TSTP Solution File: SWW584_2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW584_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 20:59:21 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW584_2 : TPTP v8.1.0. Released v6.1.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 20:12:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(tptp_fun_J_5_type, type, (
% 0.21/0.44 tptp_fun_J_5: $int)).
% 0.21/0.44 tff(tptp_fun_I_1_type, type, (
% 0.21/0.44 tptp_fun_I_1: $int)).
% 0.21/0.44 tff(tptp_fun_A_3_type, type, (
% 0.21/0.44 tptp_fun_A_3: $int)).
% 0.21/0.44 tff(tb2t_type, type, (
% 0.21/0.44 tb2t: uni > $int)).
% 0.21/0.44 tff(get_type, type, (
% 0.21/0.44 get: ( ty * ty * uni * uni ) > uni)).
% 0.21/0.44 tff(t2tb_type, type, (
% 0.21/0.44 t2tb: $int > uni)).
% 0.21/0.44 tff(t2tb2_type, type, (
% 0.21/0.44 t2tb2: map_int_int > uni)).
% 0.21/0.44 tff(tptp_fun_A1_2_type, type, (
% 0.21/0.44 tptp_fun_A1_2: map_int_int)).
% 0.21/0.44 tff(int_type, type, (
% 0.21/0.44 int: ty)).
% 0.21/0.44 tff(tptp_fun_Result_4_type, type, (
% 0.21/0.44 tptp_fun_Result_4: $int)).
% 0.21/0.44 tff(tptp_fun_J_6_type, type, (
% 0.21/0.44 tptp_fun_J_6: $int)).
% 0.21/0.44 tff(decrease11_type, type, (
% 0.21/0.44 decrease11: array_int > $o)).
% 0.21/0.44 tff(tb2t1_type, type, (
% 0.21/0.44 tb2t1: uni > array_int)).
% 0.21/0.44 tff(mk_array1_type, type, (
% 0.21/0.44 mk_array1: ( ty * $int * uni ) > uni)).
% 0.21/0.44 tff(get2_type, type, (
% 0.21/0.44 get2: ( ty * uni * $int ) > uni)).
% 0.21/0.44 tff(t2tb1_type, type, (
% 0.21/0.44 t2tb1: array_int > uni)).
% 0.21/0.44 tff(elts_type, type, (
% 0.21/0.44 elts: ( ty * uni ) > uni)).
% 0.21/0.44 tff(sort1_type, type, (
% 0.21/0.44 sort1: ( ty * uni ) > $o)).
% 0.21/0.44 tff(map_type, type, (
% 0.21/0.44 map: ( ty * ty ) > ty)).
% 0.21/0.44 tff(length1_type, type, (
% 0.21/0.44 length1: ( ty * uni ) > $int)).
% 0.21/0.44 tff(1,assumption,(~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | $lesseq($sum(A!3, $product(-1, Result!4)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))))), introduced(assumption)).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | $lesseq($sum(A!3, $product(-1, Result!4)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0)))) | (~$lesseq($sum(A!3, $product(-1, Result!4)), 0))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (~$lesseq($sum(A!3, $product(-1, Result!4)), 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | $lesseq($sum(A!3, $product(-1, Result!4)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0)))) | (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))) = 0)) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0)) & (~$lesseq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0)) & ($greatereq(I!1, 0) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0))) & (decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq($sum(I!1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))), 0)) & (((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!5)), 0) & (~$lesseq($sum(A!3, $product(-1, J!5)), 0))))))) & ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!6)), 0) & (~$lesseq($sum(Result!4, $product(-1, J!6)), 0)))))) | $lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (((Result!4 = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, A!3)), 0)))))) | ($lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0) & (~$lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, Result!4)), 0)))))))) & ($greatereq(A!3, 0) & decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq(I!1, 0))) <=> ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))) = 0)) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0)) & (~$lesseq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0)) & $greatereq(I!1, 0) & decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq($sum(I!1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))), 0) & ((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!5)), 0) & (~$lesseq($sum(A!3, $product(-1, J!5)), 0))))))) & ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!6)), 0) & (~$lesseq($sum(Result!4, $product(-1, J!6)), 0)))))) | $lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (((Result!4 = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, A!3)), 0)))))) | ($lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0) & (~$lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, Result!4)), 0))))))) & $greatereq(A!3, 0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 ((~(~($greatereq(A!3, 0) & decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq(I!1, 0)))) <=> ($greatereq(A!3, 0) & decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq(I!1, 0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 ((((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!5)), 0) & (~$greatereq($sum(J!5, $product(-1, A!3)), 0))))))) & ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(~$greatereq($sum(Result!4, $product(-1, A!3)), 0))) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!6)), 0) & (~$lesseq($sum(Result!4, $product(-1, J!6)), 0))))))) & (((Result!4 = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($lesseq($sum(I!1, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))))), 0) & (~$greatereq($sum(J, $product(-1, A!3)), 0)))))) | ($lesseq($sum(I!1, $sum($product(-1, Result!4), tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))))), 0) & (~$greatereq($sum(Result!4, $product(-1, A!3)), 0)) & (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($lesseq($sum(I!1, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))))), 0) & (~$lesseq($sum(Result!4, $product(-1, J)), 0)))))))) <=> (((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!5)), 0) & (~$lesseq($sum(A!3, $product(-1, J!5)), 0))))))) & ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!6)), 0) & (~$lesseq($sum(Result!4, $product(-1, J!6)), 0)))))) | $lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (((Result!4 = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, A!3)), 0)))))) | ($lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0) & (~$lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, Result!4)), 0))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 ((~(~(decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq($sum(I!1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))), 0)))) <=> (decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq($sum(I!1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))), 0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 ((~(~($greatereq(I!1, 0) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0))))) <=> ($greatereq(I!1, 0) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 ((~($greatereq(I!1, 0) & (~$lesseq($sum(A!3, $product(-1, I!1)), 0)))) <=> (~($greatereq(I!1, 0) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 ((~(~($greatereq(I!1, 0) & (~$lesseq($sum(A!3, $product(-1, I!1)), 0))))) <=> (~(~($greatereq(I!1, 0) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[11])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 ((~(~($greatereq(I!1, 0) & (~$lesseq($sum(A!3, $product(-1, I!1)), 0))))) <=> ($greatereq(I!1, 0) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[12, 10])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 ((~$lesseq($sum(A!3, $product(-1, I!1)), 0)) <=> (~$greatereq($sum(I!1, $product(-1, A!3)), 0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))) = 0)) & (~$lesseq($sum(A!3, $product(-1, I!1)), 0)) & (~$lesseq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0)) & (~(~($greatereq(I!1, 0) & (~$lesseq($sum(A!3, $product(-1, I!1)), 0))))) & (~(~(decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq($sum(I!1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))), 0)))) & (((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!5)), 0) & (~$greatereq($sum(J!5, $product(-1, A!3)), 0))))))) & ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(~$greatereq($sum(Result!4, $product(-1, A!3)), 0))) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!6)), 0) & (~$lesseq($sum(Result!4, $product(-1, J!6)), 0))))))) & (((Result!4 = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($lesseq($sum(I!1, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))))), 0) & (~$greatereq($sum(J, $product(-1, A!3)), 0)))))) | ($lesseq($sum(I!1, $sum($product(-1, Result!4), tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))))), 0) & (~$greatereq($sum(Result!4, $product(-1, A!3)), 0)) & (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($lesseq($sum(I!1, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))))), 0) & (~$lesseq($sum(Result!4, $product(-1, J)), 0)))))))) & (~(~($greatereq(A!3, 0) & decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq(I!1, 0))))) <=> ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))) = 0)) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0)) & (~$lesseq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0)) & ($greatereq(I!1, 0) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0))) & (decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq($sum(I!1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))), 0)) & (((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!5)), 0) & (~$lesseq($sum(A!3, $product(-1, J!5)), 0))))))) & ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!6)), 0) & (~$lesseq($sum(Result!4, $product(-1, J!6)), 0)))))) | $lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (((Result!4 = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, A!3)), 0)))))) | ($lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0) & (~$lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, Result!4)), 0)))))))) & ($greatereq(A!3, 0) & decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq(I!1, 0)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[14, 13, 9, 8, 7])).
