TSTP Solution File: SWW594_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW594_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 20:59:23 EDT 2022
% Result : Theorem 0.50s 0.63s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW594_2 : TPTP v8.1.0. Released v6.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.31 % Computer : n024.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Sun Sep 4 20:15:48 EDT 2022
% 0.12/0.31 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 0.50/0.63 % SZS status Theorem
% 0.50/0.63 % SZS output start Proof
% 0.50/0.63 tff(tptp_fun_J1_26_type, type, (
% 0.50/0.63 tptp_fun_J1_26: $int)).
% 0.50/0.63 tff(f_type, type, (
% 0.50/0.63 f: $int)).
% 0.50/0.63 tff(tb2t_type, type, (
% 0.50/0.63 tb2t: uni > $int)).
% 0.50/0.63 tff(get_type, type, (
% 0.50/0.63 get: ( ty * ty * uni * uni ) > uni)).
% 0.50/0.63 tff(t2tb_type, type, (
% 0.50/0.63 t2tb: $int > uni)).
% 0.50/0.63 tff(t2tb2_type, type, (
% 0.50/0.63 t2tb2: map_int_int > uni)).
% 0.50/0.63 tff(tptp_fun_A3_22_type, type, (
% 0.50/0.63 tptp_fun_A3_22: map_int_int)).
% 0.50/0.63 tff(int_type, type, (
% 0.50/0.63 int: ty)).
% 0.50/0.63 tff(tptp_fun_A2_19_type, type, (
% 0.50/0.63 tptp_fun_A2_19: map_int_int)).
% 0.50/0.63 tff(get1_type, type, (
% 0.50/0.63 get1: ( ty * uni * $int ) > uni)).
% 0.50/0.63 tff(t2tb1_type, type, (
% 0.50/0.63 t2tb1: array_int > uni)).
% 0.50/0.63 tff(tb2t1_type, type, (
% 0.50/0.63 tb2t1: uni > array_int)).
% 0.50/0.63 tff(mk_array_type, type, (
% 0.50/0.63 mk_array: ( ty * $int * uni ) > uni)).
% 0.50/0.63 tff(tptp_fun_A_18_type, type, (
% 0.50/0.63 tptp_fun_A_18: $int)).
% 0.50/0.63 tff(tptp_fun_I1_25_type, type, (
% 0.50/0.63 tptp_fun_I1_25: $int)).
% 0.50/0.63 tff(tptp_fun_M_20_type, type, (
% 0.50/0.63 tptp_fun_M_20: $int)).
% 0.50/0.63 tff(tptp_fun_N_21_type, type, (
% 0.50/0.63 tptp_fun_N_21: $int)).
% 0.50/0.63 tff(tptp_fun_J2_27_type, type, (
% 0.50/0.63 tptp_fun_J2_27: $int)).
% 0.50/0.63 tff(tptp_fun_J_24_type, type, (
% 0.50/0.63 tptp_fun_J_24: $int)).
% 0.50/0.63 tff(usN_type, type, (
% 0.50/0.63 usN: $int)).
% 0.50/0.63 tff(permut_all_type, type, (
% 0.50/0.63 permut_all: ( ty * uni * uni ) > $o)).
% 0.50/0.63 tff(tptp_fun_A1_17_type, type, (
% 0.50/0.63 tptp_fun_A1_17: map_int_int)).
% 0.50/0.63 tff(n_invariant_type, type, (
% 0.50/0.63 n_invariant: ( $int * array_int ) > $o)).
% 0.50/0.63 tff(m_invariant_type, type, (
% 0.50/0.63 m_invariant: ( $int * array_int ) > $o)).
% 0.50/0.63 tff(termination_type, type, (
% 0.50/0.63 termination: ( $int * $int * $int * $int * $int * array_int ) > $o)).
% 0.50/0.63 tff(tptp_fun_I_23_type, type, (
% 0.50/0.63 tptp_fun_I_23: $int)).
% 0.50/0.63 tff(j_invariant_type, type, (
% 0.50/0.63 j_invariant: ( $int * $int * $int * $int * array_int ) > $o)).
% 0.50/0.63 tff(i_invariant_type, type, (
% 0.50/0.63 i_invariant: ( $int * $int * $int * $int * array_int ) > $o)).
% 0.50/0.63 tff(tptp_fun_Q_15_type, type, (
% 0.50/0.63 tptp_fun_Q_15: ( array_int * $int * $int * $int ) > $int)).
% 0.50/0.63 tff(tptp_fun_Q_16_type, type, (
% 0.50/0.63 tptp_fun_Q_16: ( array_int * $int * $int ) > $int)).
% 0.50/0.63 tff(elts_type, type, (
% 0.50/0.63 elts: ( ty * uni ) > uni)).
% 0.50/0.63 tff(sort_type, type, (
% 0.50/0.63 sort: ( ty * uni ) > $o)).
% 0.50/0.63 tff(map_type, type, (
% 0.50/0.63 map: ( ty * ty ) > ty)).
% 0.50/0.63 tff(1,plain,
% 0.50/0.63 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.50/0.63 inference(rewrite,[status(thm)],[])).
% 0.50/0.63 tff(2,plain,
% 0.50/0.63 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.50/0.63 inference(rewrite,[status(thm)],[])).
% 0.50/0.63 tff(3,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR')).
% 0.50/0.63 tff(4,plain,
% 0.50/0.63 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.50/0.63 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.50/0.63 tff(5,plain,(
% 0.50/0.63 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.50/0.63 inference(skolemize,[status(sab)],[4])).
% 0.50/0.63 tff(6,plain,
% 0.50/0.63 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.50/0.63 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.50/0.63 tff(7,plain,
% 0.50/0.63 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(get(int, int, t2tb2(A2!19), t2tb(f)))) = get(int, int, t2tb2(A2!19), t2tb(f)))),
% 0.50/0.63 inference(quant_inst,[status(thm)],[])).
% 0.50/0.63 tff(8,plain,
% 0.50/0.63 (t2tb(tb2t(get(int, int, t2tb2(A2!19), t2tb(f)))) = get(int, int, t2tb2(A2!19), t2tb(f))),
% 0.50/0.63 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.50/0.63 tff(9,plain,
% 0.50/0.63 ((($greatereq(A!18, 0) & ($sum(usN, $product(-1, A!18)) = -1)) & ((~$greatereq($sum(M!20, $product(-1, N!21)), 0)) & $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0)) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0))) <=> ($greatereq(A!18, 0) & ($sum(usN, $product(-1, A!18)) = -1) & (~$greatereq($sum(M!20, $product(-1, N!21)), 0)) & $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0)) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0))),
% 0.62/0.63 inference(rewrite,[status(thm)],[])).
% 0.62/0.63 tff(10,plain,
% 0.62/0.63 (((~$greatereq($sum(M!20, $product(-1, N!21)), 0)) & ($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17)))) & ($greatereq(A!18, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0))) & (m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0))) <=> ((~$greatereq($sum(M!20, $product(-1, N!21)), 0)) & $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0)) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(11,plain,
% 0.62/0.64 ((~(~(m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0)))) <=> (m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(12,plain,
% 0.62/0.64 ((~(~($greatereq(A!18, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0))))) <=> ($greatereq(A!18, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0)))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(13,plain,
% 0.62/0.64 ((($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & (i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))))) <=> ($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(14,plain,
% 0.62/0.65 ((~(~(i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17)))))) <=> (i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(15,plain,
% 0.62/0.65 ((~(~$lesseq($sum(I!23, $product(-1, J!24)), 0))) <=> $lesseq($sum(I!23, $product(-1, J!24)), 0)),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(16,plain,
% 0.62/0.65 ((~$greatereq($sum(J!24, $product(-1, I!23)), 0)) <=> (~$lesseq($sum(I!23, $product(-1, J!24)), 0))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(17,plain,
% 0.62/0.65 ((~(~$greatereq($sum(J!24, $product(-1, I!23)), 0))) <=> (~(~$lesseq($sum(I!23, $product(-1, J!24)), 0)))),
% 0.62/0.65 inference(monotonicity,[status(thm)],[16])).
% 0.62/0.65 tff(18,plain,
% 0.62/0.65 ((~(~$greatereq($sum(J!24, $product(-1, I!23)), 0))) <=> $lesseq($sum(I!23, $product(-1, J!24)), 0)),
% 0.62/0.65 inference(transitivity,[status(thm)],[17, 15])).
% 0.62/0.65 tff(19,plain,
% 0.62/0.65 (($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) & ($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0))) & (i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) <=> ($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(20,plain,
% 0.62/0.65 ((~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))))) <=> (i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(21,plain,
% 0.62/0.65 ((~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $lesseq($sum(I1!25, $product(-1, N!21)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) <=> (~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(22,plain,
% 0.62/0.65 ((~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $lesseq($sum(I1!25, $product(-1, N!21)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))))) <=> (~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[21])).
% 0.62/0.66 tff(23,plain,
% 0.62/0.66 ((~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $lesseq($sum(I1!25, $product(-1, N!21)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))))) <=> (i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))),
% 0.62/0.66 inference(transitivity,[status(thm)],[22, 20])).
% 0.62/0.66 tff(24,plain,
% 0.62/0.66 ((~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0))))) <=> ($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(25,plain,
% 0.62/0.66 ((~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$greatereq($sum(I1!25, $product(-1, A!18)), 0)))) <=> (~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(26,plain,
% 0.62/0.66 ((~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$greatereq($sum(I1!25, $product(-1, A!18)), 0))))) <=> (~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[25])).
% 0.62/0.66 tff(27,plain,
% 0.62/0.66 ((~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$greatereq($sum(I1!25, $product(-1, A!18)), 0))))) <=> ($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)))),
% 0.62/0.66 inference(transitivity,[status(thm)],[26, 24])).
% 0.62/0.66 tff(28,plain,
% 0.62/0.66 (((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & ($greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0))) & (j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) <=> ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(29,plain,
% 0.62/0.66 ((~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))))) <=> (j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(30,plain,
% 0.62/0.66 ((~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) <=> (~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(31,plain,
% 0.62/0.66 ((~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))))) <=> (~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[30])).
% 0.62/0.66 tff(32,plain,
% 0.62/0.66 ((~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))))) <=> (j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))),
% 0.62/0.66 inference(transitivity,[status(thm)],[31, 29])).
% 0.62/0.66 tff(33,plain,
% 0.62/0.66 ((~(~($greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0))))) <=> ($greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(34,plain,
% 0.62/0.66 ((~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0)))) <=> (~($greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(35,plain,
% 0.62/0.66 ((~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) <=> (~(~($greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[34])).
% 0.62/0.66 tff(36,plain,
% 0.62/0.66 ((~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) <=> ($greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)))),
% 0.62/0.66 inference(transitivity,[status(thm)],[35, 33])).
% 0.62/0.66 tff(37,plain,
% 0.62/0.66 (((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & (~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) & (~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) <=> ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & ($greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0))) & (j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))))),
% 0.62/0.67 inference(monotonicity,[status(thm)],[36, 32])).
% 0.62/0.67 tff(38,plain,
% 0.62/0.67 (((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & (~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) & (~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) <=> ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))),
% 0.62/0.67 inference(transitivity,[status(thm)],[37, 28])).
% 0.62/0.67 tff(39,plain,
% 0.62/0.67 ((~(~$lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0))) <=> $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0)),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(40,plain,
% 0.62/0.67 (((~(~$lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0))) & ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & (~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) & (~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$greatereq($sum(I1!25, $product(-1, A!18)), 0))))) & (~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $lesseq($sum(I1!25, $product(-1, N!21)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) <=> ($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) & ($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0))) & (i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[39, 38, 27, 23])).
% 0.62/0.68 tff(41,plain,
% 0.62/0.68 (((~(~$lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0))) & ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & (~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) & (~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$greatereq($sum(I1!25, $product(-1, A!18)), 0))))) & (~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $lesseq($sum(I1!25, $product(-1, N!21)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) <=> ($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))),
% 0.62/0.68 inference(transitivity,[status(thm)],[40, 19])).
% 0.62/0.68 tff(42,plain,
% 0.62/0.68 ((((~(~$lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0))) & ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & (~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) & (~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$greatereq($sum(I1!25, $product(-1, A!18)), 0))))) & (~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $lesseq($sum(I1!25, $product(-1, N!21)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~$greatereq($sum(J!24, $product(-1, I!23)), 0))) & (~(~(i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))))))) <=> (($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & (i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17)))))),
% 0.67/0.68 inference(monotonicity,[status(thm)],[41, 18, 14])).
