TSTP Solution File: SWW606_2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW606_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 20:59:25 EDT 2022
% Result : Theorem 62.78s 40.43s
% Output : Proof 63.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW606_2 : TPTP v8.1.0. Released v6.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 20:28:01 EDT 2022
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.34 Usage: tptp [options] [-file:]file
% 0.18/0.34 -h, -? prints this message.
% 0.18/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.34 -m, -model generate model.
% 0.18/0.34 -p, -proof generate proof.
% 0.18/0.34 -c, -core generate unsat core of named formulas.
% 0.18/0.34 -st, -statistics display statistics.
% 0.18/0.34 -t:timeout set timeout (in second).
% 0.18/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.34 -<param>:<value> configuration parameter and value.
% 0.18/0.34 -o:<output-file> file to place output in.
% 62.78/40.43 % SZS status Theorem
% 62.78/40.43 % SZS output start Proof
% 62.78/40.43 tff(le_type, type, (
% 62.78/40.43 le: ( param * elt * elt ) > $o)).
% 62.78/40.43 tff(tb2t4_type, type, (
% 62.78/40.43 tb2t4: uni > elt)).
% 62.78/40.43 tff(get1_type, type, (
% 62.78/40.43 get1: ( ty * uni * $int ) > uni)).
% 62.78/40.43 tff(tptp_fun_I1_8_type, type, (
% 62.78/40.43 tptp_fun_I1_8: ( $int * $int * array_elt * param ) > $int)).
% 62.78/40.43 tff(tptp_fun_P_11_type, type, (
% 62.78/40.43 tptp_fun_P_11: param)).
% 62.78/40.43 tff(tb2t3_type, type, (
% 62.78/40.43 tb2t3: uni > array_elt)).
% 62.78/40.43 tff(mk_array_type, type, (
% 62.78/40.43 mk_array: ( ty * $int * uni ) > uni)).
% 62.78/40.43 tff(t2tb5_type, type, (
% 62.78/40.43 t2tb5: map_int_elt > uni)).
% 62.78/40.43 tff(tptp_fun_A5_17_type, type, (
% 62.78/40.43 tptp_fun_A5_17: map_int_elt)).
% 62.78/40.43 tff(tptp_fun_A_10_type, type, (
% 62.78/40.43 tptp_fun_A_10: $int)).
% 62.78/40.43 tff(elt1_type, type, (
% 62.78/40.43 elt1: ty)).
% 62.78/40.43 tff(tptp_fun_J1_18_type, type, (
% 62.78/40.43 tptp_fun_J1_18: $int)).
% 62.78/40.43 tff(tptp_fun_I_12_type, type, (
% 62.78/40.43 tptp_fun_I_12: $int)).
% 62.78/40.43 tff(t2tb3_type, type, (
% 62.78/40.43 t2tb3: array_elt > uni)).
% 62.78/40.43 tff(tptp_fun_I2_7_type, type, (
% 62.78/40.43 tptp_fun_I2_7: ( $int * $int * array_elt * param ) > $int)).
% 62.78/40.43 tff(get_type, type, (
% 62.78/40.43 get: ( ty * ty * uni * uni ) > uni)).
% 62.78/40.43 tff(t2tb_type, type, (
% 62.78/40.43 t2tb: $int > uni)).
% 62.78/40.43 tff(tptp_fun_J_15_type, type, (
% 62.78/40.43 tptp_fun_J_15: $int)).
% 62.78/40.43 tff(tptp_fun_A3_14_type, type, (
% 62.78/40.43 tptp_fun_A3_14: map_int_elt)).
% 62.78/40.43 tff(int_type, type, (
% 62.78/40.43 int: ty)).
% 62.78/40.43 tff(set_type, type, (
% 62.78/40.43 set: ( ty * ty * uni * uni * uni ) > uni)).
% 62.78/40.43 tff(sorted_sub2_type, type, (
% 62.78/40.43 sorted_sub2: ( param * array_elt * $int * $int ) > $o)).
% 62.78/40.43 tff(permut_all_type, type, (
% 62.78/40.43 permut_all: ( ty * uni * uni ) > $o)).
% 62.78/40.43 tff(tptp_fun_A1_9_type, type, (
% 62.78/40.43 tptp_fun_A1_9: map_int_elt)).
% 62.78/40.43 tff(tb2t5_type, type, (
% 62.78/40.43 tb2t5: uni > map_int_elt)).
% 62.78/40.43 tff(tptp_fun_A4_16_type, type, (
% 62.78/40.43 tptp_fun_A4_16: map_int_elt)).
% 62.78/40.43 tff(exchange1_type, type, (
% 62.78/40.43 exchange1: ( ty * uni * uni * $int * $int ) > $o)).
% 62.78/40.43 tff(tptp_fun_A2_13_type, type, (
% 62.78/40.43 tptp_fun_A2_13: map_int_elt)).
% 62.78/40.43 tff(tb2t_type, type, (
% 62.78/40.43 tb2t: uni > $int)).
% 62.78/40.43 tff(length_type, type, (
% 62.78/40.43 length: ( ty * uni ) > $int)).
% 62.78/40.43 tff(elts_type, type, (
% 62.78/40.43 elts: ( ty * uni ) > uni)).
% 62.78/40.43 tff(exchange_type, type, (
% 62.78/40.43 exchange: ( ty * uni * uni * $int * $int * $int * $int ) > $o)).
% 62.78/40.43 tff(tptp_fun_K_6_type, type, (
% 62.78/40.43 tptp_fun_K_6: ( $int * $int * $int * $int * uni * uni * ty ) > $int)).
% 62.78/40.43 tff(sort_type, type, (
% 62.78/40.43 sort: ( ty * uni ) > $o)).
% 62.78/40.43 tff(map_type, type, (
% 62.78/40.43 map: ( ty * ty ) > ty)).
% 62.78/40.43 tff(1,plain,
% 62.78/40.43 (($greatereq(A!10, 0) & $greatereq(A!10, 1) & (permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12) & (~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))) & $greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1))) <=> ($greatereq(A!10, 0) & $greatereq(A!10, 1) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12) & (~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))) & $greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1))),
% 62.78/40.43 inference(rewrite,[status(thm)],[])).
% 62.78/40.43 tff(2,plain,
% 62.78/40.43 (((permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12)) & ((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))))) & ($greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1))) <=> (permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12) & (~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))) & $greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(3,plain,
% 62.78/40.44 ((~(~($greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1)))) <=> ($greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(4,plain,
% 62.78/40.44 ((~($greatereq(I!12, 0) & $lesseq($sum(I!12, $product(-1, A!10)), -1))) <=> (~($greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1)))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(5,plain,
% 62.78/40.44 ((~(~($greatereq(I!12, 0) & $lesseq($sum(I!12, $product(-1, A!10)), -1)))) <=> (~(~($greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1))))),
% 62.78/40.44 inference(monotonicity,[status(thm)],[4])).
% 62.78/40.44 tff(6,plain,
% 62.78/40.44 ((~(~($greatereq(I!12, 0) & $lesseq($sum(I!12, $product(-1, A!10)), -1)))) <=> ($greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1))),
% 62.78/40.44 inference(transitivity,[status(thm)],[5, 3])).
% 62.78/40.44 tff(7,plain,
% 62.78/40.44 (((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & ($greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0))) & ($greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1))) & ((~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))))) & ($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0))) & ($greatereq(J!15, 0) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))))) <=> ((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(8,plain,
% 62.78/40.44 (($greatereq(J!15, 0) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))))) <=> ($greatereq(J!15, 0) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(9,plain,
% 62.78/40.44 ((~(~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0))))) <=> ($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(10,plain,
% 62.78/40.44 ((~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0)))) <=> (~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0))))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(11,plain,
% 62.78/40.44 ((~(~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) <=> (~(~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)))))),
% 62.78/40.44 inference(monotonicity,[status(thm)],[10])).
% 62.78/40.44 tff(12,plain,
% 62.78/40.44 ((~(~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) <=> ($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)))),
% 62.78/40.44 inference(transitivity,[status(thm)],[11, 9])).
% 62.78/40.44 tff(13,plain,
% 62.78/40.44 ((((~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))) & ($greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1))) & ($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))) <=> ((~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(14,plain,
% 62.78/40.44 ((~(~($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))))))) <=> ($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(15,plain,
% 62.78/40.44 ((~(~($greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1))))) <=> ($greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(16,plain,
% 62.78/40.44 ((~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1)))) <=> (~($greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1))))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(17,plain,
% 62.78/40.44 ((~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) <=> (~(~($greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)))))),
% 62.78/40.44 inference(monotonicity,[status(thm)],[16])).
% 62.78/40.44 tff(18,plain,
% 62.78/40.44 ((~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) <=> ($greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)))),
% 62.78/40.44 inference(transitivity,[status(thm)],[17, 15])).
% 62.78/40.44 tff(19,plain,
% 62.78/40.44 (((~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & ($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))) <=> ((~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(20,plain,
% 62.78/40.44 ((~(~($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))))) <=> ($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(21,plain,
% 62.78/40.44 ((~(~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15))) <=> exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15)),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(22,plain,
% 62.78/40.44 ((~((~($sum(J1!18, $product(-1, J!15)) = -1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) <=> (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))))),
% 62.78/40.44 inference(rewrite,[status(thm)],[])).
% 62.78/40.44 tff(23,plain,
% 62.78/40.44 (((~((~($sum(J1!18, $product(-1, J!15)) = -1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & (~(~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15))) & (~(~($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))))) <=> ((~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & ($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))))),
% 62.78/40.44 inference(monotonicity,[status(thm)],[22, 21, 20])).
% 62.78/40.44 tff(24,plain,
% 62.78/40.44 (((~((~($sum(J1!18, $product(-1, J!15)) = -1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & (~(~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15))) & (~(~($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))))) <=> ((~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))),
% 62.79/40.44 inference(transitivity,[status(thm)],[23, 19])).
% 62.79/40.44 tff(25,plain,
% 62.79/40.44 ((((~((~($sum(J1!18, $product(-1, J!15)) = -1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & (~(~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15))) & (~(~($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (~(~($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))))) <=> (((~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))) & ($greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1))) & ($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))))))),
% 62.79/40.44 inference(monotonicity,[status(thm)],[24, 18, 14])).
% 62.79/40.44 tff(26,plain,
% 62.79/40.44 ((((~((~($sum(J1!18, $product(-1, J!15)) = -1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & (~(~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15))) & (~(~($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (~(~($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))))) <=> ((~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))),
% 62.79/40.44 inference(transitivity,[status(thm)],[25, 13])).
% 62.79/40.44 tff(27,plain,
% 62.79/40.44 ((~(~($greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0))))) <=> ($greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)))),
% 62.79/40.44 inference(rewrite,[status(thm)],[])).
% 62.79/40.44 tff(28,plain,
% 62.79/40.44 ((~($greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0)))) <=> (~($greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0))))),
% 62.79/40.44 inference(rewrite,[status(thm)],[])).
% 62.79/40.44 tff(29,plain,
% 62.79/40.44 ((~(~($greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) <=> (~(~($greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)))))),
% 62.79/40.44 inference(monotonicity,[status(thm)],[28])).
% 62.79/40.44 tff(30,plain,
% 62.79/40.44 ((~(~($greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) <=> ($greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)))),
% 62.79/40.44 inference(transitivity,[status(thm)],[29, 27])).
% 62.79/40.44 tff(31,plain,
% 62.79/40.44 (((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (~(~($greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (((~((~($sum(J1!18, $product(-1, J!15)) = -1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & (~(~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15))) & (~(~($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (~(~($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & ($greatereq(J!15, 0) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))))) <=> ((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & ($greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0))) & ($greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1))) & ((~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))))) & ($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0))) & ($greatereq(J!15, 0) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))))))),
% 62.79/40.44 inference(monotonicity,[status(thm)],[30, 18, 26, 12, 8])).
% 62.79/40.44 tff(32,plain,
% 62.79/40.44 (((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (~(~($greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (((~((~($sum(J1!18, $product(-1, J!15)) = -1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & (~(~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15))) & (~(~($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (~(~($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & ($greatereq(J!15, 0) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))))) <=> ((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))))),
% 62.79/40.45 inference(transitivity,[status(thm)],[31, 7])).
% 62.79/40.45 tff(33,plain,
% 62.79/40.45 ((~(~(permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12)))) <=> (permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12))),
% 62.79/40.45 inference(rewrite,[status(thm)],[])).
% 62.79/40.45 tff(34,plain,
% 62.79/40.45 (((~(~(permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12)))) & ((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (~(~($greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (((~((~($sum(J1!18, $product(-1, J!15)) = -1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & (~(~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15))) & (~(~($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (~(~($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & ($greatereq(J!15, 0) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))))) & (~(~($greatereq(I!12, 0) & $lesseq($sum(I!12, $product(-1, A!10)), -1))))) <=> ((permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12)) & ((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))))) & ($greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1)))),
% 62.79/40.45 inference(monotonicity,[status(thm)],[33, 32, 6])).