% 0.21/0.45 tff(16,plain,
% 0.21/0.45 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))) = 0)) & (~$lesseq($sum(A!3, $product(-1, I!1)), 0)) & (~$lesseq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0)) & (~(~($greatereq(I!1, 0) & (~$lesseq($sum(A!3, $product(-1, I!1)), 0))))) & (~(~(decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq($sum(I!1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))), 0)))) & (((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!5)), 0) & (~$greatereq($sum(J!5, $product(-1, A!3)), 0))))))) & ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(~$greatereq($sum(Result!4, $product(-1, A!3)), 0))) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!6)), 0) & (~$lesseq($sum(Result!4, $product(-1, J!6)), 0))))))) & (((Result!4 = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($lesseq($sum(I!1, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))))), 0) & (~$greatereq($sum(J, $product(-1, A!3)), 0)))))) | ($lesseq($sum(I!1, $sum($product(-1, Result!4), tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))))), 0) & (~$greatereq($sum(Result!4, $product(-1, A!3)), 0)) & (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($lesseq($sum(I!1, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))))), 0) & (~$lesseq($sum(Result!4, $product(-1, J)), 0)))))))) & (~(~($greatereq(A!3, 0) & decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq(I!1, 0))))) <=> ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))) = 0)) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0)) & (~$lesseq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0)) & $greatereq(I!1, 0) & decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq($sum(I!1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))), 0) & ((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!5)), 0) & (~$lesseq($sum(A!3, $product(-1, J!5)), 0))))))) & ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!6)), 0) & (~$lesseq($sum(Result!4, $product(-1, J!6)), 0)))))) | $lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (((Result!4 = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, A!3)), 0)))))) | ($lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0) & (~$lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, Result!4)), 0))))))) & $greatereq(A!3, 0))),
% 0.21/0.45 inference(transitivity,[status(thm)],[15, 6])).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 ((~![A: $int, A1: map_int_int, I: $int] : ((tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq($sum(A, $product(-1, I)), 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), 0))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $product(-1, Result)), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0)))))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $sum($product(-1, Result), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0))))))))) | (~($greatereq(A, 0) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq(I, 0))))) <=> (~![A: $int, A1: map_int_int, I: $int] : ((tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq($sum(A, $product(-1, I)), 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), 0))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $product(-1, Result)), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0)))))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $sum($product(-1, Result), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0))))))))) | (~($greatereq(A, 0) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq(I, 0)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 ((~![A: $int, A1: map_int_int, I: $int] : ((tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq($sum(A, $product(-1, I)), 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), 0))) | (~($greatereq(A, 0) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq(I, 0))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))))) | ($lesseq($sum(I, $product(-1, Result)), 0) & (~$lesseq($sum(A, $product(-1, Result)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0)))))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum(tb2t(get(int, int, t2tb2(A1), t2tb(I))), $product(-1, J))), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))))) | ($lesseq($sum(I, $sum(tb2t(get(int, int, t2tb2(A1), t2tb(I))), $product(-1, Result))), 0) & (~$lesseq($sum(A, $product(-1, Result)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum(tb2t(get(int, int, t2tb2(A1), t2tb(I))), $product(-1, J))), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0))))))))))) <=> (~![A: $int, A1: map_int_int, I: $int] : ((tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq($sum(A, $product(-1, I)), 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), 0))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $product(-1, Result)), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0)))))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $sum($product(-1, Result), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0))))))))) | (~($greatereq(A, 0) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq(I, 0)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 ((~![A: $int, A1: map_int_int, I: $int] : ($lesseq(A, I) | (tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, $sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(A, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(A, J)))))) | ($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(Result, J)))))))) | ($lesseq(I, Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(Result, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, A) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, I))))) <=> (~![A: $int, A1: map_int_int, I: $int] : ((tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq($sum(A, $product(-1, I)), 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), 0))) | (~($greatereq(A, 0) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq(I, 0))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))))) | ($lesseq($sum(I, $product(-1, Result)), 0) & (~$lesseq($sum(A, $product(-1, Result)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0)))))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum(tb2t(get(int, int, t2tb2(A1), t2tb(I))), $product(-1, J))), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))))) | ($lesseq($sum(I, $sum(tb2t(get(int, int, t2tb2(A1), t2tb(I))), $product(-1, Result))), 0) & (~$lesseq($sum(A, $product(-1, Result)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum(tb2t(get(int, int, t2tb2(A1), t2tb(I))), $product(-1, J))), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0)))))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 ((~![A: $int, A1: map_int_int, I: $int] : ($lesseq(A, I) | (tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, $sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(A, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(A, J)))))) | ($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(Result, J)))))))) | ($lesseq(I, Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(Result, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, A) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, I))))) <=> (~![A: $int, A1: map_int_int, I: $int] : ($lesseq(A, I) | (tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, $sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(A, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(A, J)))))) | ($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(Result, J)))))))) | ($lesseq(I, Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(Result, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, A) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, I)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 ((~![A: $int, A1: map_int_int, I: $int] : ((($lesseq(0, A) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1))))) & $lesseq(0, I)) => ($less(I, A) => (($lesseq(0, I) & $less(I, A)) => ((~(tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0)) => (($lesseq(0, I) & $less(I, A)) => ($less(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) => (($lesseq(0, I) & $less(I, A)) => ((decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, $sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))))) => ![Result: $int] : ((((Result = $uminus(1)) & ![J: $int] : (($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & $less(J, A)) => (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | ((($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), Result) & $less(Result, A)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0)) & ![J: $int] : (($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & $less(J, Result)) => (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))) => (((Result = $uminus(1)) & ![J: $int] : (($lesseq(I, J) & $less(J, A)) => (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | ((($lesseq(I, Result) & $less(Result, A)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0)) & ![J: $int] : (($lesseq(I, J) & $less(J, Result)) => (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))))))))))))) <=> (~![A: $int, A1: map_int_int, I: $int] : ($lesseq(A, I) | (tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, $sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(A, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(A, J)))))) | ($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(Result, J)))))))) | ($lesseq(I, Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(Result, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, A) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, I)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(22,axiom,(~![A: $int, A1: map_int_int, I: $int] : ((($lesseq(0, A) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1))))) & $lesseq(0, I)) => ($less(I, A) => (($lesseq(0, I) & $less(I, A)) => ((~(tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0)) => (($lesseq(0, I) & $less(I, A)) => ($less(0, tb2t(get(int, int, t2tb2(A1), t2tb(I)))) => (($lesseq(0, I) & $less(I, A)) => ((decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, $sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))))) => ![Result: $int] : ((((Result = $uminus(1)) & ![J: $int] : (($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & $less(J, A)) => (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | ((($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), Result) & $less(Result, A)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0)) & ![J: $int] : (($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & $less(J, Result)) => (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))) => (((Result = $uminus(1)) & ![J: $int] : (($lesseq(I, J) & $less(J, A)) => (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | ((($lesseq(I, Result) & $less(Result, A)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0)) & ![J: $int] : (($lesseq(I, J) & $less(J, Result)) => (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_search_rec')).