% 0.67/0.68 tff(43,plain,
% 0.67/0.68 ((((~(~$lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0))) & ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & (~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) & (~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$greatereq($sum(I1!25, $product(-1, A!18)), 0))))) & (~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $lesseq($sum(I1!25, $product(-1, N!21)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~$greatereq($sum(J!24, $product(-1, I!23)), 0))) & (~(~(i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))))))) <=> ($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))))),
% 0.67/0.69 inference(transitivity,[status(thm)],[42, 13])).
% 0.67/0.69 tff(44,plain,
% 0.67/0.69 ((~$lesseq($sum(N!21, $product(-1, M!20)), 0)) <=> (~$greatereq($sum(M!20, $product(-1, N!21)), 0))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(45,plain,
% 0.67/0.69 (((~$lesseq($sum(N!21, $product(-1, M!20)), 0)) & (((~(~$lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0))) & ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & (~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) & (~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$greatereq($sum(I1!25, $product(-1, A!18)), 0))))) & (~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $lesseq($sum(I1!25, $product(-1, N!21)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~$greatereq($sum(J!24, $product(-1, I!23)), 0))) & (~(~(i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))))))) & (~(~($greatereq(A!18, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0))))) & (~(~(m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0))))) <=> ((~$greatereq($sum(M!20, $product(-1, N!21)), 0)) & ($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17)))) & ($greatereq(A!18, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0))) & (m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0)))),
% 0.67/0.70 inference(monotonicity,[status(thm)],[44, 43, 12, 11])).
% 0.67/0.70 tff(46,plain,
% 0.67/0.70 (((~$lesseq($sum(N!21, $product(-1, M!20)), 0)) & (((~(~$lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0))) & ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & (~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) & (~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$greatereq($sum(I1!25, $product(-1, A!18)), 0))))) & (~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $lesseq($sum(I1!25, $product(-1, N!21)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~$greatereq($sum(J!24, $product(-1, I!23)), 0))) & (~(~(i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))))))) & (~(~($greatereq(A!18, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0))))) & (~(~(m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0))))) <=> ((~$greatereq($sum(M!20, $product(-1, N!21)), 0)) & $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0)) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0))),
% 0.67/0.70 inference(transitivity,[status(thm)],[45, 10])).
% 0.67/0.70 tff(47,plain,
% 0.67/0.70 ((~(~($greatereq(A!18, 0) & ($sum(usN, $product(-1, A!18)) = -1)))) <=> ($greatereq(A!18, 0) & ($sum(usN, $product(-1, A!18)) = -1))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(48,plain,
% 0.67/0.70 (((~(~($greatereq(A!18, 0) & ($sum(usN, $product(-1, A!18)) = -1)))) & ((~$lesseq($sum(N!21, $product(-1, M!20)), 0)) & (((~(~$lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0))) & ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & (~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) & (~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$greatereq($sum(I1!25, $product(-1, A!18)), 0))))) & (~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $lesseq($sum(I1!25, $product(-1, N!21)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~$greatereq($sum(J!24, $product(-1, I!23)), 0))) & (~(~(i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))))))) & (~(~($greatereq(A!18, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0))))) & (~(~(m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0)))))) <=> (($greatereq(A!18, 0) & ($sum(usN, $product(-1, A!18)) = -1)) & ((~$greatereq($sum(M!20, $product(-1, N!21)), 0)) & $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0)) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0)))),
% 0.67/0.71 inference(monotonicity,[status(thm)],[47, 46])).
% 0.67/0.71 tff(49,plain,
% 0.67/0.71 (((~(~($greatereq(A!18, 0) & ($sum(usN, $product(-1, A!18)) = -1)))) & ((~$lesseq($sum(N!21, $product(-1, M!20)), 0)) & (((~(~$lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0))) & ((~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & (~(~($greatereq(J1!26, 0) & (~$greatereq($sum(J1!26, $product(-1, A!18)), 0))))) & (~(~(j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(J1!26, $product(-1, J!24)), 0) & $greatereq($sum(J1!26, $product(-1, M!20)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~($greatereq(A!18, 0) & $greatereq(I1!25, 0) & (~$greatereq($sum(I1!25, $product(-1, A!18)), 0))))) & (~(~(i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $lesseq($sum(I1!25, $product(-1, N!21)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))))) & (~(~$greatereq($sum(J!24, $product(-1, I!23)), 0))) & (~(~(i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))))))) & (~(~($greatereq(A!18, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0))))) & (~(~(m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0)))))) <=> ($greatereq(A!18, 0) & ($sum(usN, $product(-1, A!18)) = -1) & (~$greatereq($sum(M!20, $product(-1, N!21)), 0)) & $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0)) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0))),
% 0.67/0.72 inference(transitivity,[status(thm)],[48, 9])).
% 0.67/0.72 tff(50,plain,
% 0.67/0.72 ((~![A: $int, A1: map_int_int] : ((~($greatereq(A, 0) & ($sum(usN, $product(-1, A)) = -1))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq($sum(N, $product(-1, M)), 0) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(I1))))), 0)) | ![J1: $int] : ($greatereq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(J1))))), 0) | ![J2: $int] : ((~($sum(J1, $product(-1, J2)) = 1)) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($greatereq(J1, 0) & (~$greatereq($sum(J1, $product(-1, A)), 0)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(J1, $product(-1, J)), 0) & $greatereq($sum(J1, $product(-1, M)), 0) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($greatereq(A, 0) & $greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, A)), 0)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(I, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, N)), 0) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$greatereq($sum(J, $product(-1, I)), 0)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $greatereq(J, 0) & $greatereq($sum(usN, $product(-1, I)), -1) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($greatereq(A, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A)), 0)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $greatereq(M, 1) & $greatereq($sum(usN, $product(-1, N)), 0)))))) <=> (~![A: $int, A1: map_int_int] : ((~($greatereq(A, 0) & ($sum(usN, $product(-1, A)) = -1))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq($sum(N, $product(-1, M)), 0) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(I1))))), 0)) | ![J1: $int] : ($greatereq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(J1))))), 0) | ![J2: $int] : ((~($sum(J1, $product(-1, J2)) = 1)) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($greatereq(J1, 0) & (~$greatereq($sum(J1, $product(-1, A)), 0)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(J1, $product(-1, J)), 0) & $greatereq($sum(J1, $product(-1, M)), 0) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($greatereq(A, 0) & $greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, A)), 0)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(I, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, N)), 0) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$greatereq($sum(J, $product(-1, I)), 0)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $greatereq(J, 0) & $greatereq($sum(usN, $product(-1, I)), -1) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($greatereq(A, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A)), 0)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $greatereq(M, 1) & $greatereq($sum(usN, $product(-1, N)), 0))))))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(51,plain,
% 0.67/0.72 ((~![A: $int, A1: map_int_int] : ((~($greatereq(A, 0) & ($sum(A, $product(-1, usN)) = 1))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq($sum(N, $product(-1, M)), 0) | ![J: $int, I: $int, A3: map_int_int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | ![I1: $int] : ((~$lesseq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(I1))))), 0)) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(I, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, N)), 0) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))))) | ![J1: $int] : ($lesseq($sum(tb2t(get(int, int, t2tb2(A3), t2tb(J1))), $product(-1, tb2t(get(int, int, t2tb2(A2), t2tb(f))))), 0) | ![J2: $int] : ((~($sum(J2, $product(-1, J1)) = -1)) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($greatereq(J1, 0) & (~$lesseq($sum(A, $product(-1, J1)), 0)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(J1, $product(-1, J)), 0) & $lesseq($sum(M, $product(-1, J1)), 0) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($greatereq(A, 0) & $greatereq(I1, 0) & (~$lesseq($sum(A, $product(-1, I1)), 0))))) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $greatereq(J, 0) & $lesseq($sum(I, $product(-1, usN)), 1) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($greatereq(A, 0) & $greatereq(f, 0) & (~$lesseq($sum(A, $product(-1, f)), 0)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $greatereq(M, 1) & $lesseq($sum(N, $product(-1, usN)), 0)))))) <=> (~![A: $int, A1: map_int_int] : ((~($greatereq(A, 0) & ($sum(usN, $product(-1, A)) = -1))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq($sum(N, $product(-1, M)), 0) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(I1))))), 0)) | ![J1: $int] : ($greatereq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(J1))))), 0) | ![J2: $int] : ((~($sum(J1, $product(-1, J2)) = 1)) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($greatereq(J1, 0) & (~$greatereq($sum(J1, $product(-1, A)), 0)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(J1, $product(-1, J)), 0) & $greatereq($sum(J1, $product(-1, M)), 0) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($greatereq(A, 0) & $greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, A)), 0)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(I, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, N)), 0) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$greatereq($sum(J, $product(-1, I)), 0)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $greatereq(J, 0) & $greatereq($sum(usN, $product(-1, I)), -1) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($greatereq(A, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A)), 0)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $greatereq(M, 1) & $greatereq($sum(usN, $product(-1, N)), 0))))))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(52,plain,
% 0.67/0.73 ((~![A: $int, A1: map_int_int] : ((~($lesseq(0, A) & (A = $sum(1, usN)))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq(N, M) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq(tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t(get(int, int, t2tb2(A3), t2tb(I1))))) | ![J1: $int] : ($lesseq(tb2t(get(int, int, t2tb2(A3), t2tb(J1))), tb2t(get(int, int, t2tb2(A2), t2tb(f)))) | ![J2: $int] : ((~(J2 = $sum(-1, J1))) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($lesseq(0, J1) & (~$lesseq(A, J1)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(J1, J) & $lesseq(M, J1) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($lesseq(0, A) & $lesseq(0, I1) & (~$lesseq(A, I1)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(I, I1) & $lesseq(I1, N) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$lesseq(I, J)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(0, J) & $lesseq(I, $sum(1, usN)) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($lesseq(0, A) & $lesseq(0, f) & (~$lesseq(A, f)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $lesseq(1, M) & $lesseq(N, usN)))))) <=> (~![A: $int, A1: map_int_int] : ((~($greatereq(A, 0) & ($sum(A, $product(-1, usN)) = 1))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq($sum(N, $product(-1, M)), 0) | ![J: $int, I: $int, A3: map_int_int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | ![I1: $int] : ((~$lesseq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(I1))))), 0)) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(I, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, N)), 0) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))))) | ![J1: $int] : ($lesseq($sum(tb2t(get(int, int, t2tb2(A3), t2tb(J1))), $product(-1, tb2t(get(int, int, t2tb2(A2), t2tb(f))))), 0) | ![J2: $int] : ((~($sum(J2, $product(-1, J1)) = -1)) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($greatereq(J1, 0) & (~$lesseq($sum(A, $product(-1, J1)), 0)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(J1, $product(-1, J)), 0) & $lesseq($sum(M, $product(-1, J1)), 0) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($greatereq(A, 0) & $greatereq(I1, 0) & (~$lesseq($sum(A, $product(-1, I1)), 0))))) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $greatereq(J, 0) & $lesseq($sum(I, $product(-1, usN)), 1) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($greatereq(A, 0) & $greatereq(f, 0) & (~$lesseq($sum(A, $product(-1, f)), 0)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $greatereq(M, 1) & $lesseq($sum(N, $product(-1, usN)), 0))))))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(53,plain,
