (~((~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J))))))),
% 1.51/1.25 inference(bind,[status(th)],[])).
% 1.51/1.25 tff(181,plain,
% 1.51/1.25 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> (~((~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J))))) <=> ![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> (~((~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J)))))),
% 1.51/1.25 inference(quant_intro,[status(thm)],[180])).
% 1.51/1.25 tff(182,plain,
% 1.51/1.25 (^[A: ty, A1: uni, A2: uni, I: $int, J: $int] : rewrite((exchange3(A, A1, A2, I, J) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J))) <=> (exchange3(A, A1, A2, I, J) <=> (~((~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J))))))),
% 1.51/1.25 inference(bind,[status(th)],[])).
% 1.51/1.25 tff(183,plain,
% 1.51/1.25 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J))) <=> ![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> (~((~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J)))))),
% 1.51/1.25 inference(quant_intro,[status(thm)],[182])).
% 1.51/1.25 tff(184,plain,
% 1.51/1.25 (^[A: ty, A1: uni, A2: uni, I: $int, J: $int] : rewrite((exchange3(A, A1, A2, I, J) <=> ((length1(A, A1) = length1(A, A2)) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J))) <=> (exchange3(A, A1, A2, I, J) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J))))),
% 1.51/1.25 inference(bind,[status(th)],[])).
% 1.51/1.25 tff(185,plain,
% 1.51/1.25 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> ((length1(A, A1) = length1(A, A2)) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J))) <=> ![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J)))),
% 1.51/1.25 inference(quant_intro,[status(thm)],[184])).
% 1.51/1.25 tff(186,plain,
% 1.51/1.25 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> ((length1(A, A1) = length1(A, A2)) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J))) <=> ![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> ((length1(A, A1) = length1(A, A2)) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J)))),
% 1.51/1.25 inference(rewrite,[status(thm)],[])).
% 1.51/1.25 tff(187,axiom,(![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> ((length1(A, A1) = length1(A, A2)) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','exchange_def1')).
% 1.51/1.25 tff(188,plain,
% 1.51/1.25 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> ((length1(A, A1) = length1(A, A2)) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J)))),
% 1.51/1.25 inference(modus_ponens,[status(thm)],[187, 186])).
% 1.51/1.25 tff(189,plain,
% 1.51/1.25 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J)))),
% 1.51/1.25 inference(modus_ponens,[status(thm)],[188, 185])).
% 1.51/1.25 tff(190,plain,(
% 1.51/1.25 ![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> (($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0) & exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J)))),
% 1.51/1.25 inference(skolemize,[status(sab)],[189])).
% 1.51/1.25 tff(191,plain,
% 1.51/1.25 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> (~((~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J)))))),
% 1.51/1.25 inference(modus_ponens,[status(thm)],[190, 183])).
% 1.51/1.25 tff(192,plain,
% 1.51/1.25 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> (~((~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J)))))),
% 1.51/1.25 inference(modus_ponens,[status(thm)],[191, 181])).
% 1.51/1.25 tff(193,plain,
% 1.51/1.25 ((~![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange3(A, A1, A2, I, J) <=> (~((~($sum(length1(A, A1), $product(-1, length1(A, A2))) = 0)) | (~exchange2(A, elts(A, A1), elts(A, A2), 0, length1(A, A1), I, J)))))) | (exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) <=> (~((~($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))) = 0)) | (~exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)))))),
% 1.51/1.25 inference(quant_inst,[status(thm)],[])).
% 1.51/1.25 tff(194,plain,
% 1.51/1.25 (exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) <=> (~((~($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))) = 0)) | (~exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14))))),
% 1.51/1.25 inference(unit_resolution,[status(thm)],[193, 192])).
% 1.51/1.25 tff(195,plain,
% 1.51/1.25 (exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14)),
% 1.51/1.25 inference(and_elim,[status(thm)],[96])).
% 1.51/1.25 tff(196,plain,
% 1.51/1.25 ((~(exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) <=> (~((~($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))) = 0)) | (~exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)))))) | (~exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14)) | (~((~($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))) = 0)) | (~exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14))))),
% 1.51/1.25 inference(tautology,[status(thm)],[])).
% 1.51/1.25 tff(197,plain,
% 1.51/1.25 ((~(exchange3(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))), $sum(-1, J!14), J!14) <=> (~((~($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))) = 0)) | (~exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)))))) | (~((~($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))) = 0)) | (~exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14))))),
% 1.51/1.25 inference(unit_resolution,[status(thm)],[196, 195])).
% 1.51/1.25 tff(198,plain,
% 1.51/1.25 (~((~($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))) = 0)) | (~exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)))),
% 1.51/1.25 inference(unit_resolution,[status(thm)],[197, 194])).
% 1.51/1.25 tff(199,plain,
% 1.51/1.25 (((~($sum(length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))) = 0)) | (~exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14))) | exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)),
% 1.51/1.25 inference(tautology,[status(thm)],[])).
% 1.51/1.25 tff(200,plain,
% 1.51/1.25 (exchange2(elt, elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), elts(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)),
% 1.51/1.25 inference(unit_resolution,[status(thm)],[199, 198])).
% 1.51/1.25 tff(201,plain,
% 1.51/1.25 (exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)),
% 1.51/1.25 inference(modus_ponens,[status(thm)],[200, 179])).
% 1.51/1.25 tff(202,plain,
% 1.51/1.25 ((~((~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))))))) | (~exchange2(elt, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), 0, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))), $sum(-1, J!14), J!14)) | (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)))))),
% 1.51/1.26 inference(tautology,[status(thm)],[])).
% 1.51/1.26 tff(203,plain,
% 1.51/1.26 (~((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))))),
% 1.51/1.26 inference(unit_resolution,[status(thm)],[202, 201, 146])).
% 1.51/1.26 tff(204,plain,
% 1.51/1.26 (((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))),
% 1.51/1.26 inference(tautology,[status(thm)],[])).
% 1.51/1.26 tff(205,plain,
% 1.51/1.26 (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14))),
% 1.51/1.26 inference(unit_resolution,[status(thm)],[204, 203])).
% 1.51/1.26 tff(206,assumption,(t2tb(J!14) = t2tb($sum(-1, J!14))), introduced(assumption)).
% 1.51/1.26 tff(207,plain,
% 1.51/1.26 (tb2t(t2tb(J!14)) = tb2t(t2tb($sum(-1, J!14)))),
% 1.51/1.26 inference(monotonicity,[status(thm)],[206])).
% 1.51/1.26 tff(208,plain,
% 1.51/1.26 (tb2t(t2tb($sum(-1, J!14))) = tb2t(t2tb(J!14))),
% 1.51/1.26 inference(symmetry,[status(thm)],[207])).
% 1.51/1.26 tff(209,assumption,($greatereq($sum(tb2t(t2tb($sum(-1, J!14))), $product(-1, tb2t(t2tb(J!14)))), 0)), introduced(assumption)).
% 1.51/1.26 tff(210,plain,
% 1.51/1.26 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J!14, $product(-1, tb2t(t2tb(J!14)))) = 0)),
% 1.51/1.26 inference(quant_inst,[status(thm)],[])).