% 0.21/0.46 tff(23,plain,
% 0.21/0.46 (~![A: $int, A1: map_int_int, I: $int] : ($lesseq(A, I) | (tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, $sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(A, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(A, J)))))) | ($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(Result, J)))))))) | ($lesseq(I, Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(Result, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, A) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, I))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 (~![A: $int, A1: map_int_int, I: $int] : ($lesseq(A, I) | (tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, $sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(A, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(A, J)))))) | ($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(Result, J)))))))) | ($lesseq(I, Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(Result, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, A) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, I))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 (~![A: $int, A1: map_int_int, I: $int] : ($lesseq(A, I) | (tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, $sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(A, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(A, J)))))) | ($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(Result, J)))))))) | ($lesseq(I, Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(Result, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, A) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, I))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 (~![A: $int, A1: map_int_int, I: $int] : ($lesseq(A, I) | (tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, $sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I))))))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(A, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(A, J)))))) | ($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), J) & (~$lesseq(Result, J)))))))) | ($lesseq(I, Result) & (~$lesseq(A, Result)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~($lesseq(I, J) & (~$lesseq(Result, J)))) | (~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0))))) | (~($lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, A) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $lesseq(0, I))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 (~![A: $int, A1: map_int_int, I: $int] : ((tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq($sum(A, $product(-1, I)), 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), 0))) | (~($greatereq(A, 0) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq(I, 0))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))))) | ($lesseq($sum(I, $product(-1, Result)), 0) & (~$lesseq($sum(A, $product(-1, Result)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0)))))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum(tb2t(get(int, int, t2tb2(A1), t2tb(I))), $product(-1, J))), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))))) | ($lesseq($sum(I, $sum(tb2t(get(int, int, t2tb2(A1), t2tb(I))), $product(-1, Result))), 0) & (~$lesseq($sum(A, $product(-1, Result)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum(tb2t(get(int, int, t2tb2(A1), t2tb(I))), $product(-1, J))), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0))))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 (~![A: $int, A1: map_int_int, I: $int] : ((tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq($sum(A, $product(-1, I)), 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), 0))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $product(-1, Result)), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0)))))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $sum($product(-1, Result), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0))))))))) | (~($greatereq(A, 0) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq(I, 0))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[27, 18])).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 (~![A: $int, A1: map_int_int, I: $int] : ((tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq($sum(A, $product(-1, I)), 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), 0))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $product(-1, Result)), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0)))))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $sum($product(-1, Result), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0))))))))) | (~($greatereq(A, 0) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq(I, 0))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[28, 17])).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 (~![A: $int, A1: map_int_int, I: $int] : ((tb2t(get(int, int, t2tb2(A1), t2tb(I))) = 0) | $lesseq($sum(A, $product(-1, I)), 0) | $lesseq(tb2t(get(int, int, t2tb2(A1), t2tb(I))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~(decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq($sum(I, tb2t(get(int, int, t2tb2(A1), t2tb(I)))), 0))) | ![Result: $int] : (((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $product(-1, Result)), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0)))))) | (~(((Result = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))))) | ($lesseq($sum(I, $sum($product(-1, Result), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$greatereq($sum(Result, $product(-1, A)), 0)) & (tb2t(get(int, int, t2tb2(A1), t2tb(Result))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1), t2tb(J))) = 0)) | (~($lesseq($sum(I, $sum($product(-1, J), tb2t(get(int, int, t2tb2(A1), t2tb(I))))), 0) & (~$lesseq($sum(Result, $product(-1, J)), 0))))))))) | (~($greatereq(A, 0) & decrease11(tb2t1(mk_array1(int, A, t2tb2(A1)))) & $greatereq(I, 0))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[29, 17])).
% 0.21/0.46 tff(31,plain,
% 0.21/0.46 ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))) = 0)) & (~$greatereq($sum(I!1, $product(-1, A!3)), 0)) & (~$lesseq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0)) & $greatereq(I!1, 0) & decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) & $greatereq($sum(I!1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))), 0) & ((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!5)), 0) & (~$lesseq($sum(A!3, $product(-1, J!5)), 0))))))) & ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!6)), 0) & (~$lesseq($sum(Result!4, $product(-1, J!6)), 0)))))) | $lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (((Result!4 = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, A!3)), 0)))))) | ($lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0) & (~$lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, Result!4)), 0))))))) & $greatereq(A!3, 0)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[30, 16])).
% 0.21/0.46 tff(32,plain,
% 0.21/0.46 (~$lesseq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0)),
% 0.21/0.46 inference(and_elim,[status(thm)],[31])).
% 0.21/0.46 tff(33,plain,
% 0.21/0.46 ($greatereq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0) | $lesseq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0)),
% 0.21/0.46 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.46 tff(34,plain,
% 0.21/0.46 ($greatereq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.46 tff(35,plain,
% 0.21/0.46 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | $lesseq($sum(A!3, $product(-1, Result!4)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0)))) | $lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(36,plain,
% 0.21/0.46 ($lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[35, 1])).
% 0.21/0.46 tff(37,plain,
% 0.21/0.46 ($lesseq($sum(I!1, $product(-1, Result!4)), 0) | (~$greatereq(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), 0)) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0))),
% 0.21/0.46 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.46 tff(38,plain,
% 0.21/0.46 ($lesseq($sum(I!1, $product(-1, Result!4)), 0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[37, 36, 34])).
% 0.21/0.46 tff(39,plain,
% 0.21/0.46 (((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!6)), 0) & (~$lesseq($sum(Result!4, $product(-1, J!6)), 0)))))) | $lesseq($sum(A!3, $product(-1, Result!4)), 0)) <=> ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0) | (~$lesseq($sum(I!1, $product(-1, J!6)), 0)))) | $lesseq($sum(A!3, $product(-1, Result!4)), 0))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(40,plain,
% 0.21/0.46 ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!6)), 0) & (~$lesseq($sum(Result!4, $product(-1, J!6)), 0)))))) | $lesseq($sum(A!3, $product(-1, Result!4)), 0)),
% 0.21/0.46 inference(and_elim,[status(thm)],[31])).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 ((~$lesseq($sum(I!1, $product(-1, Result!4)), 0)) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0) | (~$lesseq($sum(I!1, $product(-1, J!6)), 0)))) | $lesseq($sum(A!3, $product(-1, Result!4)), 0)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0) | (~$lesseq($sum(I!1, $product(-1, J!6)), 0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[41, 38, 5, 3])).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0) | (~$lesseq($sum(I!1, $product(-1, J!6)), 0))) | $lesseq($sum(I!1, $product(-1, J!6)), 0)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 ($lesseq($sum(I!1, $product(-1, J!6)), 0)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.21/0.47 tff(45,plain,
% 0.21/0.47 (^[I: $int] : refl(($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.47 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 (^[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)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.47 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 (^[I: $int] : rewrite((tb2t(t2tb(I)) = I) <=> ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.21/0.47 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(52,axiom,(![I: $int] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeL')).
% 0.21/0.47 tff(53,plain,
% 0.21/0.47 (![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.47 tff(54,plain,
% 0.21/0.47 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.21/0.47 tff(55,plain,
% 0.21/0.47 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[54, 48])).
% 0.21/0.47 tff(56,plain,(
% 0.21/0.47 ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.47 inference(skolemize,[status(sab)],[55])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.21/0.47 tff(58,plain,
% 0.21/0.47 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(I!1, $product(-1, tb2t(t2tb(I!1)))) = 0)),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 ($sum(I!1, $product(-1, tb2t(t2tb(I!1)))) = 0),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.21/0.47 tff(60,plain,
% 0.21/0.47 ((~($sum(I!1, $product(-1, tb2t(t2tb(I!1)))) = 0)) | $greatereq($sum(I!1, $product(-1, tb2t(t2tb(I!1)))), 0)),
% 0.21/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.47 tff(61,plain,
% 0.21/0.47 ($greatereq($sum(I!1, $product(-1, tb2t(t2tb(I!1)))), 0)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.21/0.47 tff(62,plain,
% 0.21/0.47 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | $lesseq($sum(A!3, $product(-1, Result!4)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0)))) | ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(63,plain,
% 0.21/0.47 (![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[62, 1])).