% 0.67/0.73 ((~![A: $int, A1: map_int_int] : ((~($lesseq(0, A) & (A = $sum(1, usN)))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq(N, M) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq(tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t(get(int, int, t2tb2(A3), t2tb(I1))))) | ![J1: $int] : ($lesseq(tb2t(get(int, int, t2tb2(A3), t2tb(J1))), tb2t(get(int, int, t2tb2(A2), t2tb(f)))) | ![J2: $int] : ((~(J2 = $sum(-1, J1))) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($lesseq(0, J1) & (~$lesseq(A, J1)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(J1, J) & $lesseq(M, J1) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($lesseq(0, A) & $lesseq(0, I1) & (~$lesseq(A, I1)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(I, I1) & $lesseq(I1, N) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$lesseq(I, J)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(0, J) & $lesseq(I, $sum(1, usN)) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($lesseq(0, A) & $lesseq(0, f) & (~$lesseq(A, f)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $lesseq(1, M) & $lesseq(N, usN)))))) <=> (~![A: $int, A1: map_int_int] : ((~($lesseq(0, A) & (A = $sum(1, usN)))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq(N, M) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq(tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t(get(int, int, t2tb2(A3), t2tb(I1))))) | ![J1: $int] : ($lesseq(tb2t(get(int, int, t2tb2(A3), t2tb(J1))), tb2t(get(int, int, t2tb2(A2), t2tb(f)))) | ![J2: $int] : ((~(J2 = $sum(-1, J1))) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($lesseq(0, J1) & (~$lesseq(A, J1)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(J1, J) & $lesseq(M, J1) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($lesseq(0, A) & $lesseq(0, I1) & (~$lesseq(A, I1)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(I, I1) & $lesseq(I1, N) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$lesseq(I, J)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(0, J) & $lesseq(I, $sum(1, usN)) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($lesseq(0, A) & $lesseq(0, f) & (~$lesseq(A, f)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $lesseq(1, M) & $lesseq(N, usN))))))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(54,plain,
% 0.67/0.73 ((~![A: $int, A1: map_int_int] : (($lesseq(0, A) & (A = $sum(usN, 1))) => ![N: $int, M: $int, A2: map_int_int] : (((((m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2))))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1)))) & $lesseq(1, M)) & $lesseq(N, usN)) => ($less(M, N) => ((($lesseq(0, A) & $lesseq(0, f)) & $less(f, A)) => ![J: $int, I: $int, A3: map_int_int] : ((((((((i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3))))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3))))) & $lesseq(0, J)) & $lesseq(I, $sum(usN, 1))) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))) => ($lesseq(I, J) => ![I1: $int] : ((((i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(I, I1)) & $lesseq(I1, N)) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) => ((($lesseq(0, A) & $lesseq(0, I1)) & $less(I1, A)) => ((~$less(tb2t(get(int, int, t2tb2(A3), t2tb(I1))), tb2t(get(int, int, t2tb2(A2), t2tb(f))))) => ![J1: $int] : ((((j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(J1, J)) & $lesseq(M, J1)) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) => (($lesseq(0, J1) & $less(J1, A)) => ($less(tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t(get(int, int, t2tb2(A3), t2tb(J1)))) => ![J2: $int] : ((J2 = $difference(J1, 1)) => termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))))))))))))))))) <=> (~![A: $int, A1: map_int_int] : ((~($lesseq(0, A) & (A = $sum(1, usN)))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq(N, M) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq(tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t(get(int, int, t2tb2(A3), t2tb(I1))))) | ![J1: $int] : ($lesseq(tb2t(get(int, int, t2tb2(A3), t2tb(J1))), tb2t(get(int, int, t2tb2(A2), t2tb(f)))) | ![J2: $int] : ((~(J2 = $sum(-1, J1))) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($lesseq(0, J1) & (~$lesseq(A, J1)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(J1, J) & $lesseq(M, J1) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($lesseq(0, A) & $lesseq(0, I1) & (~$lesseq(A, I1)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(I, I1) & $lesseq(I1, N) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$lesseq(I, J)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(0, J) & $lesseq(I, $sum(1, usN)) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($lesseq(0, A) & $lesseq(0, f) & (~$lesseq(A, f)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $lesseq(1, M) & $lesseq(N, usN))))))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(55,axiom,(~![A: $int, A1: map_int_int] : (($lesseq(0, A) & (A = $sum(usN, 1))) => ![N: $int, M: $int, A2: map_int_int] : (((((m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2))))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1)))) & $lesseq(1, M)) & $lesseq(N, usN)) => ($less(M, N) => ((($lesseq(0, A) & $lesseq(0, f)) & $less(f, A)) => ![J: $int, I: $int, A3: map_int_int] : ((((((((i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3))))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3))))) & $lesseq(0, J)) & $lesseq(I, $sum(usN, 1))) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))) => ($lesseq(I, J) => ![I1: $int] : ((((i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(I, I1)) & $lesseq(I1, N)) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) => ((($lesseq(0, A) & $lesseq(0, I1)) & $less(I1, A)) => ((~$less(tb2t(get(int, int, t2tb2(A3), t2tb(I1))), tb2t(get(int, int, t2tb2(A2), t2tb(f))))) => ![J1: $int] : ((((j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(J1, J)) & $lesseq(M, J1)) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) => (($lesseq(0, J1) & $less(J1, A)) => ($less(tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t(get(int, int, t2tb2(A3), t2tb(J1)))) => ![J2: $int] : ((J2 = $difference(J1, 1)) => termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_find')).
% 0.67/0.74 tff(56,plain,
% 0.67/0.74 (~![A: $int, A1: map_int_int] : ((~($lesseq(0, A) & (A = $sum(1, usN)))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq(N, M) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq(tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t(get(int, int, t2tb2(A3), t2tb(I1))))) | ![J1: $int] : ($lesseq(tb2t(get(int, int, t2tb2(A3), t2tb(J1))), tb2t(get(int, int, t2tb2(A2), t2tb(f)))) | ![J2: $int] : ((~(J2 = $sum(-1, J1))) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($lesseq(0, J1) & (~$lesseq(A, J1)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(J1, J) & $lesseq(M, J1) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($lesseq(0, A) & $lesseq(0, I1) & (~$lesseq(A, I1)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(I, I1) & $lesseq(I1, N) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$lesseq(I, J)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(0, J) & $lesseq(I, $sum(1, usN)) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($lesseq(0, A) & $lesseq(0, f) & (~$lesseq(A, f)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $lesseq(1, M) & $lesseq(N, usN)))))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.67/0.74 tff(57,plain,
% 0.67/0.74 (~![A: $int, A1: map_int_int] : ((~($lesseq(0, A) & (A = $sum(1, usN)))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq(N, M) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq(tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t(get(int, int, t2tb2(A3), t2tb(I1))))) | ![J1: $int] : ($lesseq(tb2t(get(int, int, t2tb2(A3), t2tb(J1))), tb2t(get(int, int, t2tb2(A2), t2tb(f)))) | ![J2: $int] : ((~(J2 = $sum(-1, J1))) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($lesseq(0, J1) & (~$lesseq(A, J1)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(J1, J) & $lesseq(M, J1) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($lesseq(0, A) & $lesseq(0, I1) & (~$lesseq(A, I1)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(I, I1) & $lesseq(I1, N) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$lesseq(I, J)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(0, J) & $lesseq(I, $sum(1, usN)) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($lesseq(0, A) & $lesseq(0, f) & (~$lesseq(A, f)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $lesseq(1, M) & $lesseq(N, usN)))))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[56, 53])).
% 0.67/0.74 tff(58,plain,
% 0.67/0.74 (~![A: $int, A1: map_int_int] : ((~($lesseq(0, A) & (A = $sum(1, usN)))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq(N, M) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq(tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t(get(int, int, t2tb2(A3), t2tb(I1))))) | ![J1: $int] : ($lesseq(tb2t(get(int, int, t2tb2(A3), t2tb(J1))), tb2t(get(int, int, t2tb2(A2), t2tb(f)))) | ![J2: $int] : ((~(J2 = $sum(-1, J1))) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($lesseq(0, J1) & (~$lesseq(A, J1)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(J1, J) & $lesseq(M, J1) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($lesseq(0, A) & $lesseq(0, I1) & (~$lesseq(A, I1)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(I, I1) & $lesseq(I1, N) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$lesseq(I, J)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(0, J) & $lesseq(I, $sum(1, usN)) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($lesseq(0, A) & $lesseq(0, f) & (~$lesseq(A, f)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $lesseq(1, M) & $lesseq(N, usN)))))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.67/0.74 tff(59,plain,
% 0.67/0.74 (~![A: $int, A1: map_int_int] : ((~($lesseq(0, A) & (A = $sum(1, usN)))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq(N, M) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq(tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t(get(int, int, t2tb2(A3), t2tb(I1))))) | ![J1: $int] : ($lesseq(tb2t(get(int, int, t2tb2(A3), t2tb(J1))), tb2t(get(int, int, t2tb2(A2), t2tb(f)))) | ![J2: $int] : ((~(J2 = $sum(-1, J1))) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($lesseq(0, J1) & (~$lesseq(A, J1)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(J1, J) & $lesseq(M, J1) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($lesseq(0, A) & $lesseq(0, I1) & (~$lesseq(A, I1)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(I, I1) & $lesseq(I1, N) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$lesseq(I, J)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq(0, J) & $lesseq(I, $sum(1, usN)) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($lesseq(0, A) & $lesseq(0, f) & (~$lesseq(A, f)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $lesseq(1, M) & $lesseq(N, usN)))))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[58, 53])).
% 0.67/0.74 tff(60,plain,
% 0.67/0.74 (~![A: $int, A1: map_int_int] : ((~($greatereq(A, 0) & ($sum(A, $product(-1, usN)) = 1))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq($sum(N, $product(-1, M)), 0) | ![J: $int, I: $int, A3: map_int_int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | ![I1: $int] : ((~$lesseq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(I1))))), 0)) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(I, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, N)), 0) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))))) | ![J1: $int] : ($lesseq($sum(tb2t(get(int, int, t2tb2(A3), t2tb(J1))), $product(-1, tb2t(get(int, int, t2tb2(A2), t2tb(f))))), 0) | ![J2: $int] : ((~($sum(J2, $product(-1, J1)) = -1)) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($greatereq(J1, 0) & (~$lesseq($sum(A, $product(-1, J1)), 0)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(J1, $product(-1, J)), 0) & $lesseq($sum(M, $product(-1, J1)), 0) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($greatereq(A, 0) & $greatereq(I1, 0) & (~$lesseq($sum(A, $product(-1, I1)), 0))))) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $greatereq(J, 0) & $lesseq($sum(I, $product(-1, usN)), 1) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($greatereq(A, 0) & $greatereq(f, 0) & (~$lesseq($sum(A, $product(-1, f)), 0)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $greatereq(M, 1) & $lesseq($sum(N, $product(-1, usN)), 0)))))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.67/0.74 tff(61,plain,
% 0.67/0.74 (~![A: $int, A1: map_int_int] : ((~($greatereq(A, 0) & ($sum(usN, $product(-1, A)) = -1))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq($sum(N, $product(-1, M)), 0) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(I1))))), 0)) | ![J1: $int] : ($greatereq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(J1))))), 0) | ![J2: $int] : ((~($sum(J1, $product(-1, J2)) = 1)) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($greatereq(J1, 0) & (~$greatereq($sum(J1, $product(-1, A)), 0)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(J1, $product(-1, J)), 0) & $greatereq($sum(J1, $product(-1, M)), 0) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($greatereq(A, 0) & $greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, A)), 0)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(I, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, N)), 0) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$greatereq($sum(J, $product(-1, I)), 0)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $greatereq(J, 0) & $greatereq($sum(usN, $product(-1, I)), -1) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($greatereq(A, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A)), 0)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $greatereq(M, 1) & $greatereq($sum(usN, $product(-1, N)), 0)))))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[60, 51])).
% 0.67/0.74 tff(62,plain,
% 0.67/0.74 (~![A: $int, A1: map_int_int] : ((~($greatereq(A, 0) & ($sum(usN, $product(-1, A)) = -1))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq($sum(N, $product(-1, M)), 0) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(I1))))), 0)) | ![J1: $int] : ($greatereq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(J1))))), 0) | ![J2: $int] : ((~($sum(J1, $product(-1, J2)) = 1)) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($greatereq(J1, 0) & (~$greatereq($sum(J1, $product(-1, A)), 0)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(J1, $product(-1, J)), 0) & $greatereq($sum(J1, $product(-1, M)), 0) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($greatereq(A, 0) & $greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, A)), 0)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(I, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, N)), 0) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$greatereq($sum(J, $product(-1, I)), 0)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $greatereq(J, 0) & $greatereq($sum(usN, $product(-1, I)), -1) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($greatereq(A, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A)), 0)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $greatereq(M, 1) & $greatereq($sum(usN, $product(-1, N)), 0)))))),
% 0.74/0.75 inference(modus_ponens,[status(thm)],[61, 50])).