% 62.79/40.45 tff(35,plain,
% 62.79/40.45 (((~(~(permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12)))) & ((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (~(~($greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (((~((~($sum(J1!18, $product(-1, J!15)) = -1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & (~(~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15))) & (~(~($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (~(~($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & ($greatereq(J!15, 0) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))))) & (~(~($greatereq(I!12, 0) & $lesseq($sum(I!12, $product(-1, A!10)), -1))))) <=> (permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12) & (~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))) & $greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1))),
% 62.79/40.45 inference(transitivity,[status(thm)],[34, 2])).
% 62.79/40.45 tff(36,plain,
% 62.79/40.45 ((~(~$greatereq(A!10, 1))) <=> $greatereq(A!10, 1)),
% 62.79/40.45 inference(rewrite,[status(thm)],[])).
% 62.79/40.45 tff(37,plain,
% 62.79/40.45 ((~(~$greatereq(A!10, 0))) <=> $greatereq(A!10, 0)),
% 62.79/40.45 inference(rewrite,[status(thm)],[])).
% 62.79/40.45 tff(38,plain,
% 62.79/40.45 (((~(~$greatereq(A!10, 0))) & (~(~$greatereq(A!10, 1))) & ((~(~(permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12)))) & ((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (~(~($greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (((~((~($sum(J1!18, $product(-1, J!15)) = -1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & (~(~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15))) & (~(~($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (~(~($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & ($greatereq(J!15, 0) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))))) & (~(~($greatereq(I!12, 0) & $lesseq($sum(I!12, $product(-1, A!10)), -1)))))) <=> ($greatereq(A!10, 0) & $greatereq(A!10, 1) & (permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12) & (~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & $greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))) & $greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1)))),
% 62.79/40.45 inference(monotonicity,[status(thm)],[37, 36, 35])).
% 62.79/40.45 tff(39,plain,
% 62.79/40.45 (((~(~$greatereq(A!10, 0))) & (~(~$greatereq(A!10, 1))) & ((~(~(permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12)))) & ((~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (~(~($greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (((~((~($sum(J1!18, $product(-1, J!15)) = -1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & (~(~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15))) & (~(~($greatereq(A!10, 0) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))))))) & (~(~($greatereq(J!15, 1) & (~$greatereq($sum(J!15, $product(-1, A!10)), 1))))) & (~(~($greatereq(A!10, 0) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))))))) & (~(~($greatereq(A!10, 0) & $greatereq(J!15, 0) & (~$greatereq($sum(J!15, $product(-1, A!10)), 0))))) & ($greatereq(J!15, 0) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))))) & (~(~($greatereq(I!12, 0) & $lesseq($sum(I!12, $product(-1, A!10)), -1)))))) <=> ($greatereq(A!10, 0) & $greatereq(A!10, 1) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12) & (~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))) & $greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1))),
% 62.79/40.45 inference(transitivity,[status(thm)],[38, 1])).
% 62.79/40.45 tff(40,plain,
% 62.79/40.45 ((~![P: param, A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 1)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(A, 0) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J)), 0)) & $greatereq($sum(K2, $product(-1, J)), 1) & $lesseq($sum(K2, $product(-1, I)), 0))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, A)), -1)))))) <=> (~![P: param, A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 1)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(A, 0) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J)), 0)) & $greatereq($sum(K2, $product(-1, J)), 1) & $lesseq($sum(K2, $product(-1, I)), 0))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, A)), -1))))))),
% 62.79/40.46 inference(rewrite,[status(thm)],[])).
% 62.79/40.46 tff(41,plain,
% 62.79/40.46 ((~![P: param, A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 1)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, A)), -1))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($greatereq(J, 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($greatereq(A, 0) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))))))) | (~($greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1))))) | (~($greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1)))) | (~($greatereq(A, 0) & $greatereq(J, 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), 0) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$lesseq($sum(J, $product(-1, K1)), 0)) & $lesseq($sum(J, $product(-1, K2)), -1) & $lesseq($sum(K2, $product(-1, I)), 0))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2))))))))))) <=> (~![P: param, A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 1)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(A, 0) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J)), 0)) & $greatereq($sum(K2, $product(-1, J)), 1) & $lesseq($sum(K2, $product(-1, I)), 0))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, A)), -1))))))),
% 62.79/40.46 inference(rewrite,[status(thm)],[])).
% 62.79/40.46 tff(42,plain,
% 62.79/40.46 ((~![P: param, A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(1, A)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : ((~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~($lesseq(0, A) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & $lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($lesseq(0, K1) & (~$lesseq(J, K1)) & $lesseq(J, $sum(-1, K2)) & $lesseq(K2, I))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, A))))))) <=> (~![P: param, A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 1)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, A)), -1))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($greatereq(J, 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($greatereq(A, 0) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))))))) | (~($greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1))))) | (~($greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1)))) | (~($greatereq(A, 0) & $greatereq(J, 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), 0) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$lesseq($sum(J, $product(-1, K1)), 0)) & $lesseq($sum(J, $product(-1, K2)), -1) & $lesseq($sum(K2, $product(-1, I)), 0))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))))))),
% 62.79/40.46 inference(rewrite,[status(thm)],[])).
% 62.79/40.46 tff(43,plain,
% 62.79/40.46 ((~![P: param, A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(1, A)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : ((~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~($lesseq(0, A) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & $lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($lesseq(0, K1) & (~$lesseq(J, K1)) & $lesseq(J, $sum(-1, K2)) & $lesseq(K2, I))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, A))))))) <=> (~![P: param, A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(1, A)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : ((~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~($lesseq(0, A) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & $lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($lesseq(0, K1) & (~$lesseq(J, K1)) & $lesseq(J, $sum(-1, K2)) & $lesseq(K2, I))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, A)))))))),
% 62.79/40.46 inference(rewrite,[status(thm)],[])).
% 62.79/40.46 tff(44,plain,
% 62.79/40.46 ((~![P: param, A: $int, A1: map_int_elt] : ($lesseq(0, A) => ($lesseq(0, $difference(A, 1)) => ![A2: map_int_elt, I: $int] : (($lesseq(0, I) & $lesseq(I, $difference(A, 1))) => ((permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I)) => ![J: $int, A3: map_int_elt] : (((((($lesseq(0, J) & $lesseq(J, I)) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3)))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J)) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(I, 1))) & ![K1: $int, K2: $int] : (((($lesseq(0, K1) & $less(K1, J)) & $lesseq($sum(J, 1), K2)) & $lesseq(K2, I)) => le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))) => ($less(0, J) => ((($lesseq(0, A) & $lesseq(0, J)) & $less(J, A)) => (($lesseq(0, $difference(J, 1)) & $less($difference(J, 1), A)) => ((~le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($difference(J, 1)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J))))) => (($lesseq(0, J) & $less(J, A)) => (($lesseq(0, $difference(J, 1)) & $less($difference(J, 1), A)) => (($lesseq(0, J) & $less(J, A)) => ![A4: map_int_elt] : (($lesseq(0, A) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($difference(J, 1))))))) => (($lesseq(0, $difference(J, 1)) & $less($difference(J, 1), A)) => ![A5: map_int_elt] : (($lesseq(0, A) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($difference(J, 1)), get(elt1, int, t2tb5(A3), t2tb(J)))))) => (exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $difference(J, 1), J) => ![J1: $int] : ((J1 = $difference(J, 1)) => sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(I, 1)))))))))))))))))))) <=> (~![P: param, A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(1, A)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : ((~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~($lesseq(0, A) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & $lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($lesseq(0, K1) & (~$lesseq(J, K1)) & $lesseq(J, $sum(-1, K2)) & $lesseq(K2, I))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, A)))))))),
% 62.79/40.46 inference(rewrite,[status(thm)],[])).
% 62.79/40.46 tff(45,axiom,(~![P: param, A: $int, A1: map_int_elt] : ($lesseq(0, A) => ($lesseq(0, $difference(A, 1)) => ![A2: map_int_elt, I: $int] : (($lesseq(0, I) & $lesseq(I, $difference(A, 1))) => ((permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I)) => ![J: $int, A3: map_int_elt] : (((((($lesseq(0, J) & $lesseq(J, I)) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3)))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J)) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(I, 1))) & ![K1: $int, K2: $int] : (((($lesseq(0, K1) & $less(K1, J)) & $lesseq($sum(J, 1), K2)) & $lesseq(K2, I)) => le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))) => ($less(0, J) => ((($lesseq(0, A) & $lesseq(0, J)) & $less(J, A)) => (($lesseq(0, $difference(J, 1)) & $less($difference(J, 1), A)) => ((~le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($difference(J, 1)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J))))) => (($lesseq(0, J) & $less(J, A)) => (($lesseq(0, $difference(J, 1)) & $less($difference(J, 1), A)) => (($lesseq(0, J) & $less(J, A)) => ![A4: map_int_elt] : (($lesseq(0, A) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($difference(J, 1))))))) => (($lesseq(0, $difference(J, 1)) & $less($difference(J, 1), A)) => ![A5: map_int_elt] : (($lesseq(0, A) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($difference(J, 1)), get(elt1, int, t2tb5(A3), t2tb(J)))))) => (exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $difference(J, 1), J) => ![J1: $int] : ((J1 = $difference(J, 1)) => sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(I, 1)))))))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_sort1')).
% 62.79/40.46 tff(46,plain,
% 62.79/40.46 (~![P: param, A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(1, A)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : ((~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~($lesseq(0, A) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & $lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($lesseq(0, K1) & (~$lesseq(J, K1)) & $lesseq(J, $sum(-1, K2)) & $lesseq(K2, I))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, A))))))),
% 62.79/40.46 inference(modus_ponens,[status(thm)],[45, 44])).
% 62.79/40.46 tff(47,plain,
% 62.79/40.46 (~![P: param, A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(1, A)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : ((~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~($lesseq(0, A) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & $lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($lesseq(0, K1) & (~$lesseq(J, K1)) & $lesseq(J, $sum(-1, K2)) & $lesseq(K2, I))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, A))))))),
% 62.79/40.46 inference(modus_ponens,[status(thm)],[46, 43])).
% 62.79/40.46 tff(48,plain,
% 62.79/40.46 (~![P: param, A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(1, A)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : ((~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~($lesseq(0, A) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & $lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($lesseq(0, K1) & (~$lesseq(J, K1)) & $lesseq(J, $sum(-1, K2)) & $lesseq(K2, I))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, A))))))),
% 62.79/40.46 inference(modus_ponens,[status(thm)],[47, 43])).
% 62.79/40.46 tff(49,plain,
% 62.79/40.46 (~![P: param, A: $int, A1: map_int_elt] : ((~$lesseq(0, A)) | (~$lesseq(1, A)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($lesseq(0, J) & (~$lesseq(A, J)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : ((~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | ![J1: $int] : ((~(J1 = $sum(-1, J))) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~($lesseq(0, A) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($lesseq(1, J) & (~$lesseq(A, $sum(-1, J))))) | (~($lesseq(0, A) & $lesseq(0, J) & (~$lesseq(A, J)))) | (~($lesseq(0, J) & $lesseq(J, I) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($lesseq(0, K1) & (~$lesseq(J, K1)) & $lesseq(J, $sum(-1, K2)) & $lesseq(K2, I))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($lesseq(0, I) & $lesseq(I, $sum(-1, A))))))),
% 62.79/40.46 inference(modus_ponens,[status(thm)],[48, 43])).
% 62.79/40.46 tff(50,plain,
% 62.79/40.46 (~![P: param, A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 1)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, A)), -1))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($greatereq(J, 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($greatereq(A, 0) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))))))) | (~($greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1))))) | (~($greatereq(J, 1) & (~$lesseq($sum(A, $product(-1, J)), -1)))) | (~($greatereq(A, 0) & $greatereq(J, 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), 0) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$lesseq($sum(J, $product(-1, K1)), 0)) & $lesseq($sum(J, $product(-1, K2)), -1) & $lesseq($sum(K2, $product(-1, I)), 0))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2))))))))))),
% 62.79/40.46 inference(modus_ponens,[status(thm)],[49, 42])).
% 62.79/40.46 tff(51,plain,
% 62.79/40.46 (~![P: param, A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 1)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(A, 0) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J)), 0)) & $greatereq($sum(K2, $product(-1, J)), 1) & $lesseq($sum(K2, $product(-1, I)), 0))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, A)), -1)))))),
% 62.79/40.46 inference(modus_ponens,[status(thm)],[50, 41])).
% 62.79/40.46 tff(52,plain,
% 62.79/40.46 (~![P: param, A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 1)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(A, 0) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J)), 0)) & $greatereq($sum(K2, $product(-1, J)), 1) & $lesseq($sum(K2, $product(-1, I)), 0))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, A)), -1)))))),
% 62.79/40.46 inference(modus_ponens,[status(thm)],[51, 40])).