% 0.21/0.47 tff(64,plain,
% 0.21/0.47 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0) | (~$lesseq($sum(I!1, $product(-1, J!6)), 0))) | (~$lesseq($sum(Result!4, $product(-1, J!6)), 0))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(65,plain,
% 0.21/0.47 (~$lesseq($sum(Result!4, $product(-1, J!6)), 0)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[64, 42])).
% 0.21/0.47 tff(66,plain,
% 0.21/0.47 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0) | (~$lesseq($sum(I!1, $product(-1, J!6)), 0))) | (tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(67,plain,
% 0.21/0.47 (tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[66, 42])).
% 0.21/0.47 tff(68,plain,
% 0.21/0.47 (((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))) | ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!6))), 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0))) <=> ((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!6))), 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(69,plain,
% 0.21/0.47 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~$greatereq($sum(J!6, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J!6, $product(-1, Result!4)), 0)) <=> ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!6))), 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(70,plain,
% 0.21/0.47 (((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))) | ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~$greatereq($sum(J!6, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J!6, $product(-1, Result!4)), 0))) <=> ((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))) | ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!6))), 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.47 tff(71,plain,
% 0.21/0.47 (((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))) | ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~$greatereq($sum(J!6, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J!6, $product(-1, Result!4)), 0))) <=> ((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!6))), 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0))),
% 0.21/0.47 inference(transitivity,[status(thm)],[70, 68])).
% 0.21/0.47 tff(72,plain,
% 0.21/0.47 ((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))) | ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~$greatereq($sum(J!6, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J!6, $product(-1, Result!4)), 0))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(73,plain,
% 0.21/0.47 ((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = 0)) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!6))), 0)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.47 tff(74,plain,
% 0.21/0.47 (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!6))), 0)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[73, 67, 65, 63])).
% 0.21/0.47 tff(75,plain,
% 0.21/0.47 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(76,plain,
% 0.21/0.47 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(77,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR')).
% 0.21/0.47 tff(78,plain,
% 0.21/0.47 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.47 tff(79,plain,(
% 0.21/0.47 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.47 inference(skolemize,[status(sab)],[78])).
% 0.21/0.47 tff(80,plain,
% 0.21/0.47 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4)))) = get(int, int, t2tb2(A1!2), t2tb(Result!4)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(82,plain,
% 0.21/0.47 (t2tb(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4)))) = get(int, int, t2tb2(A1!2), t2tb(Result!4))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.21/0.47 tff(83,plain,
% 0.21/0.47 (0 = tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4)))),
% 0.21/0.47 inference(symmetry,[status(thm)],[5])).
% 0.21/0.47 tff(84,plain,
% 0.21/0.47 (tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))) = tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[67, 83])).
% 0.21/0.47 tff(85,plain,
% 0.21/0.47 (t2tb(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6)))) = t2tb(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.47 tff(86,plain,
% 0.21/0.47 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6)))) = get(int, int, t2tb2(A1!2), t2tb(J!6)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 (t2tb(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6)))) = get(int, int, t2tb2(A1!2), t2tb(J!6))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[86, 80])).
% 0.21/0.47 tff(88,plain,
% 0.21/0.47 (get(int, int, t2tb2(A1!2), t2tb(J!6)) = t2tb(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!6))))),
% 0.21/0.47 inference(symmetry,[status(thm)],[87])).
% 0.21/0.47 tff(89,plain,
% 0.21/0.47 (^[X: map_int_int] : refl(sort1(map(int, int), t2tb2(X)) <=> sort1(map(int, int), t2tb2(X)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(90,plain,
% 0.21/0.47 (![X: map_int_int] : sort1(map(int, int), t2tb2(X)) <=> ![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.47 tff(91,plain,
% 0.21/0.47 (![X: map_int_int] : sort1(map(int, int), t2tb2(X)) <=> ![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(92,axiom,(![X: map_int_int] : sort1(map(int, int), t2tb2(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2tb_sort2')).
% 0.21/0.47 tff(93,plain,
% 0.21/0.47 (![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.47 tff(94,plain,(
% 0.21/0.47 ![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.21/0.47 inference(skolemize,[status(sab)],[93])).
% 0.21/0.47 tff(95,plain,
% 0.21/0.47 (![X: map_int_int] : sort1(map(int, int), t2tb2(X))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.21/0.47 tff(96,plain,
% 0.21/0.47 ((~![X: map_int_int] : sort1(map(int, int), t2tb2(X))) | sort1(map(int, int), t2tb2(A1!2))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(97,plain,
% 0.21/0.47 (sort1(map(int, int), t2tb2(A1!2))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.21/0.47 tff(98,plain,
% 0.21/0.47 (^[A: ty, U: $int, U1: uni] : refl(((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(99,plain,
% 0.21/0.47 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.47 tff(100,plain,
% 0.21/0.47 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(101,plain,
% 0.21/0.47 (^[A: ty, U: $int, U1: uni] : rewrite((sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(102,plain,
% 0.21/0.47 (![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.47 tff(103,axiom,(![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','elts_def1')).
% 0.21/0.47 tff(104,plain,
% 0.21/0.47 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.47 tff(105,plain,
% 0.21/0.47 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.21/0.47 tff(106,plain,(
% 0.21/0.47 ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.21/0.47 inference(skolemize,[status(sab)],[105])).
% 0.21/0.47 tff(107,plain,
% 0.21/0.47 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.21/0.47 tff(108,plain,
% 0.21/0.47 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(A1!2))) | (elts(int, mk_array1(int, A!3, t2tb2(A1!2))) = t2tb2(A1!2)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(A1!2))) | (elts(int, mk_array1(int, A!3, t2tb2(A1!2))) = t2tb2(A1!2)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(109,plain,
% 0.21/0.47 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, int), t2tb2(A1!2))) | (elts(int, mk_array1(int, A!3, t2tb2(A1!2))) = t2tb2(A1!2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(110,plain,
% 0.21/0.47 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, int), t2tb2(A1!2))) | (elts(int, mk_array1(int, A!3, t2tb2(A1!2))) = t2tb2(A1!2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 ((~sort1(map(int, int), t2tb2(A1!2))) | (elts(int, mk_array1(int, A!3, t2tb2(A1!2))) = t2tb2(A1!2))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[110, 107])).
% 0.21/0.47 tff(112,plain,
% 0.21/0.47 (elts(int, mk_array1(int, A!3, t2tb2(A1!2))) = t2tb2(A1!2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[111, 97])).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 (get(int, int, elts(int, mk_array1(int, A!3, t2tb2(A1!2))), t2tb(J!6)) = get(int, int, t2tb2(A1!2), t2tb(J!6))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[112])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 (^[A: ty, A1: uni, I: $int] : refl((get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[114])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(117,axiom,(![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','get_def')).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.47 tff(119,plain,(
% 0.21/0.47 ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[118])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.21/0.47 tff(121,plain,
% 0.21/0.47 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, A!3, t2tb2(A1!2)), J!6) = get(int, int, elts(int, mk_array1(int, A!3, t2tb2(A1!2))), t2tb(J!6)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 (get2(int, mk_array1(int, A!3, t2tb2(A1!2)), J!6) = get(int, int, elts(int, mk_array1(int, A!3, t2tb2(A1!2))), t2tb(J!6))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(124,plain,
% 0.21/0.47 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(125,axiom,(![J: uni] : (t2tb1(tb2t1(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR1')).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.47 tff(127,plain,(
% 0.21/0.47 ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.47 inference(skolemize,[status(sab)],[126])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) = mk_array1(int, A!3, t2tb2(A1!2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 (t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))) = mk_array1(int, A!3, t2tb2(A1!2))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6) = get2(int, mk_array1(int, A!3, t2tb2(A1!2)), J!6)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[130])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6) = get(int, int, t2tb2(A1!2), t2tb(Result!4))),
% 0.21/0.47 inference(transitivity,[status(thm)],[131, 122, 113, 88, 85, 82])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6)) = tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[132])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6)) = 0),
% 0.21/0.48 inference(transitivity,[status(thm)],[133, 5])).