% 0.74/0.75 tff(63,plain,
% 0.74/0.75 (~![A: $int, A1: map_int_int] : ((~($greatereq(A, 0) & ($sum(usN, $product(-1, A)) = -1))) | ![N: $int, M: $int, A2: map_int_int] : ($lesseq($sum(N, $product(-1, M)), 0) | ![J: $int, I: $int, A3: map_int_int] : (![I1: $int] : ((~$lesseq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(I1))))), 0)) | ![J1: $int] : ($greatereq($sum(tb2t(get(int, int, t2tb2(A2), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3), t2tb(J1))))), 0) | ![J2: $int] : ((~($sum(J1, $product(-1, J2)) = 1)) | termination(I1, J2, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))) | (~($greatereq(J1, 0) & (~$greatereq($sum(J1, $product(-1, A)), 0)))) | (~(j_invariant(M, N, J1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(J1, $product(-1, J)), 0) & $greatereq($sum(J1, $product(-1, M)), 0) & termination(I1, J1, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~($greatereq(A, 0) & $greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, A)), 0)))) | (~(i_invariant(M, N, I1, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & $lesseq($sum(I, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, N)), 0) & termination(I1, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3))))))) | (~$greatereq($sum(J, $product(-1, I)), 0)) | (~(i_invariant(M, N, I, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & j_invariant(M, N, J, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A3)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A3)))) & $greatereq(J, 0) & $greatereq($sum(usN, $product(-1, I)), -1) & termination(I, J, M, N, tb2t(get(int, int, t2tb2(A2), t2tb(f))), tb2t1(mk_array(int, A, t2tb2(A3)))) & permut_all(int, mk_array(int, A, t2tb2(A3)), mk_array(int, A, t2tb2(A1)))))) | (~($greatereq(A, 0) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A)), 0)))) | (~(m_invariant(M, tb2t1(mk_array(int, A, t2tb2(A2)))) & n_invariant(N, tb2t1(mk_array(int, A, t2tb2(A2)))) & permut_all(int, mk_array(int, A, t2tb2(A2)), mk_array(int, A, t2tb2(A1))) & $greatereq(M, 1) & $greatereq($sum(usN, $product(-1, N)), 0)))))),
% 0.74/0.75 inference(modus_ponens,[status(thm)],[62, 50])).
% 0.74/0.75 tff(64,plain,
% 0.74/0.75 ($greatereq(A!18, 0) & ($sum(usN, $product(-1, A!18)) = -1) & (~$greatereq($sum(M!20, $product(-1, N!21)), 0)) & $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(I1!25))))), 0) & (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)) & (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))) & $greatereq(J1!26, 0) & (~$lesseq($sum(A!18, $product(-1, J1!26)), 0)) & j_invariant(M!20, N!21, J1!26, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq($sum(J!24, $product(-1, J1!26)), 0) & $lesseq($sum(M!20, $product(-1, J1!26)), 0) & termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(I1!25, 0) & (~$lesseq($sum(A!18, $product(-1, I1!25)), 0)) & i_invariant(M!20, N!21, I1!25, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, I1!25)), 0) & $greatereq($sum(N!21, $product(-1, I1!25)), 0) & termination(I1!25, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $lesseq($sum(I!23, $product(-1, J!24)), 0) & i_invariant(M!20, N!21, I!23, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & $greatereq(J!24, 0) & $greatereq($sum(usN, $product(-1, I!23)), -1) & termination(I!23, J!24, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) & permut_all(int, mk_array(int, A!18, t2tb2(A3!22)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(f, 0) & (~$greatereq($sum(f, $product(-1, A!18)), 0)) & m_invariant(M!20, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & n_invariant(N!21, tb2t1(mk_array(int, A!18, t2tb2(A2!19)))) & permut_all(int, mk_array(int, A!18, t2tb2(A2!19)), mk_array(int, A!18, t2tb2(A1!17))) & $greatereq(M!20, 1) & $greatereq($sum(usN, $product(-1, N!21)), 0)),
% 0.74/0.75 inference(modus_ponens,[status(thm)],[63, 49])).
% 0.74/0.75 tff(65,plain,
% 0.74/0.75 ($greatereq($sum(J!24, $product(-1, J1!26)), 0)),
% 0.74/0.75 inference(and_elim,[status(thm)],[64])).
% 0.74/0.75 tff(66,plain,
% 0.74/0.75 (~((~($sum(J1!26, $product(-1, J2!27)) = 1)) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))))),
% 0.74/0.75 inference(and_elim,[status(thm)],[64])).
% 0.74/0.75 tff(67,plain,
% 0.74/0.75 ($sum(J1!26, $product(-1, J2!27)) = 1),
% 0.74/0.75 inference(or_elim,[status(thm)],[66])).
% 0.74/0.75 tff(68,plain,
% 0.74/0.75 ((~($sum(J1!26, $product(-1, J2!27)) = 1)) | $greatereq($sum(J1!26, $product(-1, J2!27)), 1)),
% 0.74/0.75 inference(theory_lemma,[status(thm)],[])).
% 0.74/0.75 tff(69,plain,
% 0.74/0.75 ($greatereq($sum(J1!26, $product(-1, J2!27)), 1)),
% 0.74/0.75 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.74/0.75 tff(70,assumption,($lesseq($sum(N!21, $product(-1, J2!27)), 0)), introduced(assumption)).
% 0.74/0.75 tff(71,plain,
% 0.74/0.75 (^[M: $int, N: $int, J: $int, R: $int, A: array_int] : rewrite((~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))))) <=> (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))))))))),
% 0.74/0.75 inference(bind,[status(th)],[])).
% 0.74/0.75 tff(72,plain,
% 0.74/0.75 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))))) <=> ![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))))))),
% 0.74/0.75 inference(quant_intro,[status(thm)],[71])).
% 0.74/0.75 tff(73,plain,
% 0.74/0.75 (^[M: $int, N: $int, J: $int, R: $int, A: array_int] : refl((~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))))) <=> (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))))))),
% 0.74/0.75 inference(bind,[status(th)],[])).
% 0.74/0.75 tff(74,plain,
% 0.74/0.75 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))))) <=> ![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))))))),
% 0.74/0.76 inference(quant_intro,[status(thm)],[73])).
% 0.74/0.76 tff(75,plain,
% 0.74/0.76 (^[M: $int, N: $int, J: $int, R: $int, A: array_int] : rewrite((~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))))) <=> (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))))))),
% 0.74/0.76 inference(bind,[status(th)],[])).
% 0.74/0.76 tff(76,plain,
% 0.74/0.76 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))))) <=> ![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))))))),
% 0.74/0.76 inference(quant_intro,[status(thm)],[75])).
% 0.74/0.76 tff(77,plain,
% 0.74/0.76 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))))) <=> ![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))))))),
% 0.74/0.76 inference(transitivity,[status(thm)],[76, 74])).
% 0.74/0.76 tff(78,plain,
% 0.74/0.76 (^[M: $int, N: $int, J: $int, R: $int, A: array_int] : trans(monotonicity(rewrite(((~j_invariant(M, N, J, R, A)) | ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ($lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))) <=> ((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Q: $int] : trans(monotonicity(rewrite(($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) <=> (~((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))), ((~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))) <=> (~(~((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))), rewrite((~(~((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))) <=> ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))), ((~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))) <=> ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))), (![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))) <=> ![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))), (($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))) <=> ($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))), rewrite(($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))) <=> (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))), (($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))) <=> (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))))), rewrite((~((~((~$greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0))) <=> (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))), ((j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | ($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0)))) <=> (j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))))), rewrite((j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))) <=> (j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))), ((j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | ($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0)))) <=> (j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))))), ((((~j_invariant(M, N, J, R, A)) | ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ($lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))) & (j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | ($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0))))) <=> (((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))))))) & (j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))))), rewrite((((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))))))) & (j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))))) <=> (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))))))), ((((~j_invariant(M, N, J, R, A)) | ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ($lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))) & (j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | ($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0))))) <=> (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))))))))),
% 0.75/0.76 inference(bind,[status(th)],[])).
% 0.75/0.76 tff(79,plain,
% 0.75/0.76 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (((~j_invariant(M, N, J, R, A)) | ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ($lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))) & (j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | ($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0))))) <=> ![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))))))),
% 0.75/0.76 inference(quant_intro,[status(thm)],[78])).
% 0.75/0.76 tff(80,plain,
% 0.75/0.76 (^[M: $int, N: $int, J: $int, R: $int, A: array_int] : rewrite((((~j_invariant(M, N, J, R, A)) | ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ($greatereq($sum(tptp_fun_Q_15(A, R, J, M), $product(-1, M)), 0) & $lesseq($sum(tptp_fun_Q_15(A, R, J, M), $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))) & (j_invariant(M, N, J, R, A) | ((~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~((~$lesseq($sum(tptp_fun_Q_16(A, R, J), $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0))) | ((~(~$greatereq($sum(J, $product(-1, M)), 0))) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))) <=> (((~j_invariant(M, N, J, R, A)) | ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ($lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))) & (j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | ($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0))))))),
% 0.75/0.76 inference(bind,[status(th)],[])).
% 0.75/0.76 tff(81,plain,
% 0.75/0.76 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (((~j_invariant(M, N, J, R, A)) | ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ($greatereq($sum(tptp_fun_Q_15(A, R, J, M), $product(-1, M)), 0) & $lesseq($sum(tptp_fun_Q_15(A, R, J, M), $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))) & (j_invariant(M, N, J, R, A) | ((~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~((~$lesseq($sum(tptp_fun_Q_16(A, R, J), $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0))) | ((~(~$greatereq($sum(J, $product(-1, M)), 0))) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))) <=> ![M: $int, N: $int, J: $int, R: $int, A: array_int] : (((~j_invariant(M, N, J, R, A)) | ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ($lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))) & (j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | ($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0)))))),
% 0.75/0.76 inference(quant_intro,[status(thm)],[80])).
% 0.75/0.76 tff(82,plain,
% 0.75/0.76 (^[M: $int, N: $int, J: $int, R: $int, A: array_int] : rewrite((j_invariant(M, N, J, R, A) <=> ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $lesseq($sum(Q, $product(-1, usN)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$lesseq($sum(M, $product(-1, J)), 0)) | ?[Q: $int] : ($lesseq($sum(M, $product(-1, Q)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $lesseq($sum(tb2t(get1(int, t2tb1(A), Q)), $product(-1, R)), 0))))) <=> (j_invariant(M, N, J, R, A) <=> ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ?[Q: $int] : ($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))),
% 0.75/0.77 inference(bind,[status(th)],[])).
% 0.75/0.77 tff(83,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $lesseq($sum(Q, $product(-1, usN)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$lesseq($sum(M, $product(-1, J)), 0)) | ?[Q: $int] : ($lesseq($sum(M, $product(-1, Q)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $lesseq($sum(tb2t(get1(int, t2tb1(A), Q)), $product(-1, R)), 0))))) <=> ![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ?[Q: $int] : ($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))),
% 0.75/0.77 inference(quant_intro,[status(thm)],[82])).
% 0.75/0.77 tff(84,plain,
% 0.75/0.77 (^[M: $int, N: $int, J: $int, R: $int, A: array_int] : rewrite((j_invariant(M, N, J, R, A) <=> ($lesseq(J, N) & ![Q: $int] : ((~((~$lesseq(Q, J)) & $lesseq(Q, usN))) | $lesseq(R, tb2t(get1(int, t2tb1(A), Q)))) & ((~$lesseq(M, J)) | ?[Q: $int] : ($lesseq(M, Q) & $lesseq(Q, J) & $lesseq(tb2t(get1(int, t2tb1(A), Q)), R))))) <=> (j_invariant(M, N, J, R, A) <=> ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $lesseq($sum(Q, $product(-1, usN)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$lesseq($sum(M, $product(-1, J)), 0)) | ?[Q: $int] : ($lesseq($sum(M, $product(-1, Q)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $lesseq($sum(tb2t(get1(int, t2tb1(A), Q)), $product(-1, R)), 0))))))),
% 0.75/0.77 inference(bind,[status(th)],[])).
% 0.75/0.77 tff(85,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> ($lesseq(J, N) & ![Q: $int] : ((~((~$lesseq(Q, J)) & $lesseq(Q, usN))) | $lesseq(R, tb2t(get1(int, t2tb1(A), Q)))) & ((~$lesseq(M, J)) | ?[Q: $int] : ($lesseq(M, Q) & $lesseq(Q, J) & $lesseq(tb2t(get1(int, t2tb1(A), Q)), R))))) <=> ![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $lesseq($sum(Q, $product(-1, usN)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$lesseq($sum(M, $product(-1, J)), 0)) | ?[Q: $int] : ($lesseq($sum(M, $product(-1, Q)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $lesseq($sum(tb2t(get1(int, t2tb1(A), Q)), $product(-1, R)), 0)))))),
% 0.75/0.77 inference(quant_intro,[status(thm)],[84])).