% 1.51/1.26 tff(211,plain,
% 1.51/1.26 ($sum(J!14, $product(-1, tb2t(t2tb(J!14)))) = 0),
% 1.51/1.26 inference(unit_resolution,[status(thm)],[210, 21])).
% 1.51/1.26 tff(212,plain,
% 1.51/1.26 ((~($sum(J!14, $product(-1, tb2t(t2tb(J!14)))) = 0)) | $lesseq($sum(J!14, $product(-1, tb2t(t2tb(J!14)))), 0)),
% 1.51/1.26 inference(theory_lemma,[status(thm)],[])).
% 1.51/1.26 tff(213,plain,
% 1.51/1.26 ($lesseq($sum(J!14, $product(-1, tb2t(t2tb(J!14)))), 0)),
% 1.51/1.26 inference(unit_resolution,[status(thm)],[212, 211])).
% 1.51/1.26 tff(214,plain,
% 1.51/1.26 ($false),
% 1.51/1.26 inference(theory_lemma,[status(thm)],[213, 42, 209])).
% 1.51/1.26 tff(215,plain,(~$greatereq($sum(tb2t(t2tb($sum(-1, J!14))), $product(-1, tb2t(t2tb(J!14)))), 0)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.26 tff(216,plain,
% 1.51/1.26 ((~(tb2t(t2tb($sum(-1, J!14))) = tb2t(t2tb(J!14)))) | $greatereq($sum(tb2t(t2tb($sum(-1, J!14))), $product(-1, tb2t(t2tb(J!14)))), 0)),
% 1.51/1.26 inference(theory_lemma,[status(thm)],[])).
% 1.51/1.26 tff(217,plain,
% 1.51/1.26 (~(tb2t(t2tb($sum(-1, J!14))) = tb2t(t2tb(J!14)))),
% 1.51/1.26 inference(unit_resolution,[status(thm)],[216, 215])).
% 1.51/1.26 tff(218,plain,
% 1.51/1.26 ($false),
% 1.51/1.26 inference(unit_resolution,[status(thm)],[217, 208])).
% 1.51/1.26 tff(219,plain,(~(t2tb(J!14) = t2tb($sum(-1, J!14)))), inference(lemma,lemma(discharge,[]))).
% 1.51/1.26 tff(220,plain,
% 1.51/1.26 (^[X: $int] : refl(sort1(int, t2tb(X)) <=> sort1(int, t2tb(X)))),
% 1.51/1.26 inference(bind,[status(th)],[])).
% 1.51/1.26 tff(221,plain,
% 1.51/1.26 (![X: $int] : sort1(int, t2tb(X)) <=> ![X: $int] : sort1(int, t2tb(X))),
% 1.51/1.26 inference(quant_intro,[status(thm)],[220])).
% 1.51/1.26 tff(222,plain,
% 1.51/1.26 (![X: $int] : sort1(int, t2tb(X)) <=> ![X: $int] : sort1(int, t2tb(X))),
% 1.51/1.26 inference(rewrite,[status(thm)],[])).
% 1.51/1.26 tff(223,axiom,(![X: $int] : sort1(int, t2tb(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2tb_sort3')).
% 1.51/1.26 tff(224,plain,
% 1.51/1.26 (![X: $int] : sort1(int, t2tb(X))),
% 1.51/1.26 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.51/1.26 tff(225,plain,(
% 1.51/1.26 ![X: $int] : sort1(int, t2tb(X))),
% 1.51/1.26 inference(skolemize,[status(sab)],[224])).
% 1.51/1.26 tff(226,plain,
% 1.51/1.26 (![X: $int] : sort1(int, t2tb(X))),
% 1.51/1.26 inference(modus_ponens,[status(thm)],[225, 221])).
% 1.51/1.26 tff(227,plain,
% 1.51/1.26 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb(J!14))),
% 1.51/1.26 inference(quant_inst,[status(thm)],[])).
% 1.51/1.26 tff(228,plain,
% 1.51/1.26 (sort1(int, t2tb(J!14))),
% 1.51/1.26 inference(unit_resolution,[status(thm)],[227, 226])).
% 1.51/1.26 tff(229,plain,
% 1.51/1.26 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb($sum(-1, J!14)))),
% 1.51/1.26 inference(quant_inst,[status(thm)],[])).
% 1.51/1.26 tff(230,plain,
% 1.51/1.26 (sort1(int, t2tb($sum(-1, J!14)))),
% 1.51/1.26 inference(unit_resolution,[status(thm)],[229, 226])).
% 1.51/1.26 tff(231,plain,
% 1.51/1.26 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : rewrite(((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))),
% 1.51/1.26 inference(bind,[status(th)],[])).
% 1.51/1.26 tff(232,plain,
% 1.51/1.26 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))),
% 1.51/1.26 inference(quant_intro,[status(thm)],[231])).
% 1.51/1.26 tff(233,plain,
% 1.51/1.26 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : refl(((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))))),
% 1.51/1.26 inference(bind,[status(th)],[])).
% 1.51/1.26 tff(234,plain,
% 1.51/1.26 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 1.51/1.26 inference(quant_intro,[status(thm)],[233])).
% 1.51/1.26 tff(235,plain,
% 1.51/1.26 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : rewrite(((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))))),
% 1.51/1.26 inference(bind,[status(th)],[])).
% 1.51/1.26 tff(236,plain,
% 1.51/1.26 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 1.51/1.26 inference(quant_intro,[status(thm)],[235])).
% 1.51/1.26 tff(237,plain,
% 1.51/1.26 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 1.51/1.26 inference(transitivity,[status(thm)],[236, 234])).
% 1.51/1.26 tff(238,plain,
% 1.51/1.26 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 1.51/1.26 inference(rewrite,[status(thm)],[])).
% 1.51/1.26 tff(239,plain,
% 1.51/1.26 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[B1: uni] : rewrite(((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) <=> ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), (![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) <=> ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), ((sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> (sort1(A, A2) => ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))), rewrite((sort1(A, A2) => ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), ((sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))), ((sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> (sort1(A, A1) => ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))))), rewrite((sort1(A, A1) => ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))), ((sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))))),
% 1.51/1.26 inference(bind,[status(th)],[])).
% 1.51/1.26 tff(240,plain,
% 1.51/1.26 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 1.51/1.26 inference(quant_intro,[status(thm)],[239])).
% 1.51/1.26 tff(241,axiom,(![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','select_neq')).
% 1.51/1.26 tff(242,plain,
% 1.51/1.26 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 1.51/1.26 inference(modus_ponens,[status(thm)],[241, 240])).
% 1.51/1.26 tff(243,plain,
% 1.51/1.26 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 1.51/1.26 inference(modus_ponens,[status(thm)],[242, 238])).
% 1.51/1.26 tff(244,plain,(
% 1.51/1.26 ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 1.51/1.26 inference(skolemize,[status(sab)],[243])).
% 1.51/1.26 tff(245,plain,
% 1.51/1.26 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 1.51/1.26 inference(modus_ponens,[status(thm)],[244, 237])).
% 1.51/1.26 tff(246,plain,
% 1.51/1.26 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))),
% 1.51/1.26 inference(modus_ponens,[status(thm)],[245, 232])).