% 0.21/0.48 tff(135,plain,
% 0.21/0.48 ((~(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6)) = 0)) | $lesseq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6)), 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(136,plain,
% 0.21/0.48 ($lesseq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6)), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.21/0.48 tff(137,assumption,(~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!6))), 0)), introduced(assumption)).
% 0.21/0.48 tff(138,plain,
% 0.21/0.48 (get(int, int, elts(int, mk_array1(int, A!3, t2tb2(A1!2))), t2tb(I!1)) = get(int, int, t2tb2(A1!2), t2tb(I!1))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[112])).
% 0.21/0.48 tff(139,plain,
% 0.21/0.48 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, A!3, t2tb2(A1!2)), I!1) = get(int, int, elts(int, mk_array1(int, A!3, t2tb2(A1!2))), t2tb(I!1)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(140,plain,
% 0.21/0.48 (get2(int, mk_array1(int, A!3, t2tb2(A1!2)), I!1) = get(int, int, elts(int, mk_array1(int, A!3, t2tb2(A1!2))), t2tb(I!1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[139, 120])).
% 0.21/0.48 tff(141,plain,
% 0.21/0.48 ((~($sum(I!1, $product(-1, tb2t(t2tb(I!1)))) = 0)) | $lesseq($sum(I!1, $product(-1, tb2t(t2tb(I!1)))), 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(142,plain,
% 0.21/0.48 ($lesseq($sum(I!1, $product(-1, tb2t(t2tb(I!1)))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[141, 59])).
% 0.21/0.48 tff(143,plain,
% 0.21/0.48 (I!1 = tb2t(t2tb(I!1))),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[61, 142])).
% 0.21/0.48 tff(144,plain,
% 0.21/0.48 (tb2t(t2tb(I!1)) = I!1),
% 0.21/0.48 inference(symmetry,[status(thm)],[143])).
% 0.21/0.48 tff(145,plain,
% 0.21/0.48 (get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))) = get2(int, mk_array1(int, A!3, t2tb2(A1!2)), I!1)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[130, 144])).
% 0.21/0.48 tff(146,plain,
% 0.21/0.48 (get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))) = get(int, int, t2tb2(A1!2), t2tb(I!1))),
% 0.21/0.48 inference(transitivity,[status(thm)],[145, 140, 138])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1)))) = tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[146])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 (tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))),
% 0.21/0.48 inference(symmetry,[status(thm)],[147])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))) = tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1)))))) | $lesseq($sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1)))))), 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 ($lesseq($sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1)))))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.21/0.48 tff(151,assumption,($greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0)), introduced(assumption)).
% 0.21/0.48 tff(152,assumption,($lesseq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6)), 0)), introduced(assumption)).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[152, 151, 142, 150, 137])).
% 0.21/0.48 tff(154,plain,((~$greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0)) | (~$lesseq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6)), 0)) | $lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!6))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 (~$greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[154, 136, 74])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 ($greatereq(I!1, 0)),
% 0.21/0.48 inference(and_elim,[status(thm)],[31])).
% 0.21/0.48 tff(157,plain,
% 0.21/0.48 ($greatereq(tb2t(t2tb(I!1)), 0) | (~$greatereq(I!1, 0)) | (~$lesseq($sum(I!1, $product(-1, tb2t(t2tb(I!1)))), 0))),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 ($greatereq(tb2t(t2tb(I!1)), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[157, 142, 156])).
% 0.21/0.48 tff(159,assumption,(~$lesseq($sum(A!3, $product(-1, Result!4)), 0)), introduced(assumption)).
% 0.21/0.48 tff(160,plain,
% 0.21/0.48 (^[A: ty, U: $int, U1: uni] : refl(($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0) <=> ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.21/0.48 inference(quant_intro,[status(thm)],[160])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 (^[A: ty, U: $int, U1: uni] : trans(monotonicity(rewrite($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = $sum($product(-1, U), length1(A, mk_array1(A, U, U1)))), (($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ($sum($product(-1, U), length1(A, mk_array1(A, U, U1))) = 0))), rewrite(($sum($product(-1, U), length1(A, mk_array1(A, U, U1))) = 0) <=> ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)), (($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(163,plain,
% 0.21/0.48 (![A: ty, U: $int, U1: uni] : ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.21/0.48 inference(quant_intro,[status(thm)],[162])).
% 0.21/0.48 tff(164,plain,
% 0.21/0.48 (^[A: ty, U: $int, U1: uni] : rewrite((length1(A, mk_array1(A, U, U1)) = U) <=> ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(165,plain,
% 0.21/0.48 (![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0)),
% 0.21/0.48 inference(quant_intro,[status(thm)],[164])).
% 0.21/0.48 tff(166,plain,
% 0.21/0.48 (![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(167,axiom,(![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','length_def1')).
% 0.21/0.48 tff(168,plain,
% 0.21/0.48 (![A: ty, U: $int, U1: uni] : (length1(A, mk_array1(A, U, U1)) = U)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.21/0.48 tff(169,plain,
% 0.21/0.48 (![A: ty, U: $int, U1: uni] : ($sum(length1(A, mk_array1(A, U, U1)), $product(-1, U)) = 0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[168, 165])).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[169, 163])).
% 0.21/0.48 tff(171,plain,(
% 0.21/0.48 ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.21/0.48 inference(skolemize,[status(sab)],[170])).
% 0.21/0.48 tff(172,plain,
% 0.21/0.48 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[171, 161])).
% 0.21/0.48 tff(173,plain,
% 0.21/0.48 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length1(A, mk_array1(A, U, U1)))) = 0)) | ($sum(A!3, $product(-1, length1(int, mk_array1(int, A!3, t2tb2(A1!2))))) = 0)),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(174,plain,
% 0.21/0.48 ($sum(A!3, $product(-1, length1(int, mk_array1(int, A!3, t2tb2(A1!2))))) = 0),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.21/0.48 tff(175,plain,
% 0.21/0.48 ((~($sum(A!3, $product(-1, length1(int, mk_array1(int, A!3, t2tb2(A1!2))))) = 0)) | $lesseq($sum(A!3, $product(-1, length1(int, mk_array1(int, A!3, t2tb2(A1!2))))), 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(176,plain,
% 0.21/0.48 ($lesseq($sum(A!3, $product(-1, length1(int, mk_array1(int, A!3, t2tb2(A1!2))))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.21/0.48 tff(177,plain,
% 0.21/0.48 (length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))) = length1(int, mk_array1(int, A!3, t2tb2(A1!2)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[130])).
% 0.21/0.48 tff(178,plain,
% 0.21/0.48 (length1(int, mk_array1(int, A!3, t2tb2(A1!2))) = length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))))),
% 0.21/0.48 inference(symmetry,[status(thm)],[177])).
% 0.21/0.48 tff(179,plain,
% 0.21/0.48 ((~(length1(int, mk_array1(int, A!3, t2tb2(A1!2))) = length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))) | $lesseq($sum(length1(int, mk_array1(int, A!3, t2tb2(A1!2))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(180,plain,
% 0.21/0.48 ($lesseq($sum(length1(int, mk_array1(int, A!3, t2tb2(A1!2))), $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.21/0.48 tff(181,assumption,($greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), -1)), introduced(assumption)).
% 0.21/0.48 tff(182,assumption,(~$lesseq($sum(Result!4, $product(-1, J!6)), 0)), introduced(assumption)).