% 0.75/0.77 tff(86,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> ($lesseq(J, N) & ![Q: $int] : ((~((~$lesseq(Q, J)) & $lesseq(Q, usN))) | $lesseq(R, tb2t(get1(int, t2tb1(A), Q)))) & ((~$lesseq(M, J)) | ?[Q: $int] : ($lesseq(M, Q) & $lesseq(Q, J) & $lesseq(tb2t(get1(int, t2tb1(A), Q)), R))))) <=> ![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> ($lesseq(J, N) & ![Q: $int] : ((~((~$lesseq(Q, J)) & $lesseq(Q, usN))) | $lesseq(R, tb2t(get1(int, t2tb1(A), Q)))) & ((~$lesseq(M, J)) | ?[Q: $int] : ($lesseq(M, Q) & $lesseq(Q, J) & $lesseq(tb2t(get1(int, t2tb1(A), Q)), R)))))),
% 0.75/0.77 inference(rewrite,[status(thm)],[])).
% 0.75/0.77 tff(87,plain,
% 0.75/0.77 (^[M: $int, N: $int, J: $int, R: $int, A: array_int] : rewrite((j_invariant(M, N, J, R, A) <=> (($lesseq(J, N) & ![Q: $int] : (($less(J, Q) & $lesseq(Q, usN)) => $lesseq(R, tb2t(get1(int, t2tb1(A), Q))))) & ($lesseq(M, J) => ?[Q: $int] : (($lesseq(M, Q) & $lesseq(Q, J)) & $lesseq(tb2t(get1(int, t2tb1(A), Q)), R))))) <=> (j_invariant(M, N, J, R, A) <=> ($lesseq(J, N) & ![Q: $int] : ((~((~$lesseq(Q, J)) & $lesseq(Q, usN))) | $lesseq(R, tb2t(get1(int, t2tb1(A), Q)))) & ((~$lesseq(M, J)) | ?[Q: $int] : ($lesseq(M, Q) & $lesseq(Q, J) & $lesseq(tb2t(get1(int, t2tb1(A), Q)), R))))))),
% 0.75/0.77 inference(bind,[status(th)],[])).
% 0.75/0.77 tff(88,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> (($lesseq(J, N) & ![Q: $int] : (($less(J, Q) & $lesseq(Q, usN)) => $lesseq(R, tb2t(get1(int, t2tb1(A), Q))))) & ($lesseq(M, J) => ?[Q: $int] : (($lesseq(M, Q) & $lesseq(Q, J)) & $lesseq(tb2t(get1(int, t2tb1(A), Q)), R))))) <=> ![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> ($lesseq(J, N) & ![Q: $int] : ((~((~$lesseq(Q, J)) & $lesseq(Q, usN))) | $lesseq(R, tb2t(get1(int, t2tb1(A), Q)))) & ((~$lesseq(M, J)) | ?[Q: $int] : ($lesseq(M, Q) & $lesseq(Q, J) & $lesseq(tb2t(get1(int, t2tb1(A), Q)), R)))))),
% 0.75/0.77 inference(quant_intro,[status(thm)],[87])).
% 0.75/0.77 tff(89,axiom,(![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> (($lesseq(J, N) & ![Q: $int] : (($less(J, Q) & $lesseq(Q, usN)) => $lesseq(R, tb2t(get1(int, t2tb1(A), Q))))) & ($lesseq(M, J) => ?[Q: $int] : (($lesseq(M, Q) & $lesseq(Q, J)) & $lesseq(tb2t(get1(int, t2tb1(A), Q)), R)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','j_invariant_def')).
% 0.75/0.77 tff(90,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> ($lesseq(J, N) & ![Q: $int] : ((~((~$lesseq(Q, J)) & $lesseq(Q, usN))) | $lesseq(R, tb2t(get1(int, t2tb1(A), Q)))) & ((~$lesseq(M, J)) | ?[Q: $int] : ($lesseq(M, Q) & $lesseq(Q, J) & $lesseq(tb2t(get1(int, t2tb1(A), Q)), R)))))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.75/0.77 tff(91,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> ($lesseq(J, N) & ![Q: $int] : ((~((~$lesseq(Q, J)) & $lesseq(Q, usN))) | $lesseq(R, tb2t(get1(int, t2tb1(A), Q)))) & ((~$lesseq(M, J)) | ?[Q: $int] : ($lesseq(M, Q) & $lesseq(Q, J) & $lesseq(tb2t(get1(int, t2tb1(A), Q)), R)))))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.75/0.77 tff(92,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $lesseq($sum(Q, $product(-1, usN)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$lesseq($sum(M, $product(-1, J)), 0)) | ?[Q: $int] : ($lesseq($sum(M, $product(-1, Q)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $lesseq($sum(tb2t(get1(int, t2tb1(A), Q)), $product(-1, R)), 0)))))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[91, 85])).
% 0.75/0.77 tff(93,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (j_invariant(M, N, J, R, A) <=> ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ?[Q: $int] : ($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[92, 83])).
% 0.75/0.77 tff(94,plain,(
% 0.75/0.77 ![M: $int, N: $int, J: $int, R: $int, A: array_int] : (((~j_invariant(M, N, J, R, A)) | ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ($greatereq($sum(tptp_fun_Q_15(A, R, J, M), $product(-1, M)), 0) & $lesseq($sum(tptp_fun_Q_15(A, R, J, M), $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))) & (j_invariant(M, N, J, R, A) | ((~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~((~$lesseq($sum(tptp_fun_Q_16(A, R, J), $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0))) | ((~(~$greatereq($sum(J, $product(-1, M)), 0))) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))))),
% 0.75/0.77 inference(skolemize,[status(sab)],[93])).
% 0.75/0.77 tff(95,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (((~j_invariant(M, N, J, R, A)) | ($lesseq($sum(J, $product(-1, N)), 0) & ![Q: $int] : ((~((~$lesseq($sum(Q, $product(-1, J)), 0)) & $greatereq($sum(usN, $product(-1, Q)), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)) & ((~$greatereq($sum(J, $product(-1, M)), 0)) | ($lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0))))) & (j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | ($greatereq($sum(J, $product(-1, M)), 0) & ![Q: $int] : (~($greatereq($sum(Q, $product(-1, M)), 0) & $lesseq($sum(Q, $product(-1, J)), 0) & $greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))) | (~((~((~$greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0)) & $greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0)))))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[94, 81])).
% 0.75/0.77 tff(96,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))))))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[95, 79])).
% 0.75/0.77 tff(97,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0)))))) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0))))))))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[96, 77])).
% 0.75/0.77 tff(98,plain,
% 0.75/0.77 (![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))))))),
% 0.75/0.77 inference(modus_ponens,[status(thm)],[97, 72])).
% 0.75/0.77 tff(99,plain,
% 0.75/0.77 (((~![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))))))) | (~((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))))))))))) <=> ((~![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))))))) | (~((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0)))))))))))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(100,plain,
% 0.75/0.78 ((~((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$lesseq($sum(J!24, $product(-1, N!21)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J!24, $product(-1, M!20)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~$lesseq($sum(J!24, $product(-1, N!21)), 0)) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~((~$greatereq($sum(J!24, $product(-1, M!20)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0)))))))))) <=> (~((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))))))))))),
% 0.75/0.78 inference(rewrite,[status(thm)],[])).
% 0.75/0.78 tff(101,plain,
% 0.75/0.78 (((~![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))))))) | (~((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$lesseq($sum(J!24, $product(-1, N!21)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J!24, $product(-1, M!20)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~$lesseq($sum(J!24, $product(-1, N!21)), 0)) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~((~$greatereq($sum(J!24, $product(-1, M!20)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))))))))))) <=> ((~![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))))))) | (~((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0)))))))))))),
% 0.75/0.79 inference(monotonicity,[status(thm)],[100])).
% 0.75/0.79 tff(102,plain,
% 0.75/0.79 (((~![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))))))) | (~((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$lesseq($sum(J!24, $product(-1, N!21)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J!24, $product(-1, M!20)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~$lesseq($sum(J!24, $product(-1, N!21)), 0)) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~((~$greatereq($sum(J!24, $product(-1, M!20)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))))))))))) <=> ((~![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))))))) | (~((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0)))))))))))),
% 0.75/0.79 inference(transitivity,[status(thm)],[101, 99])).
% 0.75/0.79 tff(103,plain,
% 0.75/0.79 ((~![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))))))) | (~((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$lesseq($sum(J!24, $product(-1, N!21)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J!24, $product(-1, M!20)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~$lesseq($sum(J!24, $product(-1, N!21)), 0)) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~((~$greatereq($sum(J!24, $product(-1, M!20)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))))))))))),
% 0.75/0.79 inference(quant_inst,[status(thm)],[])).
% 0.75/0.79 tff(104,plain,
% 0.75/0.79 ((~![M: $int, N: $int, J: $int, R: $int, A: array_int] : (~((~((~j_invariant(M, N, J, R, A)) | (~((~$lesseq($sum(J, $product(-1, N)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J)), 0) | $lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~((~$lesseq($sum(M, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(J, $product(-1, tptp_fun_Q_15(A, R, J, M))), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_15(A, R, J, M))))), 0)))))))))) | (~(j_invariant(M, N, J, R, A) | (~$lesseq($sum(J, $product(-1, N)), 0)) | (~($lesseq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), tptp_fun_Q_16(A, R, J))))), 0) | $greatereq($sum(J, $product(-1, tptp_fun_Q_16(A, R, J))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(A, R, J))), 0)))) | (~((~$greatereq($sum(J, $product(-1, M)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J)), 0)) | (~$greatereq($sum(Q, $product(-1, M)), 0)) | (~$greatereq($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), Q)))), 0))))))))))) | (~((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))))))))))),
% 0.75/0.80 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.75/0.80 tff(105,plain,
% 0.75/0.80 (~((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0)))))))))),
% 0.75/0.80 inference(unit_resolution,[status(thm)],[104, 98])).
% 0.75/0.80 tff(106,plain,
% 0.75/0.80 (((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~(j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))))), 0) | $greatereq($sum(J!24, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0) | (~$greatereq($sum(usN, $product(-1, tptp_fun_Q_16(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24))), 0)))) | (~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~![Q: $int] : ((~$lesseq($sum(Q, $product(-1, J!24)), 0)) | (~$greatereq($sum(Q, $product(-1, M!20)), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))))))))) | ((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))),
% 0.75/0.81 inference(tautology,[status(thm)],[])).
% 0.75/0.81 tff(107,plain,
% 0.75/0.81 ((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0))))))))),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.75/0.81 tff(108,plain,
% 0.75/0.81 (j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))),
% 0.75/0.81 inference(and_elim,[status(thm)],[64])).
% 0.75/0.81 tff(109,plain,
% 0.75/0.81 ((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0))))))))),
% 0.75/0.81 inference(tautology,[status(thm)],[])).
% 0.75/0.81 tff(110,plain,
% 0.75/0.81 ((~((~j_invariant(M!20, N!21, J!24, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))))) | (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0))))))))),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.75/0.81 tff(111,plain,
% 0.75/0.81 (~((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0)))))))),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[110, 107])).
% 0.75/0.81 tff(112,plain,
% 0.75/0.81 (((~$greatereq($sum(N!21, $product(-1, J!24)), 0)) | (~![Q: $int] : ($lesseq($sum(Q, $product(-1, J!24)), 0) | (~$greatereq($sum(usN, $product(-1, Q)), 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), Q)))), 0))) | (~((~$lesseq($sum(M!20, $product(-1, J!24)), 0)) | (~((~$lesseq($sum(M!20, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(J!24, $product(-1, tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))), 0)) | (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), tptp_fun_Q_15(tb2t1(mk_array(int, A!18, t2tb2(A3!22))), tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), J!24, M!20))))), 0))))))) | $greatereq($sum(N!21, $product(-1, J!24)), 0)),
% 0.75/0.81 inference(tautology,[status(thm)],[])).
% 0.75/0.81 tff(113,plain,
% 0.75/0.81 ($greatereq($sum(N!21, $product(-1, J!24)), 0)),
% 0.75/0.81 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.75/0.81 tff(114,plain,
% 0.75/0.81 ($false),
% 0.75/0.81 inference(theory_lemma,[status(thm)],[113, 70, 69, 65])).
% 0.81/0.81 tff(115,plain,(~$lesseq($sum(N!21, $product(-1, J2!27)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.81 tff(116,plain,
% 0.81/0.81 (^[I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : refl((termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0)))))) <=> (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0)))))))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(117,plain,
% 0.81/0.81 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0)))))) <=> ![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))),
% 0.81/0.81 inference(quant_intro,[status(thm)],[116])).