% 1.51/1.26 tff(247,plain,
% 1.51/1.26 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb($sum(-1, J!14)))) | (~sort1(int, t2tb(J!14))) | ![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort1(int, t2tb($sum(-1, J!14)))) | (~sort1(int, t2tb(J!14))) | ![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))),
% 1.51/1.26 inference(rewrite,[status(thm)],[])).
% 1.51/1.26 tff(248,plain,
% 1.51/1.26 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb($sum(-1, J!14)))) | (~sort1(int, t2tb(J!14))) | ![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))),
% 1.51/1.26 inference(quant_inst,[status(thm)],[])).
% 1.51/1.26 tff(249,plain,
% 1.51/1.26 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort1(int, t2tb($sum(-1, J!14)))) | (~sort1(int, t2tb(J!14))) | ![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.51/1.26 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.51/1.26 tff(250,plain,
% 1.51/1.26 (![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.51/1.26 inference(unit_resolution,[status(thm)],[249, 246, 230, 228])).
% 1.51/1.26 tff(251,plain,
% 1.51/1.26 (((~![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) <=> ((~![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | (t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.51/1.26 inference(rewrite,[status(thm)],[])).
% 1.51/1.26 tff(252,plain,
% 1.51/1.26 ((~![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.51/1.26 inference(quant_inst,[status(thm)],[])).
% 1.51/1.26 tff(253,plain,
% 1.51/1.26 ((~![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | (t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.51/1.26 inference(modus_ponens,[status(thm)],[252, 251])).
% 1.51/1.26 tff(254,plain,
% 1.51/1.26 ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.51/1.26 inference(unit_resolution,[status(thm)],[253, 250])).
% 1.51/1.26 tff(255,plain,
% 1.51/1.26 (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[254, 219])).
% 1.55/1.26 tff(256,plain,
% 1.55/1.26 (get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14)))),
% 1.55/1.26 inference(symmetry,[status(thm)],[255])).
% 1.55/1.26 tff(257,plain,
% 1.55/1.26 (get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14))),
% 1.55/1.26 inference(transitivity,[status(thm)],[256, 205])).
% 1.55/1.26 tff(258,plain,
% 1.55/1.26 (tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) = tb2t4(get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))),
% 1.55/1.26 inference(monotonicity,[status(thm)],[257])).
% 1.55/1.26 tff(259,plain,
% 1.55/1.26 (tb2t4(get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14))) = tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.55/1.26 inference(symmetry,[status(thm)],[258])).
% 1.55/1.26 tff(260,assumption,(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), introduced(assumption)).
% 1.55/1.26 tff(261,plain,
% 1.55/1.26 ((~![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))) | sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.55/1.26 inference(quant_inst,[status(thm)],[])).
% 1.55/1.26 tff(262,plain,
% 1.55/1.26 (sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[261, 153])).
% 1.55/1.26 tff(263,plain,
% 1.55/1.26 (^[J: uni] : refl(((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J)) <=> ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J)))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(264,plain,
% 1.55/1.26 (![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J)) <=> ![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[263])).
% 1.55/1.26 tff(265,plain,
% 1.55/1.26 (![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J)) <=> ![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(266,plain,
% 1.55/1.26 (^[J: uni] : rewrite((sort1(map(int, elt), J) => (t2tb3(tb2t3(J)) = J)) <=> ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J)))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(267,plain,
% 1.55/1.26 (![J: uni] : (sort1(map(int, elt), J) => (t2tb3(tb2t3(J)) = J)) <=> ![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[266])).
% 1.55/1.26 tff(268,axiom,(![J: uni] : (sort1(map(int, elt), J) => (t2tb3(tb2t3(J)) = J))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR3')).
% 1.55/1.26 tff(269,plain,
% 1.55/1.26 (![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.55/1.26 tff(270,plain,
% 1.55/1.26 (![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[269, 265])).
% 1.55/1.26 tff(271,plain,(
% 1.55/1.26 ![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 1.55/1.26 inference(skolemize,[status(sab)],[270])).
% 1.55/1.26 tff(272,plain,
% 1.55/1.26 (![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[271, 264])).
% 1.55/1.26 tff(273,plain,
% 1.55/1.26 (((~![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))) | ((~sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | (t2tb3(tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) = set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))) <=> ((~![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))) | (~sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | (t2tb3(tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) = set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(274,plain,
% 1.55/1.27 ((~![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))) | ((~sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | (t2tb3(tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) = set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(275,plain,
% 1.55/1.27 ((~![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))) | (~sort1(map(int, elt), set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | (t2tb3(tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) = set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[274, 273])).
% 1.55/1.27 tff(276,plain,
% 1.55/1.27 (t2tb3(tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) = set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[275, 272, 262])).
% 1.55/1.27 tff(277,plain,
% 1.55/1.27 (A4!15 = tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.55/1.27 inference(and_elim,[status(thm)],[96])).
% 1.55/1.27 tff(278,plain,
% 1.55/1.27 (t2tb3(A4!15) = t2tb3(tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[277])).
% 1.55/1.27 tff(279,plain,
% 1.55/1.27 (t2tb3(A4!15) = set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.55/1.27 inference(transitivity,[status(thm)],[278, 276])).
% 1.55/1.27 tff(280,plain,
% 1.55/1.27 (get(elt, int, t2tb3(A4!15), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[279])).
% 1.55/1.27 tff(281,plain,
% 1.55/1.27 (get(elt, int, t2tb3(A4!15), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14))),
% 1.55/1.27 inference(transitivity,[status(thm)],[280, 260, 256, 205])).
% 1.55/1.27 tff(282,plain,
% 1.55/1.27 (tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))) = tb2t4(get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[281])).
% 1.55/1.27 tff(283,plain,
% 1.55/1.27 (tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))) = tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.55/1.27 inference(transitivity,[status(thm)],[282, 259])).
% 1.55/1.27 tff(284,plain,
% 1.55/1.27 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))) <=> le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[283])).
% 1.55/1.27 tff(285,plain,
% 1.55/1.27 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) <=> le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))),
% 1.55/1.27 inference(symmetry,[status(thm)],[284])).
% 1.55/1.27 tff(286,plain,
% 1.55/1.27 (~le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))),
% 1.55/1.27 inference(and_elim,[status(thm)],[96])).
% 1.55/1.27 tff(287,plain,
% 1.55/1.27 (^[X: elt1, Y: elt1] : refl((le1(Y, X) | le1(X, Y)) <=> (le1(Y, X) | le1(X, Y)))),
% 1.55/1.27 inference(bind,[status(th)],[])).
% 1.55/1.27 tff(288,plain,
% 1.55/1.27 (![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y)) <=> ![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y))),
% 1.55/1.27 inference(quant_intro,[status(thm)],[287])).
% 1.55/1.27 tff(289,plain,
% 1.55/1.27 (![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y)) <=> ![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(290,plain,
% 1.55/1.27 (^[X: elt1, Y: elt1] : rewrite(((~le1(X, Y)) => le1(Y, X)) <=> (le1(Y, X) | le1(X, Y)))),
% 1.55/1.27 inference(bind,[status(th)],[])).