% 62.79/40.46 tff(53,plain,
% 62.79/40.46 (~![P: param, A: $int, A1: map_int_elt] : ((~$greatereq(A, 0)) | (~$greatereq(A, 1)) | ![A2: map_int_elt, I: $int] : ((~(permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A2))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A2))), 0, I))) | ![J: $int, A3: map_int_elt] : ($lesseq(J, 0) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb($sum(-1, J)))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(J)))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | ![A4: map_int_elt] : (![A5: map_int_elt] : (![J1: $int] : ((~($sum(J1, $product(-1, J)) = -1)) | sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A5))), J1, $sum(1, I))) | (~exchange1(elt1, mk_array(elt1, A, t2tb5(A3)), mk_array(elt1, A, t2tb5(A5)), $sum(-1, J), J)) | (~($greatereq(A, 0) & (A5 = tb2t5(set(elt1, int, t2tb5(A4), t2tb($sum(-1, J)), get(elt1, int, t2tb5(A3), t2tb(J)))))))) | (~($greatereq(J, 1) & (~$greatereq($sum(J, $product(-1, A)), 1)))) | (~($greatereq(A, 0) & (A4 = tb2t5(set(elt1, int, t2tb5(A3), t2tb(J), get(elt1, int, t2tb5(A3), t2tb($sum(-1, J))))))))) | (~($greatereq(A, 0) & $greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~($greatereq(J, 0) & $greatereq($sum(I, $product(-1, J)), 0) & permut_all(elt1, mk_array(elt1, A, t2tb5(A1)), mk_array(elt1, A, t2tb5(A3))) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), 0, J) & sorted_sub2(P, tb2t3(mk_array(elt1, A, t2tb5(A3))), J, $sum(1, I)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J)), 0)) & $greatereq($sum(K2, $product(-1, J)), 1) & $lesseq($sum(K2, $product(-1, I)), 0))) | le(P, tb2t4(get(elt1, int, t2tb5(A3), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3), t2tb(K2)))))))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, A)), -1)))))),
% 62.79/40.46 inference(modus_ponens,[status(thm)],[52, 40])).
% 62.79/40.46 tff(54,plain,
% 62.79/40.46 ($greatereq(A!10, 0) & $greatereq(A!10, 1) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A2!13))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A2!13))), 0, I!12) & (~$lesseq(J!15, 0)) & (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & $greatereq(J!15, 0) & (~$lesseq($sum(A!10, $product(-1, J!15)), 0)) & $greatereq(J!15, 1) & (~$lesseq($sum(A!10, $product(-1, J!15)), -1)) & (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))) & exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) & (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) & (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) & $greatereq($sum(I!12, $product(-1, J!15)), 0) & permut_all(elt1, mk_array(elt1, A!10, t2tb5(A1!9)), mk_array(elt1, A!10, t2tb5(A3!14))) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), 0, J!15) & sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) & ![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))) & $greatereq(I!12, 0) & $greatereq($sum(A!10, $product(-1, I!12)), 1)),
% 62.79/40.46 inference(modus_ponens,[status(thm)],[53, 39])).
% 62.79/40.46 tff(55,plain,
% 62.79/40.46 (~((~($sum(J!15, $product(-1, J1!18)) = 1)) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)))),
% 62.79/40.46 inference(and_elim,[status(thm)],[54])).
% 62.79/40.46 tff(56,plain,
% 62.79/40.46 ($sum(J!15, $product(-1, J1!18)) = 1),
% 62.79/40.46 inference(or_elim,[status(thm)],[55])).
% 62.79/40.46 tff(57,plain,
% 62.79/40.46 ((~($sum(J!15, $product(-1, J1!18)) = 1)) | $lesseq($sum(J!15, $product(-1, J1!18)), 1)),
% 62.79/40.46 inference(theory_lemma,[status(thm)],[])).
% 62.79/40.46 tff(58,plain,
% 62.79/40.46 ($lesseq($sum(J!15, $product(-1, J1!18)), 1)),
% 62.79/40.46 inference(unit_resolution,[status(thm)],[57, 56])).
% 62.79/40.46 tff(59,plain,
% 62.79/40.46 (^[P: param, A: array_elt, L: $int, U: $int] : refl((~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)))))))) <=> (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)))))))))),
% 62.79/40.46 inference(bind,[status(th)],[])).
% 62.79/40.46 tff(60,plain,
% 62.79/40.46 (![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)))))))) <=> ![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))),
% 62.79/40.46 inference(quant_intro,[status(thm)],[59])).
% 62.79/40.46 tff(61,plain,
% 62.79/40.46 (^[P: param, A: array_elt, L: $int, U: $int] : rewrite((~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)))))))) <=> (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)))))))))),
% 62.79/40.47 inference(bind,[status(th)],[])).
% 62.79/40.47 tff(62,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)))))))) <=> ![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))),
% 62.79/40.47 inference(quant_intro,[status(thm)],[61])).
% 62.79/40.47 tff(63,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)))))))) <=> ![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))),
% 62.79/40.47 inference(transitivity,[status(thm)],[62, 60])).
% 62.79/40.47 tff(64,plain,
% 62.79/40.47 (^[P: param, A: array_elt, L: $int, U: $int] : trans(monotonicity(rewrite(((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) <=> ((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))), trans(monotonicity(rewrite((~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & $greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))))) <=> (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))), ((sorted_sub2(P, A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & $greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P))))))) <=> (sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))), rewrite((sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))) <=> (sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)))))), ((sorted_sub2(P, A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & $greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P))))))) <=> (sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))), ((((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) & (sorted_sub2(P, A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & $greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))))))) <=> (((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0)))) & (sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)))))))), rewrite((((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0)))) & (sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)))))) <=> (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))), ((((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) & (sorted_sub2(P, A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & $greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))))))) <=> (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))))),
% 62.79/40.47 inference(bind,[status(th)],[])).
% 62.79/40.47 tff(65,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) & (sorted_sub2(P, A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & $greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))))))) <=> ![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))),
% 62.79/40.47 inference(quant_intro,[status(thm)],[64])).
% 62.79/40.47 tff(66,plain,
% 62.79/40.47 (^[P: param, A: array_elt, L: $int, U: $int] : rewrite((((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) & (sorted_sub2(P, A, L, U) | (~((~($greatereq($sum(tptp_fun_I1_8(U, L, A, P), $product(-1, L)), 0) & $lesseq($sum(tptp_fun_I1_8(U, L, A, P), $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))))))) <=> (((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) & (sorted_sub2(P, A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & $greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))))))))),
% 62.79/40.47 inference(bind,[status(th)],[])).
% 62.79/40.47 tff(67,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) & (sorted_sub2(P, A, L, U) | (~((~($greatereq($sum(tptp_fun_I1_8(U, L, A, P), $product(-1, L)), 0) & $lesseq($sum(tptp_fun_I1_8(U, L, A, P), $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))))))) <=> ![P: param, A: array_elt, L: $int, U: $int] : (((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) & (sorted_sub2(P, A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & $greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P))))))))),
% 62.79/40.47 inference(quant_intro,[status(thm)],[66])).
% 62.79/40.47 tff(68,plain,
% 62.79/40.47 (^[P: param, A: array_elt, L: $int, U: $int] : rewrite((sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq($sum(L, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) <=> (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))))),
% 62.79/40.47 inference(bind,[status(th)],[])).
% 62.79/40.47 tff(69,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq($sum(L, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) <=> ![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2)))))),
% 62.79/40.47 inference(quant_intro,[status(thm)],[68])).
% 62.79/40.47 tff(70,plain,
% 62.79/40.47 (^[P: param, A: array_elt, L: $int, U: $int] : rewrite((sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) <=> (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq($sum(L, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))))),
% 62.79/40.47 inference(bind,[status(th)],[])).
% 62.79/40.47 tff(71,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) <=> ![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq($sum(L, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2)))))),
% 62.79/40.47 inference(quant_intro,[status(thm)],[70])).
% 62.79/40.47 tff(72,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) <=> ![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2)))))),
% 62.79/40.47 inference(rewrite,[status(thm)],[])).
% 62.79/40.47 tff(73,plain,
% 62.79/40.47 (^[P: param, A: array_elt, L: $int, U: $int] : rewrite((sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((($lesseq(L, I1) & $lesseq(I1, I2)) & $less(I2, U)) => le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) <=> (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))))),
% 62.79/40.47 inference(bind,[status(th)],[])).
% 62.79/40.47 tff(74,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((($lesseq(L, I1) & $lesseq(I1, I2)) & $less(I2, U)) => le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) <=> ![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2)))))),
% 62.79/40.47 inference(quant_intro,[status(thm)],[73])).
% 62.79/40.47 tff(75,axiom,(![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((($lesseq(L, I1) & $lesseq(I1, I2)) & $less(I2, U)) => le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sorted_sub_def2')).
% 62.79/40.47 tff(76,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2)))))),
% 62.79/40.47 inference(modus_ponens,[status(thm)],[75, 74])).
% 62.79/40.47 tff(77,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq(L, I1) & $lesseq(I1, I2) & (~$lesseq(U, I2)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2)))))),
% 62.79/40.47 inference(modus_ponens,[status(thm)],[76, 72])).
% 62.79/40.47 tff(78,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($lesseq($sum(L, $product(-1, I1)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2)))))),
% 62.79/40.47 inference(modus_ponens,[status(thm)],[77, 71])).
% 62.79/40.47 tff(79,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (sorted_sub2(P, A, L, U) <=> ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2)))))),
% 62.79/40.47 inference(modus_ponens,[status(thm)],[78, 69])).
% 62.79/40.47 tff(80,plain,(
% 62.79/40.47 ![P: param, A: array_elt, L: $int, U: $int] : (((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) & (sorted_sub2(P, A, L, U) | (~((~($greatereq($sum(tptp_fun_I1_8(U, L, A, P), $product(-1, L)), 0) & $lesseq($sum(tptp_fun_I1_8(U, L, A, P), $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P))))))))),
% 62.79/40.47 inference(skolemize,[status(sab)],[79])).
% 62.79/40.47 tff(81,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : ((~($greatereq($sum(I1, $product(-1, L)), 0) & $lesseq($sum(I1, $product(-1, I2)), 0) & (~$lesseq($sum(U, $product(-1, I2)), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))))) & (sorted_sub2(P, A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & $greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0)))) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P))))))))),
% 62.79/40.47 inference(modus_ponens,[status(thm)],[80, 67])).
% 62.79/40.47 tff(82,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))),
% 62.79/40.47 inference(modus_ponens,[status(thm)],[81, 65])).
% 62.79/40.47 tff(83,plain,
% 62.79/40.47 (![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))),
% 62.79/40.47 inference(modus_ponens,[status(thm)],[82, 63])).
% 62.79/40.47 tff(84,plain,
% 62.79/40.47 (((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1)))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)))))))) <=> ((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1)))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1))))))))),
% 62.79/40.47 inference(rewrite,[status(thm)],[])).
% 62.79/40.47 tff(85,plain,
% 62.79/40.47 ((~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum($sum(1, I!12), $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~($lesseq($sum($sum(1, I!12), $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)))))))) <=> (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1)))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)))))))),
% 62.79/40.47 inference(rewrite,[status(thm)],[])).
% 62.79/40.47 tff(86,plain,
% 62.79/40.47 (((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum($sum(1, I!12), $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~($lesseq($sum($sum(1, I!12), $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0))))))))) <=> ((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1)))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1))))))))),
% 62.79/40.47 inference(monotonicity,[status(thm)],[85])).
% 62.79/40.47 tff(87,plain,
% 62.79/40.47 (((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum($sum(1, I!12), $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~($lesseq($sum($sum(1, I!12), $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0))))))))) <=> ((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1)))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1))))))))),
% 62.79/40.48 inference(transitivity,[status(thm)],[86, 84])).
% 62.79/40.48 tff(88,plain,
% 62.79/40.48 ((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum($sum(1, I!12), $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~($lesseq($sum($sum(1, I!12), $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0))))))))),
% 62.79/40.48 inference(quant_inst,[status(thm)],[])).
% 62.79/40.48 tff(89,plain,
% 62.79/40.48 ((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1)))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)))))))),
% 62.79/40.48 inference(modus_ponens,[status(thm)],[88, 87])).
% 62.79/40.48 tff(90,plain,
% 62.79/40.48 (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1)))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1))))))),
% 62.79/40.48 inference(unit_resolution,[status(thm)],[89, 83])).
% 62.79/40.48 tff(91,plain,
% 62.79/40.48 (((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), I2))) | (~$greatereq($sum(I1, $product(-1, J1!18)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1)))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)))))) | (sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1))))),
% 62.79/40.48 inference(tautology,[status(thm)],[])).
% 62.79/40.48 tff(92,plain,
% 62.79/40.48 (sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)))),
% 62.79/40.48 inference(unit_resolution,[status(thm)],[91, 90])).
% 62.79/40.48 tff(93,plain,
% 62.79/40.48 (~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12))),
% 62.79/40.48 inference(or_elim,[status(thm)],[55])).
% 62.79/40.48 tff(94,plain,
% 62.79/40.48 ((~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1))))) | sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)))),
% 62.79/40.48 inference(tautology,[status(thm)],[])).