% 0.81/0.81 tff(118,plain,
% 0.81/0.81 (^[I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : rewrite((termination(I, J, I0, J0, R, A) <=> (((~$greatereq($sum(I0, $product(-1, I)), 0)) & (~$lesseq($sum(J0, $product(-1, J)), 0))) | ($greatereq($sum(f, $product(-1, I)), 0) & $lesseq($sum(f, $product(-1, J)), 0) & ($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0)))) <=> (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0)))))))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(119,plain,
% 0.81/0.81 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$greatereq($sum(I0, $product(-1, I)), 0)) & (~$lesseq($sum(J0, $product(-1, J)), 0))) | ($greatereq($sum(f, $product(-1, I)), 0) & $lesseq($sum(f, $product(-1, J)), 0) & ($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0)))) <=> ![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))),
% 0.81/0.81 inference(quant_intro,[status(thm)],[118])).
% 0.81/0.81 tff(120,plain,
% 0.81/0.81 (^[I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : rewrite((termination(I, J, I0, J0, R, A) <=> (((~$lesseq($sum(I, $product(-1, I0)), 0)) & (~$lesseq($sum(J0, $product(-1, J)), 0))) | ($lesseq($sum(I, $product(-1, f)), 0) & $lesseq($sum(f, $product(-1, J)), 0) & ($sum(tb2t(get1(int, t2tb1(A), f)), $product(-1, R)) = 0)))) <=> (termination(I, J, I0, J0, R, A) <=> (((~$greatereq($sum(I0, $product(-1, I)), 0)) & (~$lesseq($sum(J0, $product(-1, J)), 0))) | ($greatereq($sum(f, $product(-1, I)), 0) & $lesseq($sum(f, $product(-1, J)), 0) & ($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0)))))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(121,plain,
% 0.81/0.81 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$lesseq($sum(I, $product(-1, I0)), 0)) & (~$lesseq($sum(J0, $product(-1, J)), 0))) | ($lesseq($sum(I, $product(-1, f)), 0) & $lesseq($sum(f, $product(-1, J)), 0) & ($sum(tb2t(get1(int, t2tb1(A), f)), $product(-1, R)) = 0)))) <=> ![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$greatereq($sum(I0, $product(-1, I)), 0)) & (~$lesseq($sum(J0, $product(-1, J)), 0))) | ($greatereq($sum(f, $product(-1, I)), 0) & $lesseq($sum(f, $product(-1, J)), 0) & ($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))),
% 0.81/0.82 inference(quant_intro,[status(thm)],[120])).
% 0.81/0.82 tff(122,plain,
% 0.81/0.82 (^[I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : rewrite((termination(I, J, I0, J0, R, A) <=> (((~$lesseq(I, I0)) & (~$lesseq(J0, J))) | ($lesseq(I, f) & $lesseq(f, J) & (tb2t(get1(int, t2tb1(A), f)) = R)))) <=> (termination(I, J, I0, J0, R, A) <=> (((~$lesseq($sum(I, $product(-1, I0)), 0)) & (~$lesseq($sum(J0, $product(-1, J)), 0))) | ($lesseq($sum(I, $product(-1, f)), 0) & $lesseq($sum(f, $product(-1, J)), 0) & ($sum(tb2t(get1(int, t2tb1(A), f)), $product(-1, R)) = 0)))))),
% 0.81/0.82 inference(bind,[status(th)],[])).
% 0.81/0.82 tff(123,plain,
% 0.81/0.82 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$lesseq(I, I0)) & (~$lesseq(J0, J))) | ($lesseq(I, f) & $lesseq(f, J) & (tb2t(get1(int, t2tb1(A), f)) = R)))) <=> ![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$lesseq($sum(I, $product(-1, I0)), 0)) & (~$lesseq($sum(J0, $product(-1, J)), 0))) | ($lesseq($sum(I, $product(-1, f)), 0) & $lesseq($sum(f, $product(-1, J)), 0) & ($sum(tb2t(get1(int, t2tb1(A), f)), $product(-1, R)) = 0))))),
% 0.81/0.82 inference(quant_intro,[status(thm)],[122])).
% 0.81/0.82 tff(124,plain,
% 0.81/0.82 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$lesseq(I, I0)) & (~$lesseq(J0, J))) | ($lesseq(I, f) & $lesseq(f, J) & (tb2t(get1(int, t2tb1(A), f)) = R)))) <=> ![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$lesseq(I, I0)) & (~$lesseq(J0, J))) | ($lesseq(I, f) & $lesseq(f, J) & (tb2t(get1(int, t2tb1(A), f)) = R))))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(125,plain,
% 0.81/0.82 (^[I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : rewrite((termination(I, J, I0, J0, R, A) <=> (($less(I0, I) & $less(J, J0)) | (($lesseq(I, f) & $lesseq(f, J)) & (tb2t(get1(int, t2tb1(A), f)) = R)))) <=> (termination(I, J, I0, J0, R, A) <=> (((~$lesseq(I, I0)) & (~$lesseq(J0, J))) | ($lesseq(I, f) & $lesseq(f, J) & (tb2t(get1(int, t2tb1(A), f)) = R)))))),
% 0.81/0.82 inference(bind,[status(th)],[])).
% 0.81/0.82 tff(126,plain,
% 0.81/0.82 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (($less(I0, I) & $less(J, J0)) | (($lesseq(I, f) & $lesseq(f, J)) & (tb2t(get1(int, t2tb1(A), f)) = R)))) <=> ![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$lesseq(I, I0)) & (~$lesseq(J0, J))) | ($lesseq(I, f) & $lesseq(f, J) & (tb2t(get1(int, t2tb1(A), f)) = R))))),
% 0.81/0.82 inference(quant_intro,[status(thm)],[125])).
% 0.81/0.82 tff(127,axiom,(![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (($less(I0, I) & $less(J, J0)) | (($lesseq(I, f) & $lesseq(f, J)) & (tb2t(get1(int, t2tb1(A), f)) = R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','termination_def')).
% 0.81/0.82 tff(128,plain,
% 0.81/0.82 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$lesseq(I, I0)) & (~$lesseq(J0, J))) | ($lesseq(I, f) & $lesseq(f, J) & (tb2t(get1(int, t2tb1(A), f)) = R))))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.81/0.82 tff(129,plain,
% 0.81/0.82 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$lesseq(I, I0)) & (~$lesseq(J0, J))) | ($lesseq(I, f) & $lesseq(f, J) & (tb2t(get1(int, t2tb1(A), f)) = R))))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.81/0.82 tff(130,plain,
% 0.81/0.82 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$lesseq($sum(I, $product(-1, I0)), 0)) & (~$lesseq($sum(J0, $product(-1, J)), 0))) | ($lesseq($sum(I, $product(-1, f)), 0) & $lesseq($sum(f, $product(-1, J)), 0) & ($sum(tb2t(get1(int, t2tb1(A), f)), $product(-1, R)) = 0))))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[129, 123])).
% 0.81/0.82 tff(131,plain,
% 0.81/0.82 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$greatereq($sum(I0, $product(-1, I)), 0)) & (~$lesseq($sum(J0, $product(-1, J)), 0))) | ($greatereq($sum(f, $product(-1, I)), 0) & $lesseq($sum(f, $product(-1, J)), 0) & ($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[130, 121])).
% 0.81/0.82 tff(132,plain,(
% 0.81/0.82 ![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> (((~$greatereq($sum(I0, $product(-1, I)), 0)) & (~$lesseq($sum(J0, $product(-1, J)), 0))) | ($greatereq($sum(f, $product(-1, I)), 0) & $lesseq($sum(f, $product(-1, J)), 0) & ($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))),
% 0.81/0.82 inference(skolemize,[status(sab)],[131])).
% 0.81/0.82 tff(133,plain,
% 0.81/0.82 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[132, 119])).
% 0.81/0.82 tff(134,plain,
% 0.81/0.82 (![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[133, 117])).
% 0.81/0.82 tff(135,plain,
% 0.81/0.82 ((~![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))) | (termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))))))),
% 0.81/0.82 inference(quant_inst,[status(thm)],[])).
% 0.81/0.82 tff(136,plain,
% 0.81/0.82 (termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)))))),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.81/0.82 tff(137,plain,
% 0.81/0.82 (~termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))),
% 0.81/0.82 inference(or_elim,[status(thm)],[66])).
% 0.81/0.82 tff(138,plain,
% 0.81/0.82 ((~(termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))))))) | termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) | (~((~($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))))))),
% 0.81/0.82 inference(tautology,[status(thm)],[])).
% 0.81/0.82 tff(139,plain,
% 0.81/0.82 ((~(termination(I1!25, J2!27, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))))))) | (~((~($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))))))),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.81/0.82 tff(140,plain,
% 0.81/0.82 (~((~($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)))))),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[139, 136])).
% 0.81/0.82 tff(141,plain,
% 0.81/0.82 (((~($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))))) | ($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))),
% 0.81/0.82 inference(tautology,[status(thm)],[])).
% 0.81/0.82 tff(142,plain,
% 0.81/0.82 ($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.81/0.82 tff(143,plain,
% 0.81/0.82 ((~($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | $lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0)),
% 0.81/0.82 inference(tautology,[status(thm)],[])).
% 0.81/0.82 tff(144,plain,
% 0.81/0.82 ($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.81/0.82 tff(145,plain,
% 0.81/0.82 ($greatereq($sum(M!20, $product(-1, I1!25)), 0)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[144, 115])).
% 0.81/0.82 tff(146,plain,
% 0.81/0.82 (($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0)) | (~$greatereq($sum(M!20, $product(-1, I1!25)), 0))),
% 0.81/0.82 inference(tautology,[status(thm)],[])).
% 0.81/0.82 tff(147,plain,
% 0.81/0.82 ($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.81/0.82 tff(148,plain,
% 0.81/0.82 (((~![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))) | (termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0))))))) <=> ((~![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))) | (termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)))))))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(149,plain,
% 0.81/0.83 ((termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)))))) <=> (termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0))))))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(150,plain,
% 0.81/0.83 (((~![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))) | (termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))))))) <=> ((~![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))) | (termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)))))))),
% 0.81/0.83 inference(monotonicity,[status(thm)],[149])).
% 0.81/0.83 tff(151,plain,
% 0.81/0.83 (((~![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))) | (termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))))))) <=> ((~![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))) | (termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)))))))),
% 0.81/0.83 inference(transitivity,[status(thm)],[150, 148])).
% 0.81/0.83 tff(152,plain,
% 0.81/0.83 ((~![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))) | (termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))))))),
% 0.81/0.83 inference(quant_inst,[status(thm)],[])).
% 0.81/0.83 tff(153,plain,
% 0.81/0.83 ((~![I: $int, J: $int, I0: $int, J0: $int, R: $int, A: array_int] : (termination(I, J, I0, J0, R, A) <=> ((~($lesseq($sum(J0, $product(-1, J)), 0) | $greatereq($sum(I0, $product(-1, I)), 0))) | (~((~$greatereq($sum(f, $product(-1, I)), 0)) | (~$lesseq($sum(f, $product(-1, J)), 0)) | (~($sum(R, $product(-1, tb2t(get1(int, t2tb1(A), f)))) = 0))))))) | (termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0))))))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.81/0.83 tff(154,plain,
% 0.81/0.83 (termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)))))),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[153, 134])).
% 0.81/0.83 tff(155,plain,
% 0.81/0.83 (termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))),
% 0.81/0.83 inference(and_elim,[status(thm)],[64])).
% 0.81/0.83 tff(156,plain,
% 0.81/0.83 ((~(termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0))))))) | (~termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22))))) | ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)))))),
% 0.81/0.83 inference(tautology,[status(thm)],[])).
% 0.81/0.83 tff(157,plain,
% 0.81/0.83 ((~(termination(I1!25, J1!26, M!20, N!21, tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) <=> ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0))))))) | ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)))))),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.81/0.83 tff(158,plain,
% 0.81/0.83 ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0))))),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[157, 154])).
% 0.81/0.83 tff(159,plain,
% 0.81/0.83 ((~((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)))))) | (~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0))))),
% 0.81/0.83 inference(tautology,[status(thm)],[])).
% 0.81/0.83 tff(160,plain,
% 0.81/0.83 ((~($lesseq($sum(N!21, $product(-1, J1!26)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0))))),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.81/0.83 tff(161,plain,
% 0.81/0.83 (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)))),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[160, 147])).
% 0.81/0.83 tff(162,plain,
% 0.81/0.83 (((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0))) | ($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)),
% 0.81/0.83 inference(tautology,[status(thm)],[])).
% 0.81/0.83 tff(163,plain,
% 0.81/0.83 ($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.81/0.84 tff(164,plain,
% 0.81/0.84 ((~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | $lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))), 0)),
% 0.81/0.84 inference(theory_lemma,[status(thm)],[])).