% 1.55/1.27 tff(291,plain,
% 1.55/1.27 (![X: elt1, Y: elt1] : ((~le1(X, Y)) => le1(Y, X)) <=> ![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y))),
% 1.55/1.27 inference(quant_intro,[status(thm)],[290])).
% 1.55/1.27 tff(292,axiom,(![X: elt1, Y: elt1] : ((~le1(X, Y)) => le1(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','le_asym')).
% 1.55/1.27 tff(293,plain,
% 1.55/1.27 (![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[292, 291])).
% 1.55/1.27 tff(294,plain,
% 1.55/1.27 (![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[293, 289])).
% 1.55/1.27 tff(295,plain,(
% 1.55/1.27 ![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y))),
% 1.55/1.27 inference(skolemize,[status(sab)],[294])).
% 1.55/1.27 tff(296,plain,
% 1.55/1.27 (![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[295, 288])).
% 1.55/1.27 tff(297,plain,
% 1.55/1.27 (((~![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y))) | (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11)))))) <=> ((~![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11)))))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(298,plain,
% 1.55/1.27 ((~![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y))) | (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11)))))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(299,plain,
% 1.55/1.27 ((~![X: elt1, Y: elt1] : (le1(Y, X) | le1(X, Y))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) | le1(tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.55/1.27 tff(300,plain,
% 1.55/1.27 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[299, 296, 286])).
% 1.55/1.27 tff(301,plain,
% 1.55/1.27 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[300, 285])).
% 1.55/1.27 tff(302,plain,
% 1.55/1.27 (~le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))),
% 1.55/1.27 inference(or_elim,[status(thm)],[100])).
% 1.55/1.27 tff(303,plain,
% 1.55/1.27 ($false),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[302, 301])).
% 1.55/1.27 tff(304,plain,(~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.27 tff(305,plain,
% 1.55/1.27 (^[A: ty, B: ty, X: uni, X1: uni] : refl(sort1(B, get(B, A, X, X1)) <=> sort1(B, get(B, A, X, X1)))),
% 1.55/1.27 inference(bind,[status(th)],[])).
% 1.55/1.27 tff(306,plain,
% 1.55/1.27 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1)) <=> ![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 1.55/1.27 inference(quant_intro,[status(thm)],[305])).
% 1.55/1.27 tff(307,plain,
% 1.55/1.27 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1)) <=> ![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(308,axiom,(![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','get_sort4')).
% 1.55/1.27 tff(309,plain,
% 1.55/1.27 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[308, 307])).
% 1.55/1.27 tff(310,plain,(
% 1.55/1.27 ![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 1.55/1.27 inference(skolemize,[status(sab)],[309])).
% 1.55/1.27 tff(311,plain,
% 1.55/1.27 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[310, 306])).
% 1.55/1.27 tff(312,plain,
% 1.55/1.27 ((~![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))) | sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(313,plain,
% 1.55/1.27 (sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[312, 311])).
% 1.55/1.27 tff(314,plain,
% 1.55/1.27 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : refl(((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))))),
% 1.55/1.27 inference(bind,[status(th)],[])).
% 1.55/1.27 tff(315,plain,
% 1.55/1.27 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.55/1.27 inference(quant_intro,[status(thm)],[314])).
% 1.55/1.27 tff(316,plain,
% 1.55/1.27 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(317,plain,
% 1.55/1.27 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : trans(monotonicity(rewrite(((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)) <=> ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))), ((sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> (sort1(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))))), rewrite((sort1(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))), ((sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))))),
% 1.55/1.27 inference(bind,[status(th)],[])).
% 1.55/1.27 tff(318,plain,
% 1.55/1.27 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.55/1.27 inference(quant_intro,[status(thm)],[317])).
% 1.55/1.27 tff(319,axiom,(![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','select_eq')).
% 1.55/1.27 tff(320,plain,
% 1.55/1.27 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[319, 318])).
% 1.55/1.27 tff(321,plain,
% 1.55/1.27 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[320, 316])).
% 1.55/1.27 tff(322,plain,(
% 1.55/1.27 ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.55/1.27 inference(skolemize,[status(sab)],[321])).
% 1.55/1.27 tff(323,plain,
% 1.55/1.27 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[322, 315])).
% 1.55/1.27 tff(324,plain,
% 1.55/1.27 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) | (~(t2tb(J!14) = t2tb(K!17))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) | (~(t2tb(J!14) = t2tb(K!17))))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(325,plain,
% 1.55/1.27 (((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) | (~(t2tb(J!14) = t2tb(K!17))) | (~sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) <=> ((~sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) | (~(t2tb(J!14) = t2tb(K!17))))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(326,plain,
% 1.55/1.27 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) | (~(t2tb(J!14) = t2tb(K!17))) | (~sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) | (~(t2tb(J!14) = t2tb(K!17)))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[325])).
% 1.55/1.27 tff(327,plain,
% 1.55/1.27 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) | (~(t2tb(J!14) = t2tb(K!17))) | (~sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) | (~(t2tb(J!14) = t2tb(K!17))))),
% 1.55/1.27 inference(transitivity,[status(thm)],[326, 324])).
% 1.55/1.27 tff(328,plain,
% 1.55/1.27 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) | (~(t2tb(J!14) = t2tb(K!17))) | (~sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(329,plain,
% 1.55/1.27 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(elt, get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) | (~(t2tb(J!14) = t2tb(K!17)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[328, 327])).
% 1.55/1.27 tff(330,plain,
% 1.55/1.27 ((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) | (~(t2tb(J!14) = t2tb(K!17)))),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[329, 323, 313])).
% 1.55/1.27 tff(331,plain,
% 1.55/1.27 (~(t2tb(J!14) = t2tb(K!17))),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[330, 304])).
% 1.55/1.27 tff(332,plain,
% 1.55/1.27 ($false),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[331, 109])).
% 1.55/1.27 tff(333,plain,($lesseq($sum(J!14, $product(-1, K!17)), -1)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.27 tff(334,plain,
% 1.55/1.27 (^[K: $int] : refl((le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1))) <=> (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1))))),
% 1.55/1.27 inference(bind,[status(th)],[])).
% 1.55/1.27 tff(335,plain,
% 1.55/1.27 (![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1))) <=> ![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))),
% 1.55/1.27 inference(quant_intro,[status(thm)],[334])).
% 1.55/1.27 tff(336,plain,
% 1.55/1.27 (^[K: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0)) <=> (~((~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1))))), ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) <=> (~(~((~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1))))))), rewrite((~(~((~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1))))) <=> ((~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))), ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) <=> ((~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1))))), (((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))) <=> (((~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))))), rewrite((((~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))) <=> (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))), (((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))) <=> (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))))),
% 1.55/1.27 inference(bind,[status(th)],[])).
% 1.55/1.27 tff(337,plain,
% 1.55/1.27 (![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K))))) <=> ![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))),
% 1.55/1.27 inference(quant_intro,[status(thm)],[336])).
% 1.55/1.27 tff(338,plain,
% 1.55/1.27 (![K: $int] : ((~($greatereq($sum(K, $product(-1, J!14)), 1) & $lesseq($sum(K, $product(-1, I!11)), 0))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))))),
% 1.55/1.27 inference(and_elim,[status(thm)],[96])).