% 62.79/40.48 tff(95,plain,
% 62.79/40.48 ((~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), J1!18, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1))))) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)))),
% 62.79/40.48 inference(unit_resolution,[status(thm)],[94, 93])).
% 62.79/40.48 tff(96,plain,
% 62.79/40.48 (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1))),
% 62.79/40.48 inference(unit_resolution,[status(thm)],[95, 92])).
% 62.79/40.48 tff(97,plain,
% 62.79/40.48 ((le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)) | $greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.79/40.48 inference(tautology,[status(thm)],[])).
% 62.79/40.48 tff(98,plain,
% 62.79/40.48 ($greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.79/40.48 inference(unit_resolution,[status(thm)],[97, 96])).
% 62.79/40.48 tff(99,plain,
% 62.79/40.48 ((le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)) | $lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.79/40.48 inference(tautology,[status(thm)],[])).
% 62.79/40.48 tff(100,plain,
% 62.79/40.48 ($lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.79/40.48 inference(unit_resolution,[status(thm)],[99, 96])).
% 62.79/40.48 tff(101,plain,
% 62.79/40.48 ($lesseq($sum(J!15, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 1) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$lesseq($sum(J!15, $product(-1, J1!18)), 1)) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0))),
% 62.79/40.48 inference(theory_lemma,[status(thm)],[])).
% 62.79/40.48 tff(102,plain,
% 62.79/40.48 ($lesseq($sum(J!15, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 1)),
% 62.79/40.48 inference(unit_resolution,[status(thm)],[101, 100, 98, 58])).
% 62.79/40.48 tff(103,plain,
% 62.79/40.48 ($lesseq($sum($sum(-1, J!15), $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 1))),
% 62.79/40.48 inference(theory_lemma,[status(thm)],[])).
% 62.79/40.48 tff(104,plain,
% 62.79/40.48 ($lesseq($sum($sum(-1, J!15), $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.79/40.48 inference(unit_resolution,[status(thm)],[103, 102])).
% 62.79/40.48 tff(105,plain,
% 62.79/40.48 (^[I: $int] : refl(($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0))),
% 62.79/40.48 inference(bind,[status(th)],[])).
% 62.79/40.48 tff(106,plain,
% 62.79/40.48 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 62.79/40.48 inference(quant_intro,[status(thm)],[105])).
% 62.79/40.48 tff(107,plain,
% 62.79/40.48 (^[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)))),
% 62.79/40.48 inference(bind,[status(th)],[])).
% 62.79/40.48 tff(108,plain,
% 62.79/40.48 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 62.79/40.48 inference(quant_intro,[status(thm)],[107])).
% 62.79/40.48 tff(109,plain,
% 62.79/40.48 (^[I: $int] : rewrite((tb2t(t2tb(I)) = I) <=> ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0))),
% 62.79/40.48 inference(bind,[status(th)],[])).
% 62.79/40.48 tff(110,plain,
% 62.79/40.48 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 62.79/40.48 inference(quant_intro,[status(thm)],[109])).
% 62.79/40.48 tff(111,plain,
% 62.79/40.48 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : (tb2t(t2tb(I)) = I)),
% 62.79/40.48 inference(rewrite,[status(thm)],[])).
% 62.79/40.48 tff(112,axiom,(![I: $int] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeL')).
% 62.79/40.48 tff(113,plain,
% 62.79/40.48 (![I: $int] : (tb2t(t2tb(I)) = I)),
% 62.79/40.48 inference(modus_ponens,[status(thm)],[112, 111])).
% 62.79/40.48 tff(114,plain,
% 62.79/40.48 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 62.79/40.48 inference(modus_ponens,[status(thm)],[113, 110])).
% 62.79/40.48 tff(115,plain,
% 62.79/40.48 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 62.79/40.48 inference(modus_ponens,[status(thm)],[114, 108])).
% 62.79/40.48 tff(116,plain,(
% 62.79/40.48 ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 62.79/40.48 inference(skolemize,[status(sab)],[115])).
% 62.79/40.48 tff(117,plain,
% 62.79/40.48 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 62.79/40.48 inference(modus_ponens,[status(thm)],[116, 106])).
% 62.79/40.48 tff(118,plain,
% 62.79/40.48 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.79/40.48 inference(quant_inst,[status(thm)],[])).
% 62.79/40.48 tff(119,plain,
% 62.79/40.48 ($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0),
% 62.79/40.48 inference(unit_resolution,[status(thm)],[118, 117])).
% 62.79/40.48 tff(120,plain,
% 62.79/40.48 ((~($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)) | $lesseq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.79/40.48 inference(theory_lemma,[status(thm)],[])).
% 62.79/40.48 tff(121,plain,
% 62.79/40.48 ($lesseq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.79/40.48 inference(unit_resolution,[status(thm)],[120, 119])).
% 62.79/40.48 tff(122,plain,
% 62.79/40.48 ($greatereq($sum(A!10, $product(-1, I!12)), 1)),
% 62.79/40.48 inference(and_elim,[status(thm)],[54])).
% 62.79/40.48 tff(123,assumption,($lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)), introduced(assumption)).
% 62.79/40.48 tff(124,plain,
% 62.79/40.48 ((~($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)) | $greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.79/40.48 inference(theory_lemma,[status(thm)],[])).
% 62.79/40.48 tff(125,plain,
% 62.79/40.48 ($greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.79/40.48 inference(unit_resolution,[status(thm)],[124, 119])).
% 62.79/40.48 tff(126,plain,
% 62.79/40.48 ((le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)) | (~$lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1))),
% 62.79/40.49 inference(tautology,[status(thm)],[])).
% 62.79/40.49 tff(127,plain,
% 62.79/40.49 (~$lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)),
% 62.79/40.49 inference(unit_resolution,[status(thm)],[126, 96])).
% 62.79/40.49 tff(128,plain,
% 62.79/40.49 (^[A: ty, U: $int, U1: uni] : refl(($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0) <=> ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0))),
% 62.79/40.49 inference(bind,[status(th)],[])).
% 62.79/40.49 tff(129,plain,
% 62.79/40.49 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)),
% 62.79/40.49 inference(quant_intro,[status(thm)],[128])).
% 62.79/40.49 tff(130,plain,
% 62.79/40.49 (^[A: ty, U: $int, U1: uni] : trans(monotonicity(rewrite($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = $sum($product(-1, U), length(A, mk_array(A, U, U1)))), (($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0) <=> ($sum($product(-1, U), length(A, mk_array(A, U, U1))) = 0))), rewrite(($sum($product(-1, U), length(A, mk_array(A, U, U1))) = 0) <=> ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)), (($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0) <=> ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)))),
% 62.79/40.49 inference(bind,[status(th)],[])).
% 62.79/40.49 tff(131,plain,
% 62.79/40.49 (![A: ty, U: $int, U1: uni] : ($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)),
% 62.79/40.49 inference(quant_intro,[status(thm)],[130])).
% 62.79/40.49 tff(132,plain,
% 62.79/40.49 (^[A: ty, U: $int, U1: uni] : rewrite((length(A, mk_array(A, U, U1)) = U) <=> ($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0))),
% 62.79/40.49 inference(bind,[status(th)],[])).
% 62.79/40.49 tff(133,plain,
% 62.79/40.49 (![A: ty, U: $int, U1: uni] : (length(A, mk_array(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : ($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0)),
% 62.79/40.49 inference(quant_intro,[status(thm)],[132])).
% 62.79/40.49 tff(134,plain,
% 62.79/40.49 (![A: ty, U: $int, U1: uni] : (length(A, mk_array(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : (length(A, mk_array(A, U, U1)) = U)),
% 62.79/40.49 inference(rewrite,[status(thm)],[])).
% 62.79/40.49 tff(135,axiom,(![A: ty, U: $int, U1: uni] : (length(A, mk_array(A, U, U1)) = U)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','length_def')).
% 62.79/40.49 tff(136,plain,
% 62.79/40.49 (![A: ty, U: $int, U1: uni] : (length(A, mk_array(A, U, U1)) = U)),
% 62.79/40.49 inference(modus_ponens,[status(thm)],[135, 134])).
% 62.79/40.49 tff(137,plain,
% 62.79/40.49 (![A: ty, U: $int, U1: uni] : ($sum(length(A, mk_array(A, U, U1)), $product(-1, U)) = 0)),
% 62.79/40.49 inference(modus_ponens,[status(thm)],[136, 133])).
% 62.79/40.49 tff(138,plain,
% 62.79/40.49 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)),
% 62.79/40.49 inference(modus_ponens,[status(thm)],[137, 131])).
% 62.79/40.49 tff(139,plain,(
% 62.79/40.49 ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)),
% 62.79/40.49 inference(skolemize,[status(sab)],[138])).
% 62.79/40.49 tff(140,plain,
% 62.79/40.49 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)),
% 62.79/40.49 inference(modus_ponens,[status(thm)],[139, 129])).
% 62.79/40.49 tff(141,plain,
% 62.79/40.49 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length(A, mk_array(A, U, U1)))) = 0)) | ($sum(A!10, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0)),
% 62.79/40.49 inference(quant_inst,[status(thm)],[])).
% 62.79/40.49 tff(142,plain,
% 62.79/40.49 ($sum(A!10, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0),
% 62.79/40.49 inference(unit_resolution,[status(thm)],[141, 140])).
% 62.79/40.49 tff(143,plain,
% 62.79/40.49 ((~($sum(A!10, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0)) | $lesseq($sum(A!10, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0)),
% 62.79/40.49 inference(theory_lemma,[status(thm)],[])).
% 62.79/40.49 tff(144,plain,
% 62.79/40.49 ($lesseq($sum(A!10, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0)),
% 62.79/40.49 inference(unit_resolution,[status(thm)],[143, 142])).
% 62.79/40.49 tff(145,plain,
% 62.79/40.49 ($false),
% 62.79/40.49 inference(theory_lemma,[status(thm)],[144, 127, 125, 123, 122])).
% 62.79/40.49 tff(146,plain,(~$lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)), inference(lemma,lemma(discharge,[]))).
% 62.79/40.49 tff(147,plain,
% 62.79/40.49 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> (~((~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))))))),
% 62.79/40.49 inference(bind,[status(th)],[])).
% 62.79/40.49 tff(148,plain,
% 62.79/40.49 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))),
% 62.79/40.49 inference(quant_intro,[status(thm)],[147])).
% 62.79/40.49 tff(149,plain,
% 62.79/40.49 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : refl((~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))))),
% 62.79/40.49 inference(bind,[status(th)],[])).
% 62.79/40.49 tff(150,plain,
% 62.79/40.49 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 62.79/40.49 inference(quant_intro,[status(thm)],[149])).
% 62.79/40.49 tff(151,plain,
% 62.79/40.49 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))))),
% 62.79/40.49 inference(bind,[status(th)],[])).
% 62.79/40.49 tff(152,plain,
% 62.79/40.49 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 62.79/40.49 inference(quant_intro,[status(thm)],[151])).
% 62.79/40.49 tff(153,plain,
% 62.79/40.49 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 62.79/40.49 inference(transitivity,[status(thm)],[152, 150])).
% 62.79/40.49 tff(154,plain,
% 62.79/40.49 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : trans(monotonicity(rewrite(((~exchange(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) <=> ((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))), trans(monotonicity(rewrite((~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) <=> (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))), ((exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))) <=> (exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))), rewrite((exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))) <=> (exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))), ((exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))) <=> (exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))), ((((~exchange(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> (((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))) & (exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))), rewrite((((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))) & (exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) <=> (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))), ((((~exchange(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))))),
% 62.79/40.49 inference(bind,[status(th)],[])).
% 62.79/40.49 tff(155,plain,
% 62.79/40.49 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (((~exchange(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 62.79/40.49 inference(quant_intro,[status(thm)],[154])).
% 62.79/40.49 tff(156,plain,
% 62.79/40.49 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((((~exchange(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange(A, A1, A2, L, U, I, J) | ((~$greatereq($sum(I, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, I)), 0))) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, J)), 0))) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | (~($greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, L)), 0) & (~$greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, U)), 0)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0)))))) <=> (((~exchange(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))))))),
% 62.79/40.49 inference(bind,[status(th)],[])).
% 62.79/40.49 tff(157,plain,
% 62.79/40.49 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (((~exchange(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange(A, A1, A2, L, U, I, J) | ((~$greatereq($sum(I, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, I)), 0))) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, J)), 0))) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | (~($greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, L)), 0) & (~$greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, U)), 0)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0)))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (((~exchange(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 62.79/40.49 inference(quant_intro,[status(thm)],[156])).
% 62.79/40.49 tff(158,plain,
% 62.79/40.49 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((exchange(A, A1, A2, L, U, I, J) <=> ($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | ($sum(K, $product(-1, J)) = 0) | ($sum(K, $product(-1, I)) = 0) | (~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(U, $product(-1, K)), 0))))))) <=> (exchange(A, A1, A2, L, U, I, J) <=> ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))))),
% 62.79/40.49 inference(bind,[status(th)],[])).