% 0.81/0.84 tff(165,plain,
% 0.81/0.84 ($lesseq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))), 0)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.81/0.84 tff(166,plain,
% 0.81/0.84 ((~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | $greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))), 0)),
% 0.81/0.84 inference(theory_lemma,[status(thm)],[])).
% 0.81/0.84 tff(167,plain,
% 0.81/0.84 ($greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))), 0)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[166, 163])).
% 0.81/0.84 tff(168,plain,
% 0.81/0.84 (tb2t(get(int, int, t2tb2(A2!19), t2tb(f))) = tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f))),
% 0.81/0.84 inference(theory_lemma,[status(thm)],[167, 165])).
% 0.81/0.84 tff(169,plain,
% 0.81/0.84 (tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)) = tb2t(get(int, int, t2tb2(A2!19), t2tb(f)))),
% 0.81/0.84 inference(symmetry,[status(thm)],[168])).
% 0.81/0.84 tff(170,plain,
% 0.81/0.84 (t2tb(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f))) = t2tb(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))))),
% 0.81/0.84 inference(monotonicity,[status(thm)],[169])).
% 0.81/0.84 tff(171,plain,
% 0.81/0.84 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f))) = get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f))),
% 0.81/0.84 inference(quant_inst,[status(thm)],[])).
% 0.81/0.84 tff(172,plain,
% 0.81/0.84 (t2tb(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f))) = get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[171, 6])).
% 0.81/0.84 tff(173,plain,
% 0.81/0.84 (get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f) = t2tb(tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))),
% 0.81/0.84 inference(symmetry,[status(thm)],[172])).
% 0.81/0.84 tff(174,plain,
% 0.81/0.84 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.81/0.84 inference(rewrite,[status(thm)],[])).
% 0.81/0.84 tff(175,plain,
% 0.81/0.84 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.81/0.84 inference(rewrite,[status(thm)],[])).
% 0.81/0.84 tff(176,axiom,(![J: uni] : (t2tb1(tb2t1(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR1')).
% 0.81/0.84 tff(177,plain,
% 0.81/0.84 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.81/0.84 tff(178,plain,(
% 0.81/0.84 ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.81/0.84 inference(skolemize,[status(sab)],[177])).
% 0.81/0.84 tff(179,plain,
% 0.81/0.84 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.81/0.84 tff(180,plain,
% 0.81/0.84 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) = mk_array(int, A!18, t2tb2(A3!22)))),
% 0.81/0.84 inference(quant_inst,[status(thm)],[])).
% 0.81/0.84 tff(181,plain,
% 0.81/0.84 (t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))) = mk_array(int, A!18, t2tb2(A3!22))),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.81/0.84 tff(182,plain,
% 0.81/0.84 (mk_array(int, A!18, t2tb2(A3!22)) = t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22))))),
% 0.81/0.84 inference(symmetry,[status(thm)],[181])).
% 0.81/0.84 tff(183,plain,
% 0.81/0.84 (get1(int, mk_array(int, A!18, t2tb2(A3!22)), f) = get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)),
% 0.81/0.84 inference(monotonicity,[status(thm)],[182])).
% 0.81/0.84 tff(184,plain,
% 0.81/0.84 (^[A: ty, A1: uni, I: $int] : refl((get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))))),
% 0.81/0.84 inference(bind,[status(th)],[])).
% 0.81/0.84 tff(185,plain,
% 0.81/0.84 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.81/0.84 inference(quant_intro,[status(thm)],[184])).
% 0.81/0.84 tff(186,plain,
% 0.81/0.84 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.81/0.84 inference(rewrite,[status(thm)],[])).
% 0.81/0.84 tff(187,axiom,(![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','get_def')).
% 0.81/0.84 tff(188,plain,
% 0.81/0.84 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.81/0.84 tff(189,plain,(
% 0.81/0.84 ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.81/0.84 inference(skolemize,[status(sab)],[188])).
% 0.81/0.84 tff(190,plain,
% 0.81/0.84 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.81/0.84 tff(191,plain,
% 0.81/0.84 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(int, mk_array(int, A!18, t2tb2(A3!22)), f) = get(int, int, elts(int, mk_array(int, A!18, t2tb2(A3!22))), t2tb(f)))),
% 0.81/0.84 inference(quant_inst,[status(thm)],[])).
% 0.81/0.84 tff(192,plain,
% 0.81/0.84 (get1(int, mk_array(int, A!18, t2tb2(A3!22)), f) = get(int, int, elts(int, mk_array(int, A!18, t2tb2(A3!22))), t2tb(f))),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.81/0.84 tff(193,plain,
% 0.81/0.84 (get(int, int, elts(int, mk_array(int, A!18, t2tb2(A3!22))), t2tb(f)) = get1(int, mk_array(int, A!18, t2tb2(A3!22)), f)),
% 0.81/0.84 inference(symmetry,[status(thm)],[192])).
% 0.81/0.84 tff(194,plain,
% 0.81/0.84 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(t2tb(f))) = t2tb(f))),
% 0.81/0.84 inference(quant_inst,[status(thm)],[])).
% 0.81/0.84 tff(195,plain,
% 0.81/0.84 (t2tb(tb2t(t2tb(f))) = t2tb(f)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[194, 6])).
% 0.81/0.84 tff(196,plain,
% 0.81/0.84 (get(int, int, elts(int, mk_array(int, A!18, t2tb2(A3!22))), t2tb(tb2t(t2tb(f)))) = get(int, int, elts(int, mk_array(int, A!18, t2tb2(A3!22))), t2tb(f))),
% 0.81/0.84 inference(monotonicity,[status(thm)],[195])).
% 0.81/0.84 tff(197,plain,
% 0.81/0.84 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(int, mk_array(int, A!18, t2tb2(A3!22)), tb2t(t2tb(f))) = get(int, int, elts(int, mk_array(int, A!18, t2tb2(A3!22))), t2tb(tb2t(t2tb(f)))))),
% 0.81/0.84 inference(quant_inst,[status(thm)],[])).
% 0.81/0.84 tff(198,plain,
% 0.81/0.84 (get1(int, mk_array(int, A!18, t2tb2(A3!22)), tb2t(t2tb(f))) = get(int, int, elts(int, mk_array(int, A!18, t2tb2(A3!22))), t2tb(tb2t(t2tb(f))))),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[197, 190])).
% 0.81/0.84 tff(199,plain,
% 0.81/0.84 (^[I: $int] : refl(($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0))),
% 0.81/0.84 inference(bind,[status(th)],[])).
% 0.81/0.84 tff(200,plain,
% 0.81/0.84 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.81/0.84 inference(quant_intro,[status(thm)],[199])).
% 0.81/0.84 tff(201,plain,
% 0.81/0.84 (^[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)))),
% 0.81/0.84 inference(bind,[status(th)],[])).
% 0.81/0.84 tff(202,plain,
% 0.81/0.84 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.81/0.84 inference(quant_intro,[status(thm)],[201])).
% 0.81/0.84 tff(203,plain,
% 0.81/0.84 (^[I: $int] : rewrite((tb2t(t2tb(I)) = I) <=> ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0))),
% 0.81/0.84 inference(bind,[status(th)],[])).
% 0.81/0.84 tff(204,plain,
% 0.81/0.84 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.81/0.84 inference(quant_intro,[status(thm)],[203])).
% 0.81/0.84 tff(205,plain,
% 0.81/0.84 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.81/0.84 inference(rewrite,[status(thm)],[])).
% 0.81/0.84 tff(206,axiom,(![I: $int] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeL')).
% 0.81/0.84 tff(207,plain,
% 0.81/0.84 (![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.81/0.84 tff(208,plain,
% 0.81/0.84 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[207, 204])).
% 0.81/0.84 tff(209,plain,
% 0.81/0.84 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[208, 202])).
% 0.81/0.84 tff(210,plain,(
% 0.81/0.84 ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.81/0.84 inference(skolemize,[status(sab)],[209])).
% 0.81/0.84 tff(211,plain,
% 0.81/0.84 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[210, 200])).
% 0.81/0.84 tff(212,plain,
% 0.81/0.84 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(f, $product(-1, tb2t(t2tb(f)))) = 0)),
% 0.81/0.84 inference(quant_inst,[status(thm)],[])).
% 0.81/0.84 tff(213,plain,
% 0.81/0.84 ($sum(f, $product(-1, tb2t(t2tb(f)))) = 0),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.81/0.84 tff(214,plain,
% 0.81/0.84 ((~($sum(f, $product(-1, tb2t(t2tb(f)))) = 0)) | $lesseq($sum(f, $product(-1, tb2t(t2tb(f)))), 0)),
% 0.81/0.84 inference(theory_lemma,[status(thm)],[])).
% 0.81/0.84 tff(215,plain,
% 0.81/0.84 ($lesseq($sum(f, $product(-1, tb2t(t2tb(f)))), 0)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.81/0.84 tff(216,plain,
% 0.81/0.84 ((~($sum(f, $product(-1, tb2t(t2tb(f)))) = 0)) | $greatereq($sum(f, $product(-1, tb2t(t2tb(f)))), 0)),
% 0.81/0.84 inference(theory_lemma,[status(thm)],[])).
% 0.81/0.84 tff(217,plain,
% 0.81/0.84 ($greatereq($sum(f, $product(-1, tb2t(t2tb(f)))), 0)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[216, 213])).
% 0.81/0.84 tff(218,plain,
% 0.81/0.84 (f = tb2t(t2tb(f))),
% 0.81/0.84 inference(theory_lemma,[status(thm)],[217, 215])).
% 0.81/0.84 tff(219,assumption,(f = J1!26), introduced(assumption)).
% 0.81/0.84 tff(220,plain,
% 0.81/0.84 (J1!26 = f),
% 0.81/0.84 inference(symmetry,[status(thm)],[219])).
% 0.81/0.84 tff(221,plain,
% 0.81/0.84 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J1!26, $product(-1, tb2t(t2tb(J1!26)))) = 0)),
% 0.81/0.84 inference(quant_inst,[status(thm)],[])).
% 0.81/0.84 tff(222,plain,
% 0.81/0.84 ($sum(J1!26, $product(-1, tb2t(t2tb(J1!26)))) = 0),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[221, 211])).
% 0.81/0.84 tff(223,plain,
% 0.81/0.84 ((~($sum(J1!26, $product(-1, tb2t(t2tb(J1!26)))) = 0)) | $lesseq($sum(J1!26, $product(-1, tb2t(t2tb(J1!26)))), 0)),
% 0.81/0.84 inference(theory_lemma,[status(thm)],[])).
% 0.81/0.84 tff(224,plain,
% 0.81/0.84 ($lesseq($sum(J1!26, $product(-1, tb2t(t2tb(J1!26)))), 0)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.81/0.84 tff(225,plain,
% 0.81/0.84 ((~($sum(J1!26, $product(-1, tb2t(t2tb(J1!26)))) = 0)) | $greatereq($sum(J1!26, $product(-1, tb2t(t2tb(J1!26)))), 0)),
% 0.81/0.84 inference(theory_lemma,[status(thm)],[])).
% 0.81/0.84 tff(226,plain,
% 0.81/0.84 ($greatereq($sum(J1!26, $product(-1, tb2t(t2tb(J1!26)))), 0)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[225, 222])).
% 0.81/0.84 tff(227,plain,
% 0.81/0.84 (J1!26 = tb2t(t2tb(J1!26))),
% 0.81/0.84 inference(theory_lemma,[status(thm)],[226, 224])).
% 0.81/0.84 tff(228,plain,
% 0.81/0.84 (tb2t(t2tb(J1!26)) = J1!26),
% 0.81/0.84 inference(symmetry,[status(thm)],[227])).
% 0.81/0.84 tff(229,plain,
% 0.81/0.84 (tb2t(t2tb(J1!26)) = tb2t(t2tb(f))),
% 0.81/0.84 inference(transitivity,[status(thm)],[228, 220, 218])).
% 0.81/0.84 tff(230,plain,
% 0.81/0.84 (get1(int, mk_array(int, A!18, t2tb2(A3!22)), tb2t(t2tb(J1!26))) = get1(int, mk_array(int, A!18, t2tb2(A3!22)), tb2t(t2tb(f)))),
% 0.81/0.84 inference(monotonicity,[status(thm)],[229])).
% 0.81/0.84 tff(231,plain,
% 0.81/0.84 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(int, mk_array(int, A!18, t2tb2(A3!22)), tb2t(t2tb(J1!26))) = get(int, int, elts(int, mk_array(int, A!18, t2tb2(A3!22))), t2tb(tb2t(t2tb(J1!26)))))),
% 0.81/0.84 inference(quant_inst,[status(thm)],[])).