% 1.55/1.27 tff(339,plain,
% 1.55/1.27 (![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[338, 337])).
% 1.55/1.27 tff(340,plain,
% 1.55/1.27 (![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[339, 335])).
% 1.55/1.27 tff(341,plain,
% 1.55/1.27 ($greatereq($sum(I!11, $product(-1, K!17)), 0)),
% 1.55/1.27 inference(and_elim,[status(thm)],[101])).
% 1.55/1.27 tff(342,plain,
% 1.55/1.27 (((~![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))) | (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$greatereq($sum(I!11, $product(-1, K!17)), 0)) | (~$lesseq($sum(J!14, $product(-1, K!17)), -1)))) <=> ((~![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$greatereq($sum(I!11, $product(-1, K!17)), 0)) | (~$lesseq($sum(J!14, $product(-1, K!17)), -1)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(343,plain,
% 1.55/1.27 ((le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$greatereq($sum(I!11, $product(-1, K!17)), 0)) | (~$lesseq($sum(J!14, $product(-1, K!17)), -1))) <=> (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$greatereq($sum(I!11, $product(-1, K!17)), 0)) | (~$lesseq($sum(J!14, $product(-1, K!17)), -1)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(344,plain,
% 1.55/1.27 ((~$greatereq($sum(K!17, $product(-1, J!14)), 1)) <=> (~$lesseq($sum(J!14, $product(-1, K!17)), -1))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(345,plain,
% 1.55/1.27 ((~$lesseq($sum(K!17, $product(-1, I!11)), 0)) <=> (~$greatereq($sum(I!11, $product(-1, K!17)), 0))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(346,plain,
% 1.55/1.27 ((le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$lesseq($sum(K!17, $product(-1, I!11)), 0)) | (~$greatereq($sum(K!17, $product(-1, J!14)), 1))) <=> (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$greatereq($sum(I!11, $product(-1, K!17)), 0)) | (~$lesseq($sum(J!14, $product(-1, K!17)), -1)))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[345, 344])).
% 1.55/1.27 tff(347,plain,
% 1.55/1.27 ((le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$lesseq($sum(K!17, $product(-1, I!11)), 0)) | (~$greatereq($sum(K!17, $product(-1, J!14)), 1))) <=> (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$greatereq($sum(I!11, $product(-1, K!17)), 0)) | (~$lesseq($sum(J!14, $product(-1, K!17)), -1)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[346, 343])).
% 1.55/1.27 tff(348,plain,
% 1.55/1.27 (((~![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))) | (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$lesseq($sum(K!17, $product(-1, I!11)), 0)) | (~$greatereq($sum(K!17, $product(-1, J!14)), 1)))) <=> ((~![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))) | (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$greatereq($sum(I!11, $product(-1, K!17)), 0)) | (~$lesseq($sum(J!14, $product(-1, K!17)), -1))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[347])).
% 1.55/1.28 tff(349,plain,
% 1.55/1.28 (((~![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))) | (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$lesseq($sum(K!17, $product(-1, I!11)), 0)) | (~$greatereq($sum(K!17, $product(-1, J!14)), 1)))) <=> ((~![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$greatereq($sum(I!11, $product(-1, K!17)), 0)) | (~$lesseq($sum(J!14, $product(-1, K!17)), -1)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[348, 342])).
% 1.55/1.28 tff(350,plain,
% 1.55/1.28 ((~![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))) | (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$lesseq($sum(K!17, $product(-1, I!11)), 0)) | (~$greatereq($sum(K!17, $product(-1, J!14)), 1)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(351,plain,
% 1.55/1.28 ((~![K: $int] : (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K)))) | (~$lesseq($sum(K, $product(-1, I!11)), 0)) | (~$greatereq($sum(K, $product(-1, J!14)), 1)))) | le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$greatereq($sum(I!11, $product(-1, K!17)), 0)) | (~$lesseq($sum(J!14, $product(-1, K!17)), -1))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[350, 349])).
% 1.55/1.28 tff(352,plain,
% 1.55/1.28 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~$lesseq($sum(J!14, $product(-1, K!17)), -1))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[351, 341, 340])).
% 1.55/1.28 tff(353,plain,
% 1.55/1.28 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17))))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[352, 333])).
% 1.55/1.28 tff(354,plain,
% 1.55/1.28 (t2tb3(tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) = t2tb3(A4!15)),
% 1.55/1.28 inference(symmetry,[status(thm)],[278])).
% 1.55/1.28 tff(355,plain,
% 1.55/1.28 (set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) = t2tb3(tb2t3(set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))))),
% 1.55/1.28 inference(symmetry,[status(thm)],[276])).
% 1.55/1.28 tff(356,plain,
% 1.55/1.28 (set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) = t2tb3(A4!15)),
% 1.55/1.28 inference(transitivity,[status(thm)],[355, 354])).
% 1.55/1.28 tff(357,plain,
% 1.55/1.28 (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A4!15), t2tb(K!17))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[356])).
% 1.55/1.28 tff(358,plain,
% 1.55/1.28 (get(elt, int, t2tb3(A4!15), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))),
% 1.55/1.28 inference(symmetry,[status(thm)],[357])).
% 1.55/1.28 tff(359,assumption,(le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17))))), introduced(assumption)).
% 1.55/1.28 tff(360,assumption,(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))), introduced(assumption)).
% 1.55/1.28 tff(361,assumption,(~(t2tb(J!14) = t2tb($sum(-1, J!14)))), introduced(assumption)).
% 1.55/1.28 tff(362,plain,
% 1.55/1.28 (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[254, 361])).
% 1.55/1.28 tff(363,assumption,(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), introduced(assumption)).
% 1.55/1.28 tff(364,plain,
% 1.55/1.28 (get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14)))),
% 1.55/1.28 inference(symmetry,[status(thm)],[363])).
% 1.55/1.28 tff(365,plain,
% 1.55/1.28 (get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14))),
% 1.55/1.28 inference(transitivity,[status(thm)],[364, 205])).
% 1.55/1.28 tff(366,plain,
% 1.55/1.28 (tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))) = tb2t4(get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[365])).
% 1.55/1.28 tff(367,plain,
% 1.55/1.28 (tb2t4(get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14))) = tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.55/1.28 inference(symmetry,[status(thm)],[366])).
% 1.55/1.28 tff(368,assumption,(get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))), introduced(assumption)).
% 1.55/1.28 tff(369,plain,
% 1.55/1.28 (set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))) = set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[356])).
% 1.55/1.28 tff(370,plain,
% 1.55/1.28 (set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))) = set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11)))),
% 1.55/1.28 inference(symmetry,[status(thm)],[369])).
% 1.55/1.28 tff(371,plain,
% 1.55/1.28 (get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[370])).
% 1.55/1.28 tff(372,assumption,(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17))), introduced(assumption)).
% 1.55/1.28 tff(373,plain,
% 1.55/1.28 (get(elt, int, t2tb3(A3!13), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))),
% 1.55/1.28 inference(symmetry,[status(thm)],[372])).
% 1.55/1.28 tff(374,plain,
% 1.55/1.28 (get(elt, int, t2tb3(A3!13), t2tb(K!17)) = get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))),
% 1.55/1.28 inference(transitivity,[status(thm)],[373, 360, 371])).