% 0.21/0.48 tff(183,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[182, 181, 180, 176, 159])).
% 0.21/0.48 tff(184,plain,((~$greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), -1)) | $lesseq($sum(Result!4, $product(-1, J!6)), 0) | $lesseq($sum(A!3, $product(-1, Result!4)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(185,plain,
% 0.21/0.48 (~$greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), -1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[184, 65, 3])).
% 0.21/0.48 tff(186,plain,
% 0.21/0.48 ((~$greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), -1)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(187,plain,
% 0.21/0.48 (~$greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.21/0.48 tff(188,plain,
% 0.21/0.48 (decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))),
% 0.21/0.48 inference(and_elim,[status(thm)],[31])).
% 0.21/0.48 tff(189,plain,
% 0.21/0.48 (^[A: array_int] : refl(((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)))) <=> ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(190,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)))) <=> ![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[189])).
% 0.21/0.48 tff(191,plain,
% 0.21/0.48 (^[A: array_int] : rewrite(((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)))) <=> ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)))) <=> ![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[191])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)))) <=> ![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[192, 190])).
% 0.21/0.48 tff(194,plain,
% 0.21/0.48 (^[A: array_int] : rewrite(((~decrease11(A)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0)))) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0))) <=> ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(195,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0)))) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0))) <=> ![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[194])).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 (^[A: array_int] : rewrite(((~decrease11(A)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(length1(int, t2tb1(A)), $product(-1, J)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $sum($product(-1, J), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0))) <=> ((~decrease11(A)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0)))) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(197,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(length1(int, t2tb1(A)), $product(-1, J)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $sum($product(-1, J), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0))) <=> ![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0)))) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[196])).
% 0.21/0.48 tff(198,plain,
% 0.21/0.48 (^[A: array_int] : rewrite(((~decrease11(A)) | ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J))))) <=> ((~decrease11(A)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(length1(int, t2tb1(A)), $product(-1, J)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $sum($product(-1, J), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(199,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J))))) <=> ![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(length1(int, t2tb1(A)), $product(-1, J)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $sum($product(-1, J), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[198])).
% 0.21/0.48 tff(200,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J))))) <=> ![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(201,plain,
% 0.21/0.48 (^[A: array_int] : trans(monotonicity(quant_intro(proof_bind(^[I: $int, J: $int] : trans(monotonicity(trans(monotonicity(rewrite($less(J, length1(int, t2tb1(A))) <=> (~$lesseq(length1(int, t2tb1(A)), J))), ((($lesseq(0, I) & $lesseq(I, J)) & $less(J, length1(int, t2tb1(A)))) <=> (($lesseq(0, I) & $lesseq(I, J)) & (~$lesseq(length1(int, t2tb1(A)), J))))), rewrite((($lesseq(0, I) & $lesseq(I, J)) & (~$lesseq(length1(int, t2tb1(A)), J))) <=> ($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))), ((($lesseq(0, I) & $lesseq(I, J)) & $less(J, length1(int, t2tb1(A)))) <=> ($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J))))), rewrite($lesseq($difference($sum(tb2t(get2(int, t2tb1(A), I)), I), J), tb2t(get2(int, t2tb1(A), J))) <=> $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J)))), (((($lesseq(0, I) & $lesseq(I, J)) & $less(J, length1(int, t2tb1(A)))) => $lesseq($difference($sum(tb2t(get2(int, t2tb1(A), I)), I), J), tb2t(get2(int, t2tb1(A), J)))) <=> (($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J))) => $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J)))))), rewrite((($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J))) => $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J)))) <=> ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J))))), (((($lesseq(0, I) & $lesseq(I, J)) & $less(J, length1(int, t2tb1(A)))) => $lesseq($difference($sum(tb2t(get2(int, t2tb1(A), I)), I), J), tb2t(get2(int, t2tb1(A), J)))) <=> ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J))))))), (![I: $int, J: $int] : ((($lesseq(0, I) & $lesseq(I, J)) & $less(J, length1(int, t2tb1(A)))) => $lesseq($difference($sum(tb2t(get2(int, t2tb1(A), I)), I), J), tb2t(get2(int, t2tb1(A), J)))) <=> ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J)))))), ((decrease11(A) => ![I: $int, J: $int] : ((($lesseq(0, I) & $lesseq(I, J)) & $less(J, length1(int, t2tb1(A)))) => $lesseq($difference($sum(tb2t(get2(int, t2tb1(A), I)), I), J), tb2t(get2(int, t2tb1(A), J))))) <=> (decrease11(A) => ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J))))))), rewrite((decrease11(A) => ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J))))) <=> ((~decrease11(A)) | ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J)))))), ((decrease11(A) => ![I: $int, J: $int] : ((($lesseq(0, I) & $lesseq(I, J)) & $less(J, length1(int, t2tb1(A)))) => $lesseq($difference($sum(tb2t(get2(int, t2tb1(A), I)), I), J), tb2t(get2(int, t2tb1(A), J))))) <=> ((~decrease11(A)) | ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(202,plain,
% 0.21/0.48 (![A: array_int] : (decrease11(A) => ![I: $int, J: $int] : ((($lesseq(0, I) & $lesseq(I, J)) & $less(J, length1(int, t2tb1(A)))) => $lesseq($difference($sum(tb2t(get2(int, t2tb1(A), I)), I), J), tb2t(get2(int, t2tb1(A), J))))) <=> ![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[201])).
% 0.21/0.48 tff(203,axiom,(![A: array_int] : (decrease11(A) => ![I: $int, J: $int] : ((($lesseq(0, I) & $lesseq(I, J)) & $less(J, length1(int, t2tb1(A)))) => $lesseq($difference($sum(tb2t(get2(int, t2tb1(A), I)), I), J), tb2t(get2(int, t2tb1(A), J)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','decrease1_induction')).
% 0.21/0.48 tff(204,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.21/0.48 tff(205,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($lesseq(0, I) & $lesseq(I, J) & (~$lesseq(length1(int, t2tb1(A)), J)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $product(-1, J))), tb2t(get2(int, t2tb1(A), J)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.21/0.48 tff(206,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, J)), 0) & (~$lesseq($sum(length1(int, t2tb1(A)), $product(-1, J)), 0)))) | $lesseq($sum(tb2t(get2(int, t2tb1(A), I)), $sum(I, $sum($product(-1, J), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[205, 199])).
% 0.21/0.48 tff(207,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0)))) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[206, 197])).
% 0.21/0.48 tff(208,plain,(
% 0.21/0.48 ![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, J)), 0) & (~$greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0)))) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[207])).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[208, 195])).
% 0.21/0.48 tff(210,plain,
% 0.21/0.48 (![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[209, 193])).
% 0.21/0.48 tff(211,plain,
% 0.21/0.48 (((~![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))) | ((~decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))) | ![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0)))) <=> ((~![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))) | (~decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))) | ![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 (((~decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)))) <=> ((~decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))) | ![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(213,plain,
% 0.21/0.49 (((~![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))) | ((~decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))) <=> ((~![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))) | ((~decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))) | ![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[212])).
% 0.21/0.49 tff(214,plain,
% 0.21/0.49 (((~![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))) | ((~decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))) <=> ((~![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))) | (~decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))) | ![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[213, 211])).
% 0.21/0.49 tff(215,plain,
% 0.21/0.49 ((~![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))) | ((~decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I)), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(216,plain,
% 0.21/0.49 ((~![A: array_int] : ((~decrease11(A)) | ![I: $int, J: $int] : ($greatereq($sum(J, $product(-1, length1(int, t2tb1(A)))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum(tb2t(get2(int, t2tb1(A), I)), $product(-1, tb2t(get2(int, t2tb1(A), J)))))), 0) | (~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0))))) | (~decrease11(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))) | ![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.21/0.49 tff(217,plain,
% 0.21/0.49 (![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[216, 210, 188])).