% 62.79/40.49 tff(159,plain,
% 62.79/40.49 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> ($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | ($sum(K, $product(-1, J)) = 0) | ($sum(K, $product(-1, I)) = 0) | (~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(U, $product(-1, K)), 0))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0))))),
% 62.79/40.49 inference(quant_intro,[status(thm)],[158])).
% 62.79/40.49 tff(160,plain,
% 62.79/40.49 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((exchange(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K))))))) <=> (exchange(A, A1, A2, L, U, I, J) <=> ($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | ($sum(K, $product(-1, J)) = 0) | ($sum(K, $product(-1, I)) = 0) | (~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(U, $product(-1, K)), 0))))))))),
% 62.79/40.49 inference(bind,[status(th)],[])).
% 62.79/40.49 tff(161,plain,
% 62.79/40.49 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> ($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | ($sum(K, $product(-1, J)) = 0) | ($sum(K, $product(-1, I)) = 0) | (~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(U, $product(-1, K)), 0)))))))),
% 62.79/40.49 inference(quant_intro,[status(thm)],[160])).
% 62.79/40.49 tff(162,plain,
% 62.79/40.49 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K)))))))),
% 62.79/40.49 inference(rewrite,[status(thm)],[])).
% 62.79/40.49 tff(163,plain,
% 62.79/40.49 (^[A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : rewrite((exchange(A, A1, A2, L, U, I, J) <=> (((((($lesseq(L, I) & $less(I, U)) & $lesseq(L, J)) & $less(J, U)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) & ![K: $int] : (($lesseq(L, K) & $less(K, U)) => ((~(K = I)) => ((~(K = J)) => (get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K)))))))) <=> (exchange(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K))))))))),
% 62.79/40.49 inference(bind,[status(th)],[])).
% 62.79/40.49 tff(164,plain,
% 62.79/40.49 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> (((((($lesseq(L, I) & $less(I, U)) & $lesseq(L, J)) & $less(J, U)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) & ![K: $int] : (($lesseq(L, K) & $less(K, U)) => ((~(K = I)) => ((~(K = J)) => (get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K)))))))) <=> ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K)))))))),
% 62.79/40.50 inference(quant_intro,[status(thm)],[163])).
% 62.79/40.50 tff(165,axiom,(![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> (((((($lesseq(L, I) & $less(I, U)) & $lesseq(L, J)) & $less(J, U)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) & ![K: $int] : (($lesseq(L, K) & $less(K, U)) => ((~(K = I)) => ((~(K = J)) => (get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','exchange_def')).
% 62.79/40.50 tff(166,plain,
% 62.79/40.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K)))))))),
% 62.79/40.50 inference(modus_ponens,[status(thm)],[165, 164])).
% 62.79/40.50 tff(167,plain,
% 62.79/40.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> ($lesseq(L, I) & (~$lesseq(U, I)) & $lesseq(L, J) & (~$lesseq(U, J)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (K = J) | (K = I) | (~($lesseq(L, K) & (~$lesseq(U, K)))))))),
% 62.79/40.50 inference(modus_ponens,[status(thm)],[166, 162])).
% 62.79/40.50 tff(168,plain,
% 62.79/40.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> ($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $lesseq($sum(L, $product(-1, J)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | ($sum(K, $product(-1, J)) = 0) | ($sum(K, $product(-1, I)) = 0) | (~($lesseq($sum(L, $product(-1, K)), 0) & (~$lesseq($sum(U, $product(-1, K)), 0)))))))),
% 62.79/40.50 inference(modus_ponens,[status(thm)],[167, 161])).
% 62.79/40.50 tff(169,plain,
% 62.79/40.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (exchange(A, A1, A2, L, U, I, J) <=> ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0))))),
% 62.79/40.50 inference(modus_ponens,[status(thm)],[168, 159])).
% 62.79/40.50 tff(170,plain,(
% 62.79/40.50 ![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (((~exchange(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange(A, A1, A2, L, U, I, J) | ((~$greatereq($sum(I, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, I)), 0))) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~(~$lesseq($sum(U, $product(-1, J)), 0))) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | (~($greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, L)), 0) & (~$greatereq($sum(tptp_fun_K_6(J, I, U, L, A2, A1, A), $product(-1, U)), 0)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0))))))),
% 62.79/40.50 inference(skolemize,[status(sab)],[169])).
% 62.79/40.50 tff(171,plain,
% 62.79/40.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (((~exchange(A, A1, A2, L, U, I, J)) | ($greatereq($sum(I, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)) & $greatereq($sum(J, $product(-1, L)), 0) & (~$lesseq($sum(U, $product(-1, J)), 0)) & (get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J))) & (get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I))) & ![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | (~($greatereq($sum(K, $product(-1, L)), 0) & (~$greatereq($sum(K, $product(-1, U)), 0)))) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0)))) & (exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | (~($lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 62.79/40.50 inference(modus_ponens,[status(thm)],[170, 157])).
% 62.79/40.50 tff(172,plain,
% 62.79/40.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 62.79/40.50 inference(modus_ponens,[status(thm)],[171, 155])).
% 62.79/40.50 tff(173,plain,
% 62.79/40.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0)))))))) | (~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0))))))))),
% 62.79/40.50 inference(modus_ponens,[status(thm)],[172, 153])).
% 62.79/40.50 tff(174,plain,
% 62.79/40.50 (![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))),
% 62.79/40.50 inference(modus_ponens,[status(thm)],[173, 148])).
% 62.79/40.50 tff(175,plain,
% 62.79/40.50 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 1) | (~$greatereq(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0)))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 1) | (~$greatereq(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))))))))))),
% 62.79/40.50 inference(rewrite,[status(thm)],[])).
% 62.79/40.50 tff(176,plain,
% 62.79/40.50 ((~((~(exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, $sum(-1, J!15))), 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, J!15)), 0) | (~$greatereq($sum(J!15, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!15), $product(-1, 0)), 0)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | ($sum($sum(-1, J!15), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, $sum(-1, J!15))), 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, J!15)), 0) | (~$greatereq($sum(J!15, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!15), $product(-1, 0)), 0)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | (~![K: $int] : ((get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(J!15, $product(-1, K)) = 0) | ($sum($sum(-1, J!15), $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, 0)), 0)))))))))) <=> (~((~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 1) | (~$greatereq(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0)))))))))),
% 62.79/40.51 inference(rewrite,[status(thm)],[])).
% 62.79/40.51 tff(177,plain,
% 62.79/40.51 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~(exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, $sum(-1, J!15))), 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, J!15)), 0) | (~$greatereq($sum(J!15, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!15), $product(-1, 0)), 0)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | ($sum($sum(-1, J!15), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, $sum(-1, J!15))), 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, J!15)), 0) | (~$greatereq($sum(J!15, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!15), $product(-1, 0)), 0)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | (~![K: $int] : ((get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(J!15, $product(-1, K)) = 0) | ($sum($sum(-1, J!15), $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, 0)), 0))))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 1) | (~$greatereq(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))))))))))),
% 62.86/40.51 inference(monotonicity,[status(thm)],[176])).
% 62.86/40.51 tff(178,plain,
% 62.86/40.51 (((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~(exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, $sum(-1, J!15))), 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, J!15)), 0) | (~$greatereq($sum(J!15, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!15), $product(-1, 0)), 0)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | ($sum($sum(-1, J!15), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, $sum(-1, J!15))), 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, J!15)), 0) | (~$greatereq($sum(J!15, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!15), $product(-1, 0)), 0)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | (~![K: $int] : ((get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(J!15, $product(-1, K)) = 0) | ($sum($sum(-1, J!15), $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, 0)), 0))))))))))) <=> ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 1) | (~$greatereq(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))))))))))),
% 62.86/40.51 inference(transitivity,[status(thm)],[177, 175])).
% 62.86/40.51 tff(179,plain,
% 62.86/40.51 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~(exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, $sum(-1, J!15))), 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, J!15)), 0) | (~$greatereq($sum(J!15, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!15), $product(-1, 0)), 0)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | ($sum($sum(-1, J!15), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | (~$lesseq($sum(0, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, $sum(-1, J!15))), 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, J!15)), 0) | (~$greatereq($sum(J!15, $product(-1, 0)), 0)) | (~$greatereq($sum($sum(-1, J!15), $product(-1, 0)), 0)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | (~![K: $int] : ((get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(J!15, $product(-1, K)) = 0) | ($sum($sum(-1, J!15), $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, 0)), 0))))))))))),
% 62.86/40.51 inference(quant_inst,[status(thm)],[])).
% 62.86/40.51 tff(180,plain,
% 62.86/40.51 ((~![A: ty, A1: uni, A2: uni, L: $int, U: $int, I: $int, J: $int] : (~((~(exchange(A, A1, A2, L, U, I, J) | $lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~((get(A, int, A1, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A))) = get(A, int, A2, t2tb(tptp_fun_K_6(J, I, U, L, A2, A1, A)))) | ($sum(J, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | ($sum(I, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))) = 0) | $lesseq($sum(U, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0) | (~$lesseq($sum(L, $product(-1, tptp_fun_K_6(J, I, U, L, A2, A1, A))), 0)))))) | (~((~exchange(A, A1, A2, L, U, I, J)) | (~($lesseq($sum(U, $product(-1, I)), 0) | $lesseq($sum(U, $product(-1, J)), 0) | (~$greatereq($sum(J, $product(-1, L)), 0)) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~(get(A, int, A1, t2tb(I)) = get(A, int, A2, t2tb(J)))) | (~(get(A, int, A1, t2tb(J)) = get(A, int, A2, t2tb(I)))) | (~![K: $int] : ((get(A, int, A1, t2tb(K)) = get(A, int, A2, t2tb(K))) | $greatereq($sum(K, $product(-1, U)), 0) | ($sum(J, $product(-1, K)) = 0) | ($sum(I, $product(-1, K)) = 0) | (~$greatereq($sum(K, $product(-1, L)), 0))))))))))) | (~((~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 1) | (~$greatereq(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0)))))))))),
% 62.86/40.52 inference(modus_ponens,[status(thm)],[179, 178])).
% 62.86/40.52 tff(181,plain,
% 62.86/40.52 (~((~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 1) | (~$greatereq(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))))))))),
% 62.86/40.52 inference(unit_resolution,[status(thm)],[180, 174])).
% 62.86/40.52 tff(182,plain,
% 62.86/40.52 (((~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~((get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1)))) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))), 0) | ($sum(J!15, $product(-1, tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1))) = 1) | (~$greatereq(tptp_fun_K_6(J!15, $sum(-1, J!15), length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), 0, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb5(A3!14), elt1), 0)))))) | (~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0)))))))) | ((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))))))),
% 62.86/40.52 inference(tautology,[status(thm)],[])).
% 62.86/40.52 tff(183,plain,
% 62.86/40.52 ((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0)))))),
% 62.86/40.52 inference(unit_resolution,[status(thm)],[182, 181])).
% 62.86/40.52 tff(184,plain,
% 62.86/40.52 (^[X: map_int_elt] : refl(sort(map(int, elt1), t2tb5(X)) <=> sort(map(int, elt1), t2tb5(X)))),
% 62.86/40.52 inference(bind,[status(th)],[])).
% 62.86/40.52 tff(185,plain,
% 62.86/40.52 (![X: map_int_elt] : sort(map(int, elt1), t2tb5(X)) <=> ![X: map_int_elt] : sort(map(int, elt1), t2tb5(X))),
% 62.86/40.52 inference(quant_intro,[status(thm)],[184])).
% 62.86/40.52 tff(186,plain,
% 62.86/40.52 (![X: map_int_elt] : sort(map(int, elt1), t2tb5(X)) <=> ![X: map_int_elt] : sort(map(int, elt1), t2tb5(X))),
% 62.86/40.52 inference(rewrite,[status(thm)],[])).
% 62.86/40.52 tff(187,axiom,(![X: map_int_elt] : sort(map(int, elt1), t2tb5(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2tb_sort6')).
% 62.86/40.52 tff(188,plain,
% 62.86/40.52 (![X: map_int_elt] : sort(map(int, elt1), t2tb5(X))),
% 62.86/40.52 inference(modus_ponens,[status(thm)],[187, 186])).
% 62.86/40.52 tff(189,plain,(
% 62.86/40.52 ![X: map_int_elt] : sort(map(int, elt1), t2tb5(X))),
% 62.86/40.52 inference(skolemize,[status(sab)],[188])).
% 62.86/40.52 tff(190,plain,
% 62.86/40.52 (![X: map_int_elt] : sort(map(int, elt1), t2tb5(X))),
% 62.86/40.52 inference(modus_ponens,[status(thm)],[189, 185])).
% 62.86/40.52 tff(191,plain,
% 62.86/40.52 ((~![X: map_int_elt] : sort(map(int, elt1), t2tb5(X))) | sort(map(int, elt1), t2tb5(A3!14))),
% 62.86/40.52 inference(quant_inst,[status(thm)],[])).