% 1.55/1.28 tff(375,plain,
% 1.55/1.28 (tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17))) = tb2t4(get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[374])).
% 1.55/1.28 tff(376,plain,
% 1.55/1.28 (tb2t4(get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) = tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))),
% 1.55/1.28 inference(symmetry,[status(thm)],[375])).
% 1.55/1.28 tff(377,plain,
% 1.55/1.28 (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))),
% 1.55/1.28 inference(symmetry,[status(thm)],[368])).
% 1.55/1.28 tff(378,plain,
% 1.55/1.28 (get(elt, int, t2tb3(A4!15), t2tb(K!17)) = get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))),
% 1.55/1.28 inference(transitivity,[status(thm)],[280, 377])).
% 1.55/1.28 tff(379,plain,
% 1.55/1.28 (tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))) = tb2t4(get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[378])).
% 1.55/1.28 tff(380,plain,
% 1.55/1.28 (tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))) = tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[379, 376])).
% 1.55/1.28 tff(381,plain,
% 1.55/1.28 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))) <=> le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[380])).
% 1.55/1.28 tff(382,plain,
% 1.55/1.28 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))) <=> le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))),
% 1.55/1.28 inference(symmetry,[status(thm)],[381])).
% 1.55/1.28 tff(383,plain,
% 1.55/1.28 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[359, 382])).
% 1.55/1.28 tff(384,plain,
% 1.55/1.28 ($false),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[302, 383])).
% 1.55/1.28 tff(385,plain,((~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17)))) | (~le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17))))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)))) | (~(get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.28 tff(386,plain,
% 1.55/1.28 (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17)))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[385, 368, 360, 359])).
% 1.55/1.28 tff(387,plain,
% 1.55/1.28 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb(K!17))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(388,plain,
% 1.55/1.28 (sort1(int, t2tb(K!17))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[387, 226])).
% 1.55/1.28 tff(389,plain,
% 1.55/1.28 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb(K!17))) | (~sort1(int, t2tb(J!14))) | ![B1: uni] : ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17)))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort1(int, t2tb(K!17))) | (~sort1(int, t2tb(J!14))) | ![B1: uni] : ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17)))))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(390,plain,
% 1.55/1.28 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb(K!17))) | (~sort1(int, t2tb(J!14))) | ![B1: uni] : ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17)))))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(391,plain,
% 1.55/1.28 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort1(int, t2tb(K!17))) | (~sort1(int, t2tb(J!14))) | ![B1: uni] : ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17))))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[390, 389])).
% 1.55/1.28 tff(392,plain,
% 1.55/1.28 (![B1: uni] : ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17))))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[391, 246, 388, 228])).
% 1.55/1.28 tff(393,plain,
% 1.55/1.28 (((~![B1: uni] : ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17))))) | ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17))))) <=> ((~![B1: uni] : ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17))))) | (t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17))))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(394,plain,
% 1.55/1.28 ((~![B1: uni] : ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17))))) | ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17))))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(395,plain,
% 1.55/1.28 ((~![B1: uni] : ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17))))) | (t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[394, 393])).
% 1.55/1.28 tff(396,plain,
% 1.55/1.28 ((t2tb(J!14) = t2tb(K!17)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb(K!17)))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[395, 392])).
% 1.55/1.28 tff(397,plain,
% 1.55/1.28 (t2tb(J!14) = t2tb(K!17)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[396, 386])).
% 1.55/1.28 tff(398,plain,
% 1.55/1.28 (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[330, 397])).
% 1.55/1.28 tff(399,plain,
% 1.55/1.28 (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14))),
% 1.55/1.28 inference(transitivity,[status(thm)],[368, 398, 364, 205])).
% 1.55/1.28 tff(400,plain,
% 1.55/1.28 (tb2t4(get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) = tb2t4(get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[399])).
% 1.55/1.28 tff(401,plain,
% 1.55/1.28 (tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))) = tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.55/1.28 inference(transitivity,[status(thm)],[379, 400, 367])).
% 1.55/1.28 tff(402,plain,
% 1.55/1.28 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17)))) <=> le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[401])).
% 1.55/1.28 tff(403,plain,
% 1.55/1.28 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) <=> le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))),
% 1.55/1.28 inference(symmetry,[status(thm)],[402])).
% 1.55/1.28 tff(404,plain,
% 1.55/1.28 (le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A4!15), t2tb(K!17))))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[300, 403])).
% 1.55/1.28 tff(405,plain,
% 1.55/1.28 ($false),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[302, 404])).
% 1.55/1.28 tff(406,plain,((~(get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)))) | (~le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.28 tff(407,plain,
% 1.55/1.28 (~(get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[406, 362, 360, 359])).
% 1.55/1.28 tff(408,plain,
% 1.55/1.28 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb(K!17))) | (~sort1(int, t2tb($sum(-1, J!14)))) | ![B1: uni] : ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), B1), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort1(int, t2tb(K!17))) | (~sort1(int, t2tb($sum(-1, J!14)))) | ![B1: uni] : ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), B1), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)))))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(409,plain,
% 1.55/1.28 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb(K!17))) | (~sort1(int, t2tb($sum(-1, J!14)))) | ![B1: uni] : ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), B1), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)))))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(410,plain,
% 1.55/1.29 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort1(int, t2tb(K!17))) | (~sort1(int, t2tb($sum(-1, J!14)))) | ![B1: uni] : ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), B1), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[409, 408])).
% 1.55/1.29 tff(411,plain,
% 1.55/1.29 (![B1: uni] : ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), B1), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))))),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[410, 246, 230, 388])).
% 1.55/1.29 tff(412,plain,
% 1.55/1.29 (((~![B1: uni] : ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), B1), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))))) | ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))))) <=> ((~![B1: uni] : ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), B1), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))))) | (t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(413,plain,
% 1.55/1.29 ((~![B1: uni] : ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), B1), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))))) | ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(414,plain,
% 1.55/1.29 ((~![B1: uni] : ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), B1), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))))) | (t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[413, 412])).
% 1.55/1.29 tff(415,plain,
% 1.55/1.29 ((t2tb($sum(-1, J!14)) = t2tb(K!17)) | (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17)))),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[414, 411])).
% 1.55/1.29 tff(416,plain,
% 1.55/1.29 (t2tb($sum(-1, J!14)) = t2tb(K!17)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[415, 407])).
% 1.55/1.29 tff(417,plain,
% 1.55/1.29 (t2tb(K!17) = t2tb($sum(-1, J!14))),
% 1.55/1.29 inference(symmetry,[status(thm)],[416])).
% 1.55/1.29 tff(418,plain,
% 1.55/1.29 (get(elt, int, t2tb3(A4!15), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[279, 417])).
% 1.55/1.29 tff(419,plain,
% 1.55/1.29 (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A4!15), t2tb(K!17))),
% 1.55/1.29 inference(symmetry,[status(thm)],[418])).
% 1.55/1.29 tff(420,plain,
% 1.55/1.29 (((~![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) <=> ((~![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | (t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(421,plain,
% 1.55/1.29 ((~![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(422,plain,
% 1.55/1.29 ((~![B1: uni] : ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), B1), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))))) | (t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[421, 420])).