% 0.21/0.49 tff(218,plain,
% 0.21/0.49 (((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | ((~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0))) <=> ((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(219,plain,
% 0.21/0.49 (((~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0)) <=> ((~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(220,plain,
% 0.21/0.49 ($lesseq($sum($product(-1, J!6), $sum(tb2t(t2tb(I!1)), $sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1)))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6)))))), 0) <=> $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(221,plain,
% 0.21/0.49 ($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!6), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))) = $sum($product(-1, J!6), $sum(tb2t(t2tb(I!1)), $sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1)))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(222,plain,
% 0.21/0.49 ($lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!6), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0) <=> $lesseq($sum($product(-1, J!6), $sum(tb2t(t2tb(I!1)), $sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1)))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6)))))), 0)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[221])).
% 0.21/0.49 tff(223,plain,
% 0.21/0.49 ($lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!6), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0) <=> $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0)),
% 0.21/0.49 inference(transitivity,[status(thm)],[222, 220])).
% 0.21/0.49 tff(224,plain,
% 0.21/0.49 ((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!6)), 0)) <=> (~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(225,plain,
% 0.21/0.49 (((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!6)), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!6), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0)) <=> ((~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[224, 223])).
% 0.21/0.49 tff(226,plain,
% 0.21/0.49 (((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!6)), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!6), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0)) <=> ((~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0))),
% 0.21/0.49 inference(transitivity,[status(thm)],[225, 219])).
% 0.21/0.49 tff(227,plain,
% 0.21/0.49 (((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | ((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!6)), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!6), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0))) <=> ((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | ((~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[226])).
% 0.21/0.49 tff(228,plain,
% 0.21/0.49 (((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | ((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!6)), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!6), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0))) <=> ((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0))),
% 0.21/0.49 inference(transitivity,[status(thm)],[227, 218])).
% 0.21/0.49 tff(229,plain,
% 0.21/0.49 ((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | ((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!6)), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!6), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(230,plain,
% 0.21/0.49 ((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.21/0.49 tff(231,plain,
% 0.21/0.49 ((~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!6, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!6, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!6))))), 0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[230, 217])).
% 0.21/0.49 tff(232,plain,
% 0.21/0.49 (~$greatereq($sum(J!6, $product(-1, tb2t(t2tb(I!1)))), 0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[231, 187, 158, 155])).
% 0.21/0.49 tff(233,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(theory_lemma,[status(thm)],[232, 61, 44])).
% 0.21/0.49 tff(234,plain,((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | $lesseq($sum(A!3, $product(-1, Result!4)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(235,plain,
% 0.21/0.49 (((~((~(Result!4 = -1)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))))) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | $lesseq($sum(A!3, $product(-1, Result!4)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0)))))) <=> ((~((~(Result!4 = -1)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))))) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | $lesseq($sum(A!3, $product(-1, Result!4)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(236,plain,
% 0.21/0.49 ((((Result!4 = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, A!3)), 0)))))) | ($lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0) & (~$lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, Result!4)), 0))))))) <=> ((~((~(Result!4 = -1)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))))) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | $lesseq($sum(A!3, $product(-1, Result!4)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(237,plain,
% 0.21/0.50 (((Result!4 = -1) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, A!3)), 0)))))) | ($lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0) & (~$lesseq($sum(A!3, $product(-1, Result!4)), 0)) & (tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0) & ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~($greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0) & (~$greatereq($sum(J, $product(-1, Result!4)), 0))))))),
% 0.21/0.50 inference(and_elim,[status(thm)],[31])).
% 0.21/0.50 tff(238,plain,
% 0.21/0.50 ((~((~(Result!4 = -1)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))))) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | $lesseq($sum(A!3, $product(-1, Result!4)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.21/0.50 tff(239,plain,
% 0.21/0.50 ((~((~(Result!4 = -1)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))))) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(Result!4))) = 0)) | $lesseq($sum(A!3, $product(-1, Result!4)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, Result!4))), 0)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) | $greatereq($sum(J, $product(-1, Result!4)), 0)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[238, 235])).
% 0.21/0.50 tff(240,plain,
% 0.21/0.50 (~((~(Result!4 = -1)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[239, 234])).
% 0.21/0.50 tff(241,plain,
% 0.21/0.50 (((~(Result!4 = -1)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0))))) | (Result!4 = -1)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(242,plain,
% 0.21/0.50 (Result!4 = -1),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.21/0.50 tff(243,plain,
% 0.21/0.50 (((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!5)), 0) & (~$lesseq($sum(A!3, $product(-1, J!5)), 0))))))) <=> ((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $product(-1, J!5)), 0)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(244,plain,
% 0.21/0.50 ((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | (~($lesseq($sum(I!1, $product(-1, J!5)), 0) & (~$lesseq($sum(A!3, $product(-1, J!5)), 0))))))),
% 0.21/0.50 inference(and_elim,[status(thm)],[31])).
% 0.21/0.50 tff(245,plain,
% 0.21/0.50 ((~(Result!4 = -1)) | (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $product(-1, J!5)), 0))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.21/0.50 tff(246,plain,
% 0.21/0.50 (~((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $product(-1, J!5)), 0)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[245, 242])).
% 0.21/0.50 tff(247,plain,
% 0.21/0.50 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $product(-1, J!5)), 0))) | $lesseq($sum(I!1, $product(-1, J!5)), 0)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(248,plain,
% 0.21/0.50 ($lesseq($sum(I!1, $product(-1, J!5)), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[247, 246])).
% 0.21/0.50 tff(249,plain,
% 0.21/0.50 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $product(-1, J!5)), 0))) | (~$lesseq($sum(A!3, $product(-1, J!5)), 0))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(250,plain,
% 0.21/0.50 (~$lesseq($sum(A!3, $product(-1, J!5)), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[249, 246])).
% 0.21/0.50 tff(251,assumption,($greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0)), introduced(assumption)).
% 0.21/0.50 tff(252,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[180, 176, 251, 250])).
% 0.21/0.50 tff(253,plain,(~$greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(254,plain,
% 0.21/0.50 (((~(Result!4 = -1)) | (~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0))))) | ![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(255,plain,
% 0.21/0.50 (![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[254, 240])).
% 0.21/0.50 tff(256,plain,
% 0.21/0.50 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $product(-1, J!5)), 0))) | (tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(257,plain,
% 0.21/0.50 (tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[256, 246])).
% 0.21/0.50 tff(258,plain,
% 0.21/0.50 (((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))) | ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0)))) <=> ((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(259,plain,
% 0.21/0.50 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0))) <=> ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(260,plain,
% 0.21/0.50 ((~$greatereq($sum(J!5, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)) <=> (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(261,plain,
% 0.21/0.50 ($greatereq($sum($product(-1, A!3), J!5), 0) <=> $lesseq($sum(A!3, $product(-1, J!5)), 0)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(262,plain,
% 0.21/0.50 ($sum(J!5, $product(-1, A!3)) = $sum($product(-1, A!3), J!5)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(263,plain,
% 0.21/0.50 ($greatereq($sum(J!5, $product(-1, A!3)), 0) <=> $greatereq($sum($product(-1, A!3), J!5), 0)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[262])).
% 0.21/0.50 tff(264,plain,
% 0.21/0.50 ($greatereq($sum(J!5, $product(-1, A!3)), 0) <=> $lesseq($sum(A!3, $product(-1, J!5)), 0)),
% 0.21/0.50 inference(transitivity,[status(thm)],[263, 261])).
% 0.21/0.50 tff(265,plain,
% 0.21/0.50 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $greatereq($sum(J!5, $product(-1, A!3)), 0) | (~$greatereq($sum(J!5, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0))) <=> ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[264, 260])).