% 0.81/0.84 tff(232,plain,
% 0.81/0.84 (get1(int, mk_array(int, A!18, t2tb2(A3!22)), tb2t(t2tb(J1!26))) = get(int, int, elts(int, mk_array(int, A!18, t2tb2(A3!22))), t2tb(tb2t(t2tb(J1!26))))),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[231, 190])).
% 0.81/0.84 tff(233,plain,
% 0.81/0.85 (get(int, int, elts(int, mk_array(int, A!18, t2tb2(A3!22))), t2tb(tb2t(t2tb(J1!26)))) = get1(int, mk_array(int, A!18, t2tb2(A3!22)), tb2t(t2tb(J1!26)))),
% 0.81/0.85 inference(symmetry,[status(thm)],[232])).
% 0.81/0.85 tff(234,plain,
% 0.81/0.85 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(t2tb(J1!26))) = t2tb(J1!26))),
% 0.81/0.85 inference(quant_inst,[status(thm)],[])).
% 0.81/0.85 tff(235,plain,
% 0.81/0.85 (t2tb(tb2t(t2tb(J1!26))) = t2tb(J1!26)),
% 0.81/0.85 inference(unit_resolution,[status(thm)],[234, 6])).
% 0.81/0.85 tff(236,plain,
% 0.81/0.85 (t2tb(J1!26) = t2tb(tb2t(t2tb(J1!26)))),
% 0.81/0.85 inference(symmetry,[status(thm)],[235])).
% 0.81/0.85 tff(237,plain,
% 0.81/0.85 (^[X: map_int_int] : refl(sort(map(int, int), t2tb2(X)) <=> sort(map(int, int), t2tb2(X)))),
% 0.81/0.85 inference(bind,[status(th)],[])).
% 0.81/0.85 tff(238,plain,
% 0.81/0.85 (![X: map_int_int] : sort(map(int, int), t2tb2(X)) <=> ![X: map_int_int] : sort(map(int, int), t2tb2(X))),
% 0.81/0.85 inference(quant_intro,[status(thm)],[237])).
% 0.81/0.85 tff(239,plain,
% 0.81/0.85 (![X: map_int_int] : sort(map(int, int), t2tb2(X)) <=> ![X: map_int_int] : sort(map(int, int), t2tb2(X))),
% 0.81/0.85 inference(rewrite,[status(thm)],[])).
% 0.81/0.85 tff(240,axiom,(![X: map_int_int] : sort(map(int, int), t2tb2(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2tb_sort2')).
% 0.81/0.85 tff(241,plain,
% 0.81/0.85 (![X: map_int_int] : sort(map(int, int), t2tb2(X))),
% 0.81/0.85 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.81/0.85 tff(242,plain,(
% 0.81/0.85 ![X: map_int_int] : sort(map(int, int), t2tb2(X))),
% 0.81/0.85 inference(skolemize,[status(sab)],[241])).
% 0.81/0.85 tff(243,plain,
% 0.81/0.85 (![X: map_int_int] : sort(map(int, int), t2tb2(X))),
% 0.81/0.85 inference(modus_ponens,[status(thm)],[242, 238])).
% 0.81/0.85 tff(244,plain,
% 0.81/0.85 ((~![X: map_int_int] : sort(map(int, int), t2tb2(X))) | sort(map(int, int), t2tb2(A3!22))),
% 0.81/0.85 inference(quant_inst,[status(thm)],[])).
% 0.81/0.85 tff(245,plain,
% 0.81/0.85 (sort(map(int, int), t2tb2(A3!22))),
% 0.81/0.85 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.81/0.85 tff(246,plain,
% 0.81/0.85 (^[A: ty, U: $int, U1: uni] : refl(((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)))),
% 0.81/0.85 inference(bind,[status(th)],[])).
% 0.81/0.85 tff(247,plain,
% 0.81/0.85 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.81/0.85 inference(quant_intro,[status(thm)],[246])).
% 0.81/0.85 tff(248,plain,
% 0.81/0.85 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.81/0.85 inference(rewrite,[status(thm)],[])).
% 0.81/0.85 tff(249,plain,
% 0.81/0.85 (^[A: ty, U: $int, U1: uni] : rewrite((sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1)) <=> ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)))),
% 0.81/0.85 inference(bind,[status(th)],[])).
% 0.81/0.85 tff(250,plain,
% 0.81/0.85 (![A: ty, U: $int, U1: uni] : (sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.81/0.85 inference(quant_intro,[status(thm)],[249])).
% 0.81/0.85 tff(251,axiom,(![A: ty, U: $int, U1: uni] : (sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','elts_def')).
% 0.81/0.85 tff(252,plain,
% 0.81/0.85 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.81/0.85 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.81/0.85 tff(253,plain,
% 0.81/0.85 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.81/0.85 inference(modus_ponens,[status(thm)],[252, 248])).
% 0.81/0.85 tff(254,plain,(
% 0.81/0.85 ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.81/0.85 inference(skolemize,[status(sab)],[253])).
% 0.81/0.85 tff(255,plain,
% 0.81/0.85 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.81/0.85 inference(modus_ponens,[status(thm)],[254, 247])).
% 0.81/0.85 tff(256,plain,
% 0.81/0.85 (((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | ((~sort(map(int, int), t2tb2(A3!22))) | (elts(int, mk_array(int, A!18, t2tb2(A3!22))) = t2tb2(A3!22)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | (~sort(map(int, int), t2tb2(A3!22))) | (elts(int, mk_array(int, A!18, t2tb2(A3!22))) = t2tb2(A3!22)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(257,plain,
% 0.84/0.85 ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | ((~sort(map(int, int), t2tb2(A3!22))) | (elts(int, mk_array(int, A!18, t2tb2(A3!22))) = t2tb2(A3!22)))),
% 0.84/0.85 inference(quant_inst,[status(thm)],[])).
% 0.84/0.85 tff(258,plain,
% 0.84/0.85 ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | (~sort(map(int, int), t2tb2(A3!22))) | (elts(int, mk_array(int, A!18, t2tb2(A3!22))) = t2tb2(A3!22))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.84/0.85 tff(259,plain,
% 0.84/0.85 ((~sort(map(int, int), t2tb2(A3!22))) | (elts(int, mk_array(int, A!18, t2tb2(A3!22))) = t2tb2(A3!22))),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[258, 255])).
% 0.84/0.85 tff(260,plain,
% 0.84/0.85 (elts(int, mk_array(int, A!18, t2tb2(A3!22))) = t2tb2(A3!22)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[259, 245])).
% 0.84/0.85 tff(261,plain,
% 0.84/0.85 (t2tb2(A3!22) = elts(int, mk_array(int, A!18, t2tb2(A3!22)))),
% 0.84/0.85 inference(symmetry,[status(thm)],[260])).
% 0.84/0.85 tff(262,plain,
% 0.84/0.85 (get(int, int, t2tb2(A3!22), t2tb(J1!26)) = get(int, int, elts(int, mk_array(int, A!18, t2tb2(A3!22))), t2tb(tb2t(t2tb(J1!26))))),
% 0.84/0.85 inference(monotonicity,[status(thm)],[261, 236])).
% 0.84/0.85 tff(263,plain,
% 0.84/0.85 (get(int, int, t2tb2(A3!22), t2tb(J1!26)) = get(int, int, t2tb2(A2!19), t2tb(f))),
% 0.84/0.85 inference(transitivity,[status(thm)],[262, 233, 230, 198, 196, 193, 183, 173, 170, 8])).
% 0.84/0.85 tff(264,plain,
% 0.84/0.85 (tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))) = tb2t(get(int, int, t2tb2(A2!19), t2tb(f)))),
% 0.84/0.85 inference(monotonicity,[status(thm)],[263])).
% 0.84/0.85 tff(265,plain,
% 0.84/0.85 (tb2t(get(int, int, t2tb2(A2!19), t2tb(f))) = tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26)))),
% 0.84/0.85 inference(symmetry,[status(thm)],[264])).
% 0.84/0.85 tff(266,plain,
% 0.84/0.85 (~$greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)),
% 0.84/0.85 inference(and_elim,[status(thm)],[64])).
% 0.84/0.85 tff(267,plain,
% 0.84/0.85 ((~(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))) = tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))) | $greatereq($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))), 0)),
% 0.84/0.85 inference(theory_lemma,[status(thm)],[])).
% 0.84/0.85 tff(268,plain,
% 0.84/0.85 (~(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))) = tb2t(get(int, int, t2tb2(A3!22), t2tb(J1!26))))),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[267, 266])).
% 0.84/0.85 tff(269,plain,
% 0.84/0.85 ($false),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[268, 265])).
% 0.84/0.85 tff(270,plain,(~(f = J1!26)), inference(lemma,lemma(discharge,[]))).
% 0.84/0.85 tff(271,plain,
% 0.84/0.85 (((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0))) | $lesseq($sum(f, $product(-1, J1!26)), 0)),
% 0.84/0.85 inference(tautology,[status(thm)],[])).
% 0.84/0.85 tff(272,plain,
% 0.84/0.85 ($lesseq($sum(f, $product(-1, J1!26)), 0)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[271, 161])).
% 0.84/0.85 tff(273,plain,
% 0.84/0.85 ((f = J1!26) | (~$lesseq($sum(f, $product(-1, J1!26)), 0)) | (~$greatereq($sum(f, $product(-1, J1!26)), 0))),
% 0.84/0.85 inference(theory_lemma,[status(thm)],[])).
% 0.84/0.85 tff(274,plain,
% 0.84/0.85 ((f = J1!26) | (~$greatereq($sum(f, $product(-1, J1!26)), 0))),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[273, 272])).
% 0.84/0.85 tff(275,plain,
% 0.84/0.85 (~$greatereq($sum(f, $product(-1, J1!26)), 0)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[274, 270])).
% 0.84/0.85 tff(276,plain,
% 0.84/0.85 ((~($sum(J1!26, $product(-1, J2!27)) = 1)) | $lesseq($sum(J1!26, $product(-1, J2!27)), 1)),
% 0.84/0.85 inference(theory_lemma,[status(thm)],[])).
% 0.84/0.85 tff(277,plain,
% 0.84/0.85 ($lesseq($sum(J1!26, $product(-1, J2!27)), 1)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[276, 67])).
% 0.84/0.85 tff(278,plain,
% 0.84/0.85 (((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)) | (~$lesseq($sum(f, $product(-1, J1!26)), 0))) | $greatereq($sum(f, $product(-1, I1!25)), 0)),
% 0.84/0.86 inference(tautology,[status(thm)],[])).
% 0.84/0.86 tff(279,plain,
% 0.84/0.86 ($greatereq($sum(f, $product(-1, I1!25)), 0)),
% 0.84/0.86 inference(unit_resolution,[status(thm)],[278, 161])).
% 0.84/0.86 tff(280,plain,
% 0.84/0.86 (((~($lesseq($sum(N!21, $product(-1, J2!27)), 0) | $greatereq($sum(M!20, $product(-1, I1!25)), 0))) | (~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))))) | ((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)))),
% 0.84/0.86 inference(tautology,[status(thm)],[])).
% 0.84/0.86 tff(281,plain,
% 0.84/0.86 ((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))),
% 0.84/0.86 inference(unit_resolution,[status(thm)],[280, 140])).
% 0.84/0.86 tff(282,plain,
% 0.84/0.86 ((~((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0)))) | (~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))),
% 0.84/0.86 inference(tautology,[status(thm)],[])).
% 0.84/0.86 tff(283,plain,
% 0.84/0.86 ((~$greatereq($sum(f, $product(-1, I1!25)), 0)) | (~$lesseq($sum(f, $product(-1, J2!27)), 0)) | (~($sum(tb2t(get(int, int, t2tb2(A2!19), t2tb(f))), $product(-1, tb2t(get1(int, t2tb1(tb2t1(mk_array(int, A!18, t2tb2(A3!22)))), f)))) = 0))),
% 0.84/0.86 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.84/0.86 tff(284,plain,
% 0.84/0.86 (~$lesseq($sum(f, $product(-1, J2!27)), 0)),
% 0.84/0.86 inference(unit_resolution,[status(thm)],[283, 279, 163])).
% 0.84/0.86 tff(285,plain,
% 0.84/0.86 ($false),
% 0.84/0.86 inference(theory_lemma,[status(thm)],[284, 277, 275])).
% 0.84/0.86 % SZS output end Proof
%------------------------------------------------------------------------------