% 1.55/1.29 tff(423,plain,
% 1.55/1.29 ((t2tb(J!14) = t2tb($sum(-1, J!14))) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))))),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[422, 250])).
% 1.55/1.29 tff(424,plain,
% 1.55/1.29 (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14))) = get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[423, 361])).
% 1.55/1.29 tff(425,plain,
% 1.55/1.29 (get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)))),
% 1.55/1.29 inference(symmetry,[status(thm)],[424])).
% 1.55/1.29 tff(426,plain,
% 1.55/1.29 (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[416])).
% 1.55/1.29 tff(427,plain,
% 1.55/1.29 (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14)))),
% 1.55/1.29 inference(symmetry,[status(thm)],[426])).
% 1.55/1.29 tff(428,plain,
% 1.55/1.29 (get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))),
% 1.55/1.29 inference(symmetry,[status(thm)],[360])).
% 1.55/1.29 tff(429,plain,
% 1.55/1.29 (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))),
% 1.55/1.29 inference(symmetry,[status(thm)],[371])).
% 1.55/1.29 tff(430,plain,
% 1.55/1.29 (get(elt, int, set(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A3!13), t2tb($sum(-1, J!14)))), t2tb(K!17))),
% 1.55/1.29 inference(transitivity,[status(thm)],[429, 428, 427, 362, 425, 419, 358])).
% 1.55/1.29 tff(431,plain,
% 1.55/1.29 ($false),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[407, 430])).
% 1.55/1.29 tff(432,plain,((t2tb(J!14) = t2tb($sum(-1, J!14))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)))) | (~le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.29 tff(433,plain,
% 1.55/1.29 ((~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)))) | (~le1(tb2t4(get(elt, int, t2tb3(A2!12), t2tb(I!11))), tb2t4(get(elt, int, t2tb3(A3!13), t2tb(K!17)))))),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[432, 219])).
% 1.55/1.29 tff(434,plain,
% 1.55/1.29 (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)))),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[433, 353])).
% 1.55/1.29 tff(435,plain,
% 1.55/1.29 ((~$greatereq($sum(J!14, $product(-1, K!17)), 0)) | (~$lesseq($sum(J!14, $product(-1, K!17)), -1))),
% 1.55/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.55/1.29 tff(436,plain,
% 1.55/1.29 (~$greatereq($sum(J!14, $product(-1, K!17)), 0)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[435, 333])).
% 1.55/1.29 tff(437,plain,
% 1.55/1.29 ((~($sum(J!14, $product(-1, K!17)) = 0)) | $greatereq($sum(J!14, $product(-1, K!17)), 0)),
% 1.55/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.55/1.29 tff(438,plain,
% 1.55/1.29 (~($sum(J!14, $product(-1, K!17)) = 0)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[437, 436])).
% 1.55/1.29 tff(439,plain,
% 1.55/1.29 (~$lesseq(J!14, 0)),
% 1.55/1.29 inference(and_elim,[status(thm)],[96])).
% 1.55/1.29 tff(440,assumption,(~$greatereq(tb2t(t2tb(K!17)), 0)), introduced(assumption)).
% 1.55/1.29 tff(441,plain,
% 1.55/1.29 ($false),
% 1.55/1.29 inference(theory_lemma,[status(thm)],[440, 25, 102, 99, 439])).
% 1.55/1.29 tff(442,plain,($greatereq(tb2t(t2tb(K!17)), 0)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.29 tff(443,plain,
% 1.55/1.29 ($greatereq(K!17, 0) | (~$greatereq(tb2t(t2tb(K!17)), 0)) | (~$greatereq($sum(K!17, $product(-1, tb2t(t2tb(K!17)))), 0))),
% 1.55/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.55/1.29 tff(444,plain,
% 1.55/1.29 ($greatereq(K!17, 0)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[443, 27, 442])).
% 1.55/1.29 tff(445,plain,
% 1.55/1.29 (~$lesseq($sum(A!10, $product(-1, I!11)), 0)),
% 1.55/1.29 inference(and_elim,[status(thm)],[96])).
% 1.55/1.29 tff(446,assumption,($lesseq($sum(A!10, $product(-1, tb2t(t2tb(K!17)))), 0)), introduced(assumption)).
% 1.55/1.29 tff(447,plain,
% 1.55/1.29 ($false),
% 1.55/1.29 inference(theory_lemma,[status(thm)],[341, 446, 27, 445])).
% 1.55/1.29 tff(448,plain,(~$lesseq($sum(A!10, $product(-1, tb2t(t2tb(K!17)))), 0)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.29 tff(449,plain,
% 1.55/1.29 (^[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))),
% 1.55/1.29 inference(bind,[status(th)],[])).
% 1.55/1.29 tff(450,plain,
% 1.55/1.29 (![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)),
% 1.55/1.29 inference(quant_intro,[status(thm)],[449])).
% 1.55/1.29 tff(451,plain,
% 1.55/1.29 (^[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)))),
% 1.55/1.29 inference(bind,[status(th)],[])).
% 1.55/1.29 tff(452,plain,
% 1.55/1.29 (![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)),
% 1.55/1.29 inference(quant_intro,[status(thm)],[451])).
% 1.55/1.29 tff(453,plain,
% 1.55/1.29 (^[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))),
% 1.55/1.29 inference(bind,[status(th)],[])).
% 1.55/1.29 tff(454,plain,
% 1.55/1.29 (![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)),
% 1.55/1.29 inference(quant_intro,[status(thm)],[453])).
% 1.55/1.29 tff(455,plain,
% 1.55/1.29 (![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)),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(456,axiom,(![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','length_def1')).
% 1.55/1.29 tff(457,plain,
% 1.55/1.29 (![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[456, 455])).
% 1.55/1.29 tff(458,plain,
% 1.55/1.29 (![A: ty, U: $int, U1: uni] : ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[457, 454])).
% 1.55/1.29 tff(459,plain,
% 1.55/1.29 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[458, 452])).
% 1.55/1.29 tff(460,plain,(
% 1.55/1.29 ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 1.55/1.29 inference(skolemize,[status(sab)],[459])).
% 1.55/1.29 tff(461,plain,
% 1.55/1.29 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[460, 450])).
% 1.55/1.29 tff(462,plain,
% 1.55/1.29 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)) | ($sum(A!10, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))) = 0)),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(463,plain,
% 1.55/1.29 ($sum(A!10, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))) = 0),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[462, 461])).
% 1.55/1.29 tff(464,plain,
% 1.55/1.29 ((~($sum(A!10, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))) = 0)) | $lesseq($sum(A!10, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)),
% 1.55/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.55/1.29 tff(465,plain,
% 1.55/1.29 ($lesseq($sum(A!10, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[464, 463])).
% 1.55/1.29 tff(466,plain,
% 1.55/1.29 ((~$greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)) | (~$lesseq($sum(A!10, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)) | $lesseq($sum(A!10, $product(-1, tb2t(t2tb(K!17)))), 0) | (~$lesseq($sum(K!17, $product(-1, tb2t(t2tb(K!17)))), 0))),
% 1.55/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.55/1.29 tff(467,plain,
% 1.55/1.29 (~$greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[466, 25, 465, 448])).