% 0.21/0.50 tff(266,plain,
% 0.21/0.50 (((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $greatereq($sum(J!5, $product(-1, A!3)), 0) | (~$greatereq($sum(J!5, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0))) <=> ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[265, 259])).
% 0.21/0.50 tff(267,plain,
% 0.21/0.50 (((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))) | ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $greatereq($sum(J!5, $product(-1, A!3)), 0) | (~$greatereq($sum(J!5, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))) <=> ((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))) | ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[266])).
% 0.21/0.50 tff(268,plain,
% 0.21/0.50 (((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))) | ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $greatereq($sum(J!5, $product(-1, A!3)), 0) | (~$greatereq($sum(J!5, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))) <=> ((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[267, 258])).
% 0.21/0.50 tff(269,plain,
% 0.21/0.50 ((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))) | ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $greatereq($sum(J!5, $product(-1, A!3)), 0) | (~$greatereq($sum(J!5, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(270,plain,
% 0.21/0.50 ((~![J: $int] : ((~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J))) = 0)) | $greatereq($sum(J, $product(-1, A!3)), 0) | (~$greatereq($sum(J, $sum($product(-1, I!1), $product(-1, tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1)))))), 0)))) | (~(tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5))) = 0)) | $lesseq($sum(A!3, $product(-1, J!5)), 0) | (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.21/0.50 tff(271,plain,
% 0.21/0.50 (~$lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[270, 257, 250, 255])).
% 0.21/0.50 tff(272,plain,
% 0.21/0.50 (t2tb2(A1!2) = elts(int, mk_array1(int, A!3, t2tb2(A1!2)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[112])).
% 0.21/0.50 tff(273,plain,
% 0.21/0.50 (get(int, int, t2tb2(A1!2), t2tb(J!5)) = get(int, int, elts(int, mk_array1(int, A!3, t2tb2(A1!2))), t2tb(J!5))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[272])).
% 0.21/0.50 tff(274,plain,
% 0.21/0.50 (get(int, int, elts(int, mk_array1(int, A!3, t2tb2(A1!2))), t2tb(J!5)) = get(int, int, t2tb2(A1!2), t2tb(J!5))),
% 0.21/0.50 inference(symmetry,[status(thm)],[273])).
% 0.21/0.50 tff(275,plain,
% 0.21/0.50 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(int, mk_array1(int, A!3, t2tb2(A1!2)), J!5) = get(int, int, elts(int, mk_array1(int, A!3, t2tb2(A1!2))), t2tb(J!5)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(276,plain,
% 0.21/0.50 (get2(int, mk_array1(int, A!3, t2tb2(A1!2)), J!5) = get(int, int, elts(int, mk_array1(int, A!3, t2tb2(A1!2))), t2tb(J!5))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[275, 120])).
% 0.21/0.50 tff(277,plain,
% 0.21/0.50 (get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5) = get2(int, mk_array1(int, A!3, t2tb2(A1!2)), J!5)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[130])).
% 0.21/0.50 tff(278,plain,
% 0.21/0.50 (get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5) = get(int, int, t2tb2(A1!2), t2tb(J!5))),
% 0.21/0.50 inference(transitivity,[status(thm)],[277, 276, 274])).
% 0.21/0.50 tff(279,plain,
% 0.21/0.50 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5)) = tb2t(get(int, int, t2tb2(A1!2), t2tb(J!5)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[278])).
% 0.21/0.50 tff(280,plain,
% 0.21/0.50 (tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5)) = 0),
% 0.21/0.50 inference(transitivity,[status(thm)],[279, 257])).
% 0.21/0.50 tff(281,plain,
% 0.21/0.50 ((~(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5)) = 0)) | $lesseq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5)), 0)),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.50 tff(282,plain,
% 0.21/0.50 ($lesseq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5)), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[281, 280])).
% 0.21/0.50 tff(283,plain,
% 0.21/0.50 ($lesseq($sum(I!1, $sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, J!5))), 0) | (~$lesseq($sum(I!1, $product(-1, tb2t(t2tb(I!1)))), 0)) | (~$lesseq(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5)), 0)) | (~$greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0)) | (~$lesseq($sum(tb2t(get(int, int, t2tb2(A1!2), t2tb(I!1))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1)))))), 0))),
% 0.21/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.50 tff(284,plain,
% 0.21/0.50 (~$greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[283, 282, 271, 150, 142])).
% 0.21/0.50 tff(285,plain,
% 0.21/0.50 (((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | ((~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0))) <=> ((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(286,plain,
% 0.21/0.50 (((~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0)) <=> ((~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(287,plain,
% 0.21/0.50 ($lesseq($sum($product(-1, J!5), $sum(tb2t(t2tb(I!1)), $sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1)))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5)))))), 0) <=> $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(288,plain,
% 0.21/0.50 ($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!5), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))) = $sum($product(-1, J!5), $sum(tb2t(t2tb(I!1)), $sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1)))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(289,plain,
% 0.21/0.51 ($lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!5), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0) <=> $lesseq($sum($product(-1, J!5), $sum(tb2t(t2tb(I!1)), $sum(tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1)))), $product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5)))))), 0)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[288])).
% 0.21/0.51 tff(290,plain,
% 0.21/0.51 ($lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!5), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0) <=> $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0)),
% 0.21/0.51 inference(transitivity,[status(thm)],[289, 287])).
% 0.21/0.51 tff(291,plain,
% 0.21/0.51 ((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!5)), 0)) <=> (~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(292,plain,
% 0.21/0.51 (((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!5)), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!5), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0)) <=> ((~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[291, 290])).
% 0.21/0.51 tff(293,plain,
% 0.21/0.51 (((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!5)), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!5), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0)) <=> ((~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0))),
% 0.21/0.51 inference(transitivity,[status(thm)],[292, 286])).
% 0.21/0.51 tff(294,plain,
% 0.21/0.51 (((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | ((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!5)), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!5), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0))) <=> ((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | ((~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[293])).
% 0.21/0.51 tff(295,plain,
% 0.21/0.51 (((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | ((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!5)), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!5), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0))) <=> ((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0))),
% 0.21/0.51 inference(transitivity,[status(thm)],[294, 285])).
% 0.21/0.51 tff(296,plain,
% 0.21/0.51 ((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | ((~$lesseq($sum(tb2t(t2tb(I!1)), $product(-1, J!5)), 0)) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(tb2t(t2tb(I!1)), $sum($product(-1, J!5), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))))), 0))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(297,plain,
% 0.21/0.51 ((~![I: $int, J: $int] : ((~$lesseq($sum(I, $product(-1, J)), 0)) | (~$greatereq(I, 0)) | $greatereq($sum(J, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | $lesseq($sum(I, $sum($product(-1, J), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), I))))), 0))) | (~$greatereq(tb2t(t2tb(I!1)), 0)) | $greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.21/0.51 tff(298,plain,
% 0.21/0.51 ($greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0)) | $greatereq($sum(J!5, $sum($product(-1, tb2t(t2tb(I!1))), $sum($product(-1, tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), tb2t(t2tb(I!1))))), tb2t(get2(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2)))), J!5))))), 0)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[297, 217, 158])).
% 0.21/0.51 tff(299,plain,
% 0.21/0.51 ($greatereq($sum(J!5, $product(-1, length1(int, t2tb1(tb2t1(mk_array1(int, A!3, t2tb2(A1!2))))))), 0) | (~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[298, 284])).
% 0.21/0.51 tff(300,plain,
% 0.21/0.51 (~$greatereq($sum(J!5, $product(-1, tb2t(t2tb(I!1)))), 0)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[299, 253])).
% 0.21/0.51 tff(301,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(theory_lemma,[status(thm)],[61, 300, 248])).
% 0.21/0.51 % SZS output end Proof
%------------------------------------------------------------------------------