% 62.86/40.52 tff(192,plain,
% 62.86/40.52 (sort(map(int, elt1), t2tb5(A3!14))),
% 62.86/40.52 inference(unit_resolution,[status(thm)],[191, 190])).
% 62.86/40.52 tff(193,plain,
% 62.86/40.52 (^[A: ty, U: $int, U1: uni] : refl(((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)))),
% 62.86/40.52 inference(bind,[status(th)],[])).
% 62.86/40.52 tff(194,plain,
% 62.86/40.52 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 62.86/40.52 inference(quant_intro,[status(thm)],[193])).
% 62.86/40.52 tff(195,plain,
% 62.86/40.52 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 62.86/40.52 inference(rewrite,[status(thm)],[])).
% 62.86/40.52 tff(196,plain,
% 62.86/40.52 (^[A: ty, U: $int, U1: uni] : rewrite((sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1)) <=> ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)))),
% 62.86/40.52 inference(bind,[status(th)],[])).
% 62.86/40.52 tff(197,plain,
% 62.86/40.52 (![A: ty, U: $int, U1: uni] : (sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 62.86/40.52 inference(quant_intro,[status(thm)],[196])).
% 62.86/40.52 tff(198,axiom,(![A: ty, U: $int, U1: uni] : (sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','elts_def')).
% 62.86/40.52 tff(199,plain,
% 62.86/40.52 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 62.86/40.52 inference(modus_ponens,[status(thm)],[198, 197])).
% 62.86/40.52 tff(200,plain,
% 62.86/40.52 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 62.86/40.52 inference(modus_ponens,[status(thm)],[199, 195])).
% 62.86/40.52 tff(201,plain,(
% 62.86/40.52 ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 62.86/40.52 inference(skolemize,[status(sab)],[200])).
% 62.86/40.52 tff(202,plain,
% 62.86/40.52 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 62.86/40.52 inference(modus_ponens,[status(thm)],[201, 194])).
% 62.86/40.52 tff(203,plain,
% 62.86/40.52 (((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | ((~sort(map(int, elt1), t2tb5(A3!14))) | (elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))) = t2tb5(A3!14)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | (~sort(map(int, elt1), t2tb5(A3!14))) | (elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))) = t2tb5(A3!14)))),
% 62.86/40.52 inference(rewrite,[status(thm)],[])).
% 62.86/40.52 tff(204,plain,
% 62.86/40.52 ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | ((~sort(map(int, elt1), t2tb5(A3!14))) | (elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))) = t2tb5(A3!14)))),
% 62.86/40.52 inference(quant_inst,[status(thm)],[])).
% 62.86/40.52 tff(205,plain,
% 62.86/40.52 ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | (~sort(map(int, elt1), t2tb5(A3!14))) | (elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))) = t2tb5(A3!14))),
% 62.86/40.52 inference(modus_ponens,[status(thm)],[204, 203])).
% 62.86/40.52 tff(206,plain,
% 62.86/40.52 ((~sort(map(int, elt1), t2tb5(A3!14))) | (elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))) = t2tb5(A3!14))),
% 62.86/40.52 inference(unit_resolution,[status(thm)],[205, 202])).
% 62.86/40.52 tff(207,plain,
% 62.86/40.52 (elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))) = t2tb5(A3!14)),
% 62.86/40.52 inference(unit_resolution,[status(thm)],[206, 192])).
% 62.86/40.52 tff(208,plain,
% 62.86/40.52 (t2tb5(A3!14) = elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14)))),
% 62.86/40.52 inference(symmetry,[status(thm)],[207])).
% 62.86/40.52 tff(209,plain,
% 62.86/40.52 (exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) <=> exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)),
% 62.86/40.52 inference(monotonicity,[status(thm)],[208])).
% 62.86/40.52 tff(210,plain,
% 62.86/40.52 (exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15) <=> exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)),
% 62.86/40.52 inference(symmetry,[status(thm)],[209])).
% 62.86/40.52 tff(211,plain,
% 62.86/40.52 (^[A: ty, A1: uni, A2: uni, I: $int, J: $int] : refl((exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J))))) <=> (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J))))))),
% 62.86/40.52 inference(bind,[status(th)],[])).
% 62.86/40.52 tff(212,plain,
% 62.86/40.52 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J))))) <=> ![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))),
% 62.86/40.52 inference(quant_intro,[status(thm)],[211])).
% 62.86/40.52 tff(213,plain,
% 62.86/40.52 (^[A: ty, A1: uni, A2: uni, I: $int, J: $int] : rewrite((exchange1(A, A1, A2, I, J) <=> (($sum(length(A, A1), $product(-1, length(A, A2))) = 0) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J))) <=> (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J))))))),
% 62.86/40.52 inference(bind,[status(th)],[])).
% 62.86/40.52 tff(214,plain,
% 62.86/40.52 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (($sum(length(A, A1), $product(-1, length(A, A2))) = 0) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J))) <=> ![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))),
% 62.86/40.52 inference(quant_intro,[status(thm)],[213])).
% 62.86/40.52 tff(215,plain,
% 62.86/40.52 (^[A: ty, A1: uni, A2: uni, I: $int, J: $int] : rewrite((exchange1(A, A1, A2, I, J) <=> ((length(A, A1) = length(A, A2)) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J))) <=> (exchange1(A, A1, A2, I, J) <=> (($sum(length(A, A1), $product(-1, length(A, A2))) = 0) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J))))),
% 62.86/40.52 inference(bind,[status(th)],[])).
% 62.86/40.52 tff(216,plain,
% 62.86/40.52 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> ((length(A, A1) = length(A, A2)) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J))) <=> ![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (($sum(length(A, A1), $product(-1, length(A, A2))) = 0) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))),
% 62.86/40.52 inference(quant_intro,[status(thm)],[215])).
% 62.86/40.52 tff(217,plain,
% 62.86/40.52 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> ((length(A, A1) = length(A, A2)) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J))) <=> ![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> ((length(A, A1) = length(A, A2)) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))),
% 62.86/40.52 inference(rewrite,[status(thm)],[])).
% 62.86/40.52 tff(218,axiom,(![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> ((length(A, A1) = length(A, A2)) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','exchange_def1')).
% 62.86/40.52 tff(219,plain,
% 62.86/40.52 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> ((length(A, A1) = length(A, A2)) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))),
% 62.86/40.52 inference(modus_ponens,[status(thm)],[218, 217])).
% 62.86/40.52 tff(220,plain,
% 62.86/40.52 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (($sum(length(A, A1), $product(-1, length(A, A2))) = 0) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))),
% 62.86/40.52 inference(modus_ponens,[status(thm)],[219, 216])).
% 62.86/40.52 tff(221,plain,(
% 62.86/40.52 ![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (($sum(length(A, A1), $product(-1, length(A, A2))) = 0) & exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))),
% 62.86/40.52 inference(skolemize,[status(sab)],[220])).
% 62.86/40.52 tff(222,plain,
% 62.86/40.52 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))),
% 62.86/40.52 inference(modus_ponens,[status(thm)],[221, 214])).
% 62.86/40.52 tff(223,plain,
% 62.86/40.52 (![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))),
% 62.86/40.53 inference(modus_ponens,[status(thm)],[222, 212])).
% 62.86/40.53 tff(224,plain,
% 62.86/40.53 (((~![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))) | (exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0)))))) <=> ((~![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))) | (exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0))))))),
% 62.86/40.53 inference(rewrite,[status(thm)],[])).
% 62.86/40.53 tff(225,plain,
% 62.86/40.53 ((exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))))) = 0)) | (~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15))))) <=> (exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0)))))),
% 62.86/40.53 inference(rewrite,[status(thm)],[])).
% 62.86/40.53 tff(226,plain,
% 62.86/40.53 (((~![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))) | (exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))))) = 0)) | (~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)))))) <=> ((~![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))) | (exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0))))))),
% 62.86/40.53 inference(monotonicity,[status(thm)],[225])).
% 62.86/40.53 tff(227,plain,
% 62.86/40.53 (((~![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))) | (exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))))) = 0)) | (~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)))))) <=> ((~![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))) | (exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0))))))),
% 62.86/40.53 inference(transitivity,[status(thm)],[226, 224])).
% 62.86/40.53 tff(228,plain,
% 62.86/40.53 ((~![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))) | (exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))))) = 0)) | (~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)))))),
% 62.86/40.53 inference(quant_inst,[status(thm)],[])).
% 62.86/40.53 tff(229,plain,
% 62.86/40.53 ((~![A: ty, A1: uni, A2: uni, I: $int, J: $int] : (exchange1(A, A1, A2, I, J) <=> (~((~($sum(length(A, A1), $product(-1, length(A, A2))) = 0)) | (~exchange(A, elts(A, A1), elts(A, A2), 0, length(A, A1), I, J)))))) | (exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0)))))),
% 62.86/40.53 inference(modus_ponens,[status(thm)],[228, 227])).
% 62.86/40.53 tff(230,plain,
% 62.86/40.53 (exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0))))),
% 62.86/40.53 inference(unit_resolution,[status(thm)],[229, 223])).
% 62.86/40.53 tff(231,plain,
% 62.86/40.53 (exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15)),
% 62.86/40.53 inference(and_elim,[status(thm)],[54])).
% 62.86/40.53 tff(232,plain,
% 62.86/40.53 ((~(exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0)))))) | (~exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15)) | (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0))))),
% 62.86/40.53 inference(tautology,[status(thm)],[])).
% 62.86/40.53 tff(233,plain,
% 62.86/40.53 ((~(exchange1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), mk_array(elt1, A!10, t2tb5(A5!17)), $sum(-1, J!15), J!15) <=> (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0)))))) | (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0))))),
% 62.86/40.53 inference(unit_resolution,[status(thm)],[232, 231])).
% 62.86/40.53 tff(234,plain,
% 62.86/40.53 (~((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0)))),
% 62.86/40.53 inference(unit_resolution,[status(thm)],[233, 230])).
% 62.86/40.53 tff(235,plain,
% 62.86/40.53 (((~exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = 0))) | exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)),
% 62.86/40.53 inference(tautology,[status(thm)],[])).
% 62.86/40.53 tff(236,plain,
% 62.86/40.53 (exchange(elt1, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)),
% 62.86/40.53 inference(unit_resolution,[status(thm)],[235, 234])).
% 62.86/40.53 tff(237,plain,
% 62.86/40.53 (exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)),
% 62.86/40.53 inference(modus_ponens,[status(thm)],[236, 210])).
% 62.86/40.53 tff(238,plain,
% 62.86/40.53 ((~((~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))))))) | (~exchange(elt1, t2tb5(A3!14), elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), 0, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $sum(-1, J!15), J!15)) | (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0)))))),
% 62.86/40.53 inference(tautology,[status(thm)],[])).
% 62.86/40.53 tff(239,plain,
% 62.86/40.53 (~((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))))),
% 62.86/40.53 inference(unit_resolution,[status(thm)],[238, 237, 183])).
% 62.86/40.53 tff(240,plain,
% 62.86/40.53 (((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0)))) | (get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))),
% 62.86/40.53 inference(tautology,[status(thm)],[])).
% 62.86/40.53 tff(241,plain,
% 62.86/40.53 (get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15))),
% 62.86/40.53 inference(unit_resolution,[status(thm)],[240, 239])).
% 62.86/40.53 tff(242,plain,
% 62.86/40.53 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)) = get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))),
% 62.86/40.53 inference(symmetry,[status(thm)],[241])).
% 62.86/40.53 tff(243,plain,
% 62.86/40.53 (^[A: ty, A1: uni, I: $int] : refl((get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))))),
% 62.86/40.53 inference(bind,[status(th)],[])).
% 62.86/40.53 tff(244,plain,
% 62.86/40.53 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 62.86/40.53 inference(quant_intro,[status(thm)],[243])).
% 62.86/40.53 tff(245,plain,
% 62.86/40.53 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 62.86/40.53 inference(rewrite,[status(thm)],[])).
% 62.86/40.53 tff(246,axiom,(![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','get_def')).
% 62.86/40.53 tff(247,plain,
% 62.86/40.53 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 62.86/40.53 inference(modus_ponens,[status(thm)],[246, 245])).
% 62.86/40.53 tff(248,plain,(
% 62.86/40.53 ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 62.86/40.53 inference(skolemize,[status(sab)],[247])).
% 62.86/40.53 tff(249,plain,
% 62.86/40.53 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 62.86/40.53 inference(modus_ponens,[status(thm)],[248, 244])).
% 62.86/40.53 tff(250,plain,
% 62.86/40.53 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), J!15) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))),
% 62.86/40.53 inference(quant_inst,[status(thm)],[])).
% 62.86/40.53 tff(251,plain,
% 62.86/40.53 (get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), J!15) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15))),
% 62.86/40.53 inference(unit_resolution,[status(thm)],[250, 249])).
% 62.86/40.53 tff(252,assumption,(~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)), introduced(assumption)).
% 62.86/40.53 tff(253,plain,
% 62.86/40.53 ($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | $greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)),
% 62.86/40.53 inference(theory_lemma,[status(thm)],[])).