% 1.55/1.29 tff(468,plain,
% 1.55/1.29 ((~$greatereq($sum(J!14, $product(-1, K!17)), 1)) | (~$lesseq($sum(J1!16, $product(-1, K!17)), -1)) | (~$lesseq($sum(J!14, $product(-1, J1!16)), 1))),
% 1.55/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.55/1.29 tff(469,plain,
% 1.55/1.29 (~$greatereq($sum(J!14, $product(-1, K!17)), 1)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[468, 102, 99])).
% 1.55/1.29 tff(470,plain,
% 1.55/1.29 ((~($sum(J!14, $product(-1, K!17)) = 1)) | $greatereq($sum(J!14, $product(-1, K!17)), 1)),
% 1.55/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.55/1.29 tff(471,plain,
% 1.55/1.29 (~($sum(J!14, $product(-1, K!17)) = 1)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[470, 469])).
% 1.55/1.29 tff(472,plain,
% 1.55/1.29 (((~$greatereq(J!14, 0)) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)))) | (~(get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(J!14)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb($sum(-1, J!14))))) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 1) | $greatereq($sum(J!14, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | (~$greatereq(J!14, 1)) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)))) | ![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))),
% 1.55/1.29 inference(tautology,[status(thm)],[])).
% 1.55/1.29 tff(473,plain,
% 1.55/1.29 (![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[472, 203])).
% 1.55/1.30 tff(474,plain,
% 1.55/1.30 (((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))) | ((~$greatereq(K!17, 0)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K!17)) = 1) | ($sum(J!14, $product(-1, K!17)) = 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))) | (~$greatereq(K!17, 0)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K!17)) = 1) | ($sum(J!14, $product(-1, K!17)) = 0))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(475,plain,
% 1.55/1.30 (((~$greatereq(K!17, 0)) | ($sum(J!14, $product(-1, K!17)) = 1) | ($sum(J!14, $product(-1, K!17)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)) <=> ((~$greatereq(K!17, 0)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K!17)) = 1) | ($sum(J!14, $product(-1, K!17)) = 0))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(476,plain,
% 1.55/1.30 (($sum($product(-1, J!14), K!17) = 0) <=> ($sum(J!14, $product(-1, K!17)) = 0)),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(477,plain,
% 1.55/1.30 ($sum(K!17, $product(-1, J!14)) = $sum($product(-1, J!14), K!17)),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(478,plain,
% 1.55/1.30 (($sum(K!17, $product(-1, J!14)) = 0) <=> ($sum($product(-1, J!14), K!17) = 0)),
% 1.55/1.30 inference(monotonicity,[status(thm)],[477])).
% 1.55/1.30 tff(479,plain,
% 1.55/1.30 (($sum(K!17, $product(-1, J!14)) = 0) <=> ($sum(J!14, $product(-1, K!17)) = 0)),
% 1.55/1.30 inference(transitivity,[status(thm)],[478, 476])).
% 1.55/1.30 tff(480,plain,
% 1.55/1.30 (($sum($product(-1, J!14), K!17) = -1) <=> ($sum(J!14, $product(-1, K!17)) = 1)),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(481,plain,
% 1.55/1.30 (($sum(K!17, $product(-1, J!14)) = -1) <=> ($sum($product(-1, J!14), K!17) = -1)),
% 1.55/1.30 inference(monotonicity,[status(thm)],[477])).
% 1.55/1.30 tff(482,plain,
% 1.55/1.30 (($sum(K!17, $product(-1, J!14)) = -1) <=> ($sum(J!14, $product(-1, K!17)) = 1)),
% 1.55/1.30 inference(transitivity,[status(thm)],[481, 480])).
% 1.55/1.30 tff(483,plain,
% 1.55/1.30 (((~$greatereq(K!17, 0)) | ($sum(K!17, $product(-1, J!14)) = -1) | ($sum(K!17, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)) <=> ((~$greatereq(K!17, 0)) | ($sum(J!14, $product(-1, K!17)) = 1) | ($sum(J!14, $product(-1, K!17)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[482, 479])).
% 1.55/1.30 tff(484,plain,
% 1.55/1.30 (((~$greatereq(K!17, 0)) | ($sum(K!17, $product(-1, J!14)) = -1) | ($sum(K!17, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0)) <=> ((~$greatereq(K!17, 0)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K!17)) = 1) | ($sum(J!14, $product(-1, K!17)) = 0))),
% 1.55/1.30 inference(transitivity,[status(thm)],[483, 475])).
% 1.55/1.30 tff(485,plain,
% 1.55/1.30 (((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))) | ((~$greatereq(K!17, 0)) | ($sum(K!17, $product(-1, J!14)) = -1) | ($sum(K!17, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))) | ((~$greatereq(K!17, 0)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K!17)) = 1) | ($sum(J!14, $product(-1, K!17)) = 0)))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[484])).
% 1.55/1.30 tff(486,plain,
% 1.55/1.30 (((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))) | ((~$greatereq(K!17, 0)) | ($sum(K!17, $product(-1, J!14)) = -1) | ($sum(K!17, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))) | (~$greatereq(K!17, 0)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K!17)) = 1) | ($sum(J!14, $product(-1, K!17)) = 0))),
% 1.55/1.30 inference(transitivity,[status(thm)],[485, 474])).
% 1.55/1.30 tff(487,plain,
% 1.55/1.30 ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))) | ((~$greatereq(K!17, 0)) | ($sum(K!17, $product(-1, J!14)) = -1) | ($sum(K!17, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))),
% 1.55/1.30 inference(quant_inst,[status(thm)],[])).
% 1.55/1.30 tff(488,plain,
% 1.55/1.30 ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!14)) = -1) | ($sum(K, $product(-1, J!14)) = 0) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K))) | $greatereq($sum(K, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0))) | (~$greatereq(K!17, 0)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K!17)) = 1) | ($sum(J!14, $product(-1, K!17)) = 0)),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[487, 486])).
% 1.55/1.31 tff(489,plain,
% 1.55/1.31 ((~$greatereq(K!17, 0)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K!17)) = 1) | ($sum(J!14, $product(-1, K!17)) = 0)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[488, 473])).
% 1.55/1.31 tff(490,plain,
% 1.55/1.31 ((~$greatereq(K!17, 0)) | (get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | $greatereq($sum(K!17, $product(-1, length1(elt, mk_array1(elt, A!10, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))))))), 0) | ($sum(J!14, $product(-1, K!17)) = 0)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[489, 471])).
% 1.55/1.31 tff(491,plain,
% 1.55/1.31 ((get(elt, int, set(elt, int, t2tb3(A3!13), t2tb(J!14), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17)) = get(elt, int, set(elt, int, t2tb3(A4!15), t2tb($sum(-1, J!14)), get(elt, int, t2tb3(A2!12), t2tb(I!11))), t2tb(K!17))) | ($sum(J!14, $product(-1, K!17)) = 0)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[490, 467, 444])).
% 1.55/1.31 tff(492,plain,
% 1.55/1.31 ($false),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[491, 438, 434])).
% 1.55/1.31 % SZS output end Proof
%------------------------------------------------------------------------------