% 62.86/40.53 tff(254,plain,
% 62.86/40.53 ($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.53 inference(unit_resolution,[status(thm)],[253, 252])).
% 62.86/40.53 tff(255,assumption,(~$lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)), introduced(assumption)).
% 62.86/40.53 tff(256,plain,
% 62.86/40.53 ((~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1)) | $greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)),
% 62.86/40.53 inference(theory_lemma,[status(thm)],[])).
% 62.86/40.53 tff(257,plain,
% 62.86/40.53 (~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1)),
% 62.86/40.53 inference(unit_resolution,[status(thm)],[256, 252])).
% 62.86/40.53 tff(258,plain,
% 62.86/40.53 (![J: uni] : (t2tb3(tb2t3(J)) = J) <=> ![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 62.86/40.53 inference(rewrite,[status(thm)],[])).
% 62.86/40.53 tff(259,plain,
% 62.86/40.53 (![J: uni] : (t2tb3(tb2t3(J)) = J) <=> ![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 62.86/40.53 inference(rewrite,[status(thm)],[])).
% 62.86/40.53 tff(260,axiom,(![J: uni] : (t2tb3(tb2t3(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR3')).
% 62.86/40.53 tff(261,plain,
% 62.86/40.53 (![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 62.86/40.53 inference(modus_ponens,[status(thm)],[260, 259])).
% 62.86/40.53 tff(262,plain,(
% 62.86/40.53 ![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 62.86/40.53 inference(skolemize,[status(sab)],[261])).
% 62.86/40.53 tff(263,plain,
% 62.86/40.53 (![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 62.86/40.53 inference(modus_ponens,[status(thm)],[262, 258])).
% 62.86/40.53 tff(264,plain,
% 62.86/40.53 ((~![J: uni] : (t2tb3(tb2t3(J)) = J)) | (t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))) = mk_array(elt1, A!10, t2tb5(A5!17)))),
% 62.86/40.53 inference(quant_inst,[status(thm)],[])).
% 62.86/40.53 tff(265,plain,
% 62.86/40.53 (t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))) = mk_array(elt1, A!10, t2tb5(A5!17))),
% 62.86/40.53 inference(unit_resolution,[status(thm)],[264, 263])).
% 62.86/40.53 tff(266,plain,
% 62.86/40.53 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.86/40.53 inference(monotonicity,[status(thm)],[265])).
% 62.86/40.53 tff(267,plain,
% 62.86/40.53 (get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.86/40.53 inference(symmetry,[status(thm)],[266])).
% 62.86/40.53 tff(268,plain,
% 62.86/40.53 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.86/40.54 inference(quant_inst,[status(thm)],[])).
% 62.86/40.54 tff(269,plain,
% 62.86/40.54 (get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.86/40.54 inference(unit_resolution,[status(thm)],[268, 249])).
% 62.86/40.54 tff(270,plain,
% 62.86/40.54 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.86/40.54 inference(symmetry,[status(thm)],[269])).
% 62.86/40.54 tff(271,plain,
% 62.86/40.54 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 62.86/40.54 inference(rewrite,[status(thm)],[])).
% 62.86/40.54 tff(272,plain,
% 62.86/40.54 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 62.86/40.54 inference(rewrite,[status(thm)],[])).
% 62.86/40.54 tff(273,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR')).
% 62.86/40.54 tff(274,plain,
% 62.86/40.54 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 62.86/40.54 inference(modus_ponens,[status(thm)],[273, 272])).
% 62.86/40.54 tff(275,plain,(
% 62.86/40.54 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 62.86/40.54 inference(skolemize,[status(sab)],[274])).
% 62.86/40.54 tff(276,plain,
% 62.86/40.54 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 62.86/40.54 inference(modus_ponens,[status(thm)],[275, 271])).
% 62.86/40.54 tff(277,plain,
% 62.86/40.54 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.86/40.54 inference(quant_inst,[status(thm)],[])).
% 62.86/40.54 tff(278,plain,
% 62.86/40.54 (t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.86/40.54 inference(unit_resolution,[status(thm)],[277, 276])).
% 62.86/40.54 tff(279,plain,
% 62.86/40.54 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.86/40.54 inference(monotonicity,[status(thm)],[278])).
% 62.86/40.54 tff(280,assumption,(~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1)), introduced(assumption)).
% 62.86/40.54 tff(281,assumption,($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)), introduced(assumption)).
% 62.86/40.54 tff(282,assumption,(~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)), introduced(assumption)).
% 62.86/40.54 tff(283,plain,
% 62.86/40.54 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.86/40.54 inference(quant_inst,[status(thm)],[])).
% 62.86/40.54 tff(284,plain,
% 62.86/40.54 ($sum(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0),
% 62.86/40.54 inference(unit_resolution,[status(thm)],[283, 117])).
% 62.86/40.54 tff(285,plain,
% 62.86/40.54 ((~($sum(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)) | $greatereq($sum(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.54 inference(theory_lemma,[status(thm)],[])).
% 62.86/40.54 tff(286,plain,
% 62.86/40.54 ($greatereq($sum(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.54 inference(unit_resolution,[status(thm)],[285, 284])).
% 62.86/40.54 tff(287,assumption,(~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)), introduced(assumption)).
% 62.86/40.54 tff(288,plain,
% 62.86/40.54 ($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | $greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)),
% 62.86/40.54 inference(theory_lemma,[status(thm)],[])).
% 62.86/40.54 tff(289,plain,
% 62.86/40.54 ($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.54 inference(unit_resolution,[status(thm)],[288, 287])).
% 62.86/40.54 tff(290,plain,
% 62.86/40.54 (($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))),
% 62.86/40.54 inference(theory_lemma,[status(thm)],[])).
% 62.86/40.54 tff(291,plain,
% 62.86/40.54 (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.54 inference(unit_resolution,[status(thm)],[290, 289, 282])).
% 62.86/40.54 tff(292,plain,
% 62.86/40.54 ((~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$lesseq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | $greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.54 inference(theory_lemma,[status(thm)],[])).
% 62.86/40.54 tff(293,plain,
% 62.86/40.54 (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.54 inference(unit_resolution,[status(thm)],[292, 291, 286, 98, 121])).
% 62.86/40.54 tff(294,plain,
% 62.86/40.54 ((~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)) | $greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.54 inference(theory_lemma,[status(thm)],[])).
% 62.86/40.54 tff(295,plain,
% 62.86/40.54 (~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.86/40.54 inference(unit_resolution,[status(thm)],[294, 293])).
% 62.86/40.54 tff(296,plain,
% 62.86/40.54 (~$lesseq(J!15, 0)),
% 62.86/40.54 inference(and_elim,[status(thm)],[54])).
% 62.86/40.54 tff(297,assumption,(~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)), introduced(assumption)).
% 62.86/40.54 tff(298,plain,
% 62.86/40.54 ($false),
% 62.86/40.54 inference(theory_lemma,[status(thm)],[297, 121, 98, 58, 100, 296])).
% 62.86/40.54 tff(299,plain,($greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)), inference(lemma,lemma(discharge,[]))).
% 62.86/40.54 tff(300,plain,
% 62.86/40.54 (((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0)))) | ![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))),
% 62.86/40.54 inference(tautology,[status(thm)],[])).
% 62.86/40.54 tff(301,plain,
% 62.86/40.54 (![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))),
% 62.86/40.54 inference(unit_resolution,[status(thm)],[300, 239])).
% 62.86/40.54 tff(302,plain,
% 62.86/40.54 (((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | ((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | (~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))),
% 62.86/40.54 inference(rewrite,[status(thm)],[])).
% 62.86/40.54 tff(303,plain,
% 62.86/40.54 (((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)) <=> ((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))),
% 62.86/40.54 inference(rewrite,[status(thm)],[])).
% 62.86/40.54 tff(304,plain,
% 62.86/40.54 (($sum($product(-1, J!15), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = 0) <=> ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.86/40.54 inference(rewrite,[status(thm)],[])).
% 62.86/40.54 tff(305,plain,
% 62.86/40.54 ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = $sum($product(-1, J!15), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.86/40.54 inference(rewrite,[status(thm)],[])).
% 62.86/40.54 tff(306,plain,
% 62.86/40.54 (($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0) <=> ($sum($product(-1, J!15), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = 0)),
% 62.86/40.54 inference(monotonicity,[status(thm)],[305])).
% 62.86/40.54 tff(307,plain,
% 62.86/40.54 (($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0) <=> ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.86/40.54 inference(transitivity,[status(thm)],[306, 304])).
% 62.86/40.54 tff(308,plain,
% 62.86/40.54 ($greatereq($sum($product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))), 0) <=> $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.54 inference(rewrite,[status(thm)],[])).
% 62.86/40.54 tff(309,plain,
% 62.86/40.54 ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = $sum($product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.86/40.54 inference(rewrite,[status(thm)],[])).
% 62.86/40.54 tff(310,plain,
% 62.86/40.54 ($greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) <=> $greatereq($sum($product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))), 0)),
% 62.86/40.54 inference(monotonicity,[status(thm)],[309])).
% 62.86/40.54 tff(311,plain,
% 62.86/40.54 ($greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) <=> $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.54 inference(transitivity,[status(thm)],[310, 308])).
% 62.86/40.54 tff(312,plain,
% 62.86/40.54 (($sum($product(-1, J!15), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = -1) <=> ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1)),
% 62.86/40.54 inference(rewrite,[status(thm)],[])).
% 62.86/40.54 tff(313,plain,
% 62.86/40.54 (($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) <=> ($sum($product(-1, J!15), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = -1)),
% 62.86/40.54 inference(monotonicity,[status(thm)],[305])).
% 62.86/40.54 tff(314,plain,
% 62.86/40.54 (($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) <=> ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1)),
% 62.86/40.54 inference(transitivity,[status(thm)],[313, 312])).
% 62.86/40.54 tff(315,plain,
% 62.86/40.54 (((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0)) <=> ((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))),
% 62.86/40.54 inference(monotonicity,[status(thm)],[314, 311, 307])).
% 62.86/40.54 tff(316,plain,
% 62.86/40.54 (((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0)) <=> ((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))),
% 62.86/40.55 inference(transitivity,[status(thm)],[315, 303])).
% 62.86/40.55 tff(317,plain,
% 62.86/40.55 (((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | ((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | ((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)))),
% 62.86/40.55 inference(monotonicity,[status(thm)],[316])).
% 62.86/40.55 tff(318,plain,
% 62.86/40.55 (((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | ((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | (~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))),
% 62.86/40.55 inference(transitivity,[status(thm)],[317, 302])).
% 62.86/40.55 tff(319,plain,
% 62.86/40.55 ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | ((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0))),
% 62.86/40.55 inference(quant_inst,[status(thm)],[])).
% 62.86/40.55 tff(320,plain,
% 62.86/40.55 ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | (~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.86/40.55 inference(modus_ponens,[status(thm)],[319, 318])).
% 62.86/40.55 tff(321,plain,
% 62.86/40.55 ((~$greatereq(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.86/40.55 inference(unit_resolution,[status(thm)],[320, 301])).
% 62.86/40.55 tff(322,plain,
% 62.86/40.55 ((get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.86/40.55 inference(unit_resolution,[status(thm)],[321, 299])).
% 62.86/40.55 tff(323,plain,
% 62.86/40.55 (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.86/40.55 inference(unit_resolution,[status(thm)],[322, 295, 255, 280])).
% 62.86/40.55 tff(324,plain,
% 62.86/40.55 (t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.86/40.55 inference(symmetry,[status(thm)],[278])).
% 62.86/40.55 tff(325,plain,
% 62.86/40.55 (get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.86/40.55 inference(monotonicity,[status(thm)],[324])).
% 62.86/40.55 tff(326,plain,
% 62.86/40.55 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.86/40.55 inference(monotonicity,[status(thm)],[207, 278])).
% 62.86/40.55 tff(327,plain,
% 62.86/40.55 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))),
% 62.86/40.55 inference(quant_inst,[status(thm)],[])).
% 62.86/40.55 tff(328,plain,
% 62.86/40.55 (get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.86/40.55 inference(unit_resolution,[status(thm)],[327, 249])).
% 62.86/40.55 tff(329,plain,
% 62.86/40.55 ((~![J: uni] : (t2tb3(tb2t3(J)) = J)) | (t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))) = mk_array(elt1, A!10, t2tb5(A3!14)))),
% 62.86/40.55 inference(quant_inst,[status(thm)],[])).
% 62.86/40.55 tff(330,plain,
% 62.86/40.55 (t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))) = mk_array(elt1, A!10, t2tb5(A3!14))),
% 62.86/40.55 inference(unit_resolution,[status(thm)],[329, 263])).
% 62.86/40.55 tff(331,plain,
% 62.86/40.55 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.86/40.55 inference(monotonicity,[status(thm)],[330])).
% 62.86/40.55 tff(332,plain,
% 62.86/40.55 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.86/40.55 inference(transitivity,[status(thm)],[331, 328, 326, 325, 323, 279, 270, 267])).
% 62.86/40.55 tff(333,plain,
% 62.86/40.55 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.86/40.55 inference(monotonicity,[status(thm)],[332])).
% 62.86/40.55 tff(334,plain,
% 62.86/40.55 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.86/40.55 inference(monotonicity,[status(thm)],[265])).
% 62.86/40.55 tff(335,plain,
% 62.86/40.55 (get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.86/40.55 inference(symmetry,[status(thm)],[334])).
% 62.86/40.55 tff(336,plain,
% 62.86/40.55 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.86/40.55 inference(quant_inst,[status(thm)],[])).
% 62.86/40.55 tff(337,plain,
% 62.86/40.55 (get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.86/40.55 inference(unit_resolution,[status(thm)],[336, 249])).
% 62.86/40.55 tff(338,plain,
% 62.86/40.55 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.86/40.55 inference(symmetry,[status(thm)],[337])).
% 62.86/40.55 tff(339,plain,
% 62.86/40.55 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.86/40.55 inference(quant_inst,[status(thm)],[])).
% 62.86/40.55 tff(340,plain,
% 62.86/40.55 (t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.86/40.55 inference(unit_resolution,[status(thm)],[339, 276])).
% 62.86/40.55 tff(341,plain,
% 62.86/40.55 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.86/40.55 inference(monotonicity,[status(thm)],[340])).
% 62.86/40.55 tff(342,plain,
% 62.86/40.55 ((~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1)) | $greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)),
% 62.86/40.55 inference(theory_lemma,[status(thm)],[])).
% 62.86/40.55 tff(343,plain,
% 62.86/40.55 (~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1)),
% 62.86/40.55 inference(unit_resolution,[status(thm)],[342, 287])).
% 62.86/40.55 tff(344,assumption,($lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)), introduced(assumption)).
% 62.86/40.55 tff(345,plain,
% 62.86/40.55 ($false),
% 62.86/40.55 inference(theory_lemma,[status(thm)],[127, 98, 344, 286, 144, 122])).
% 62.86/40.55 tff(346,plain,(~$lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)), inference(lemma,lemma(discharge,[]))).
% 62.86/40.55 tff(347,plain,
% 62.86/40.55 ((~($sum(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)) | $lesseq($sum(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.55 inference(theory_lemma,[status(thm)],[])).
% 62.86/40.55 tff(348,plain,
% 62.86/40.55 ($lesseq($sum(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.55 inference(unit_resolution,[status(thm)],[347, 284])).
% 62.86/40.55 tff(349,assumption,(~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)), introduced(assumption)).
% 62.86/40.55 tff(350,plain,
% 62.86/40.55 ($false),
% 62.86/40.55 inference(theory_lemma,[status(thm)],[296, 100, 349, 348, 58])).
% 62.86/40.55 tff(351,plain,($greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)), inference(lemma,lemma(discharge,[]))).
% 62.86/40.55 tff(352,plain,
% 62.86/40.55 (((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | ((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | (~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))),
% 62.86/40.56 inference(rewrite,[status(thm)],[])).
% 62.86/40.56 tff(353,plain,
% 62.86/40.56 (((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)) <=> ((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))),
% 62.86/40.56 inference(rewrite,[status(thm)],[])).
% 62.86/40.56 tff(354,plain,
% 62.86/40.56 (($sum($product(-1, J!15), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = 0) <=> ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.86/40.56 inference(rewrite,[status(thm)],[])).
% 62.86/40.56 tff(355,plain,
% 62.86/40.56 ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = $sum($product(-1, J!15), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.86/40.56 inference(rewrite,[status(thm)],[])).
% 62.86/40.56 tff(356,plain,
% 62.86/40.56 (($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0) <=> ($sum($product(-1, J!15), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = 0)),
% 62.86/40.56 inference(monotonicity,[status(thm)],[355])).
% 62.86/40.56 tff(357,plain,
% 62.86/40.56 (($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0) <=> ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.86/40.56 inference(transitivity,[status(thm)],[356, 354])).
% 62.86/40.56 tff(358,plain,
% 62.86/40.56 ($greatereq($sum($product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))), 0) <=> $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.56 inference(rewrite,[status(thm)],[])).
% 62.86/40.56 tff(359,plain,
% 62.86/40.56 ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))) = $sum($product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.86/40.56 inference(rewrite,[status(thm)],[])).
% 62.86/40.56 tff(360,plain,
% 62.86/40.56 ($greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) <=> $greatereq($sum($product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))), 0)),
% 62.86/40.56 inference(monotonicity,[status(thm)],[359])).
% 62.86/40.56 tff(361,plain,
% 62.86/40.56 ($greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) <=> $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.86/40.56 inference(transitivity,[status(thm)],[360, 358])).
% 62.86/40.56 tff(362,plain,
% 62.86/40.56 (($sum($product(-1, J!15), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = -1) <=> ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1)),
% 62.86/40.56 inference(rewrite,[status(thm)],[])).
% 62.86/40.56 tff(363,plain,
% 62.86/40.56 (($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) <=> ($sum($product(-1, J!15), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = -1)),
% 62.86/40.56 inference(monotonicity,[status(thm)],[355])).
% 62.86/40.56 tff(364,plain,
% 62.86/40.56 (($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) <=> ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1)),
% 62.86/40.56 inference(transitivity,[status(thm)],[363, 362])).
% 62.86/40.56 tff(365,plain,
% 62.86/40.56 (((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0)) <=> ((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))),
% 62.86/40.56 inference(monotonicity,[status(thm)],[364, 361, 357])).
% 62.86/40.56 tff(366,plain,
% 62.86/40.56 (((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0)) <=> ((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))),
% 62.86/40.56 inference(transitivity,[status(thm)],[365, 353])).
% 62.86/40.56 tff(367,plain,
% 62.86/40.56 (((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | ((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | ((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)))),
% 62.86/40.56 inference(monotonicity,[status(thm)],[366])).
% 62.86/40.56 tff(368,plain,
% 62.86/40.56 (((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | ((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0))) <=> ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | (~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0))),
% 62.86/40.56 inference(transitivity,[status(thm)],[367, 352])).
% 62.86/40.56 tff(369,plain,
% 62.86/40.56 ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | ((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | $greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)) = 0))),
% 62.92/40.56 inference(quant_inst,[status(thm)],[])).
% 62.92/40.56 tff(370,plain,
% 62.92/40.56 ((~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0))) | (~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.92/40.56 inference(modus_ponens,[status(thm)],[369, 368])).
% 62.92/40.56 tff(371,plain,
% 62.92/40.56 ((~$greatereq(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.92/40.56 inference(unit_resolution,[status(thm)],[370, 301])).
% 62.92/40.56 tff(372,plain,
% 62.92/40.56 ((get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.92/40.56 inference(unit_resolution,[status(thm)],[371, 351])).
% 62.92/40.56 tff(373,plain,
% 62.92/40.56 ((get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.92/40.57 inference(unit_resolution,[status(thm)],[372, 346])).
% 62.92/40.57 tff(374,plain,
% 62.92/40.57 (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.57 inference(unit_resolution,[status(thm)],[373, 343, 282])).
% 62.92/40.57 tff(375,plain,
% 62.92/40.57 (t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.57 inference(symmetry,[status(thm)],[340])).
% 62.92/40.57 tff(376,plain,
% 62.92/40.57 (get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.57 inference(monotonicity,[status(thm)],[375])).
% 62.92/40.57 tff(377,plain,
% 62.92/40.57 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, t2tb5(A3!14), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.57 inference(monotonicity,[status(thm)],[207, 340])).
% 62.92/40.57 tff(378,plain,
% 62.92/40.57 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))),
% 62.92/40.57 inference(quant_inst,[status(thm)],[])).
% 62.92/40.57 tff(379,plain,
% 62.92/40.57 (get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.57 inference(unit_resolution,[status(thm)],[378, 249])).
% 62.92/40.57 tff(380,plain,
% 62.92/40.57 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.57 inference(monotonicity,[status(thm)],[330])).
% 62.92/40.57 tff(381,plain,
% 62.92/40.57 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.92/40.57 inference(transitivity,[status(thm)],[380, 379, 377, 376, 374, 341, 338, 335])).
% 62.92/40.57 tff(382,plain,
% 62.92/40.57 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.57 inference(monotonicity,[status(thm)],[381])).
% 62.92/40.57 tff(383,plain,
% 62.92/40.57 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) <=> le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.57 inference(monotonicity,[status(thm)],[382, 333])).
% 62.92/40.57 tff(384,plain,
% 62.92/40.57 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))),
% 62.92/40.57 inference(symmetry,[status(thm)],[383])).
% 62.92/40.57 tff(385,plain,
% 62.92/40.57 ((~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) <=> (~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))),
% 62.92/40.57 inference(monotonicity,[status(thm)],[384])).
% 62.92/40.57 tff(386,plain,
% 62.92/40.57 ((le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1)) | (~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.57 inference(tautology,[status(thm)],[])).
% 62.92/40.57 tff(387,plain,
% 62.92/40.57 (~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.57 inference(unit_resolution,[status(thm)],[386, 96])).
% 62.92/40.57 tff(388,plain,
% 62.92/40.57 (~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))),
% 62.92/40.57 inference(modus_ponens,[status(thm)],[387, 385])).
% 62.92/40.57 tff(389,plain,
% 62.92/40.57 ($greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | (~$lesseq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))),
% 62.92/40.57 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.57 tff(390,plain,
% 62.92/40.57 ($greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.92/40.57 inference(unit_resolution,[status(thm)],[389, 121, 286, 98])).
% 62.92/40.57 tff(391,plain,
% 62.92/40.57 ($greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), -1) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))),
% 62.92/40.57 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.57 tff(392,plain,
% 62.92/40.57 ($greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.92/40.57 inference(unit_resolution,[status(thm)],[391, 125, 127])).
% 62.92/40.57 tff(393,plain,
% 62.92/40.57 ((~$lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)) | (~$greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))),
% 62.92/40.57 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.57 tff(394,plain,
% 62.92/40.57 (~$lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)),
% 62.92/40.57 inference(unit_resolution,[status(thm)],[393, 392])).
% 62.92/40.57 tff(395,plain,
% 62.92/40.57 (((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2)))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), -1)))))))) <=> ((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2)))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), -1))))))))),
% 62.92/40.57 inference(rewrite,[status(thm)],[])).
% 62.92/40.57 tff(396,plain,
% 62.92/40.57 ((~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum($sum(1, I!12), $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, J!15)), 0))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~($lesseq($sum($sum(1, I!12), $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)))))))) <=> (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2)))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), -1)))))))),
% 62.92/40.57 inference(rewrite,[status(thm)],[])).
% 62.92/40.57 tff(397,plain,
% 62.92/40.57 (((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum($sum(1, I!12), $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, J!15)), 0))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~($lesseq($sum($sum(1, I!12), $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0))))))))) <=> ((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2)))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), -1))))))))),
% 62.92/40.57 inference(monotonicity,[status(thm)],[396])).
% 62.92/40.57 tff(398,plain,
% 62.92/40.57 (((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum($sum(1, I!12), $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, J!15)), 0))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~($lesseq($sum($sum(1, I!12), $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0))))))))) <=> ((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2)))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), -1))))))))),
% 62.92/40.58 inference(transitivity,[status(thm)],[397, 395])).
% 62.92/40.58 tff(399,plain,
% 62.92/40.58 ((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum($sum(1, I!12), $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, J!15)), 0))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~($lesseq($sum($sum(1, I!12), $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0))))))))),
% 62.92/40.58 inference(quant_inst,[status(thm)],[])).
% 62.92/40.58 tff(400,plain,
% 62.92/40.58 ((~![P: param, A: array_elt, L: $int, U: $int] : (~((~((~sorted_sub2(P, A, L, U)) | ![I1: $int, I2: $int] : (le(P, tb2t4(get1(elt1, t2tb3(A), I1)), tb2t4(get1(elt1, t2tb3(A), I2))) | (~$lesseq($sum(I1, $product(-1, I2)), 0)) | $lesseq($sum(U, $product(-1, I2)), 0) | (~$greatereq($sum(I1, $product(-1, L)), 0))))) | (~(sorted_sub2(P, A, L, U) | (~($lesseq($sum(U, $product(-1, tptp_fun_I2_7(U, L, A, P))), 0) | le(P, tb2t4(get1(elt1, t2tb3(A), tptp_fun_I1_8(U, L, A, P))), tb2t4(get1(elt1, t2tb3(A), tptp_fun_I2_7(U, L, A, P)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I1_8(U, L, A, P))), 0)) | (~$greatereq($sum(tptp_fun_I2_7(U, L, A, P), $product(-1, tptp_fun_I1_8(U, L, A, P))), 0))))))))) | (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2)))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), -1)))))))),
% 62.92/40.58 inference(modus_ponens,[status(thm)],[399, 398])).
% 62.92/40.58 tff(401,plain,
% 62.92/40.58 (~((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2)))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), -1))))))),
% 62.92/40.58 inference(unit_resolution,[status(thm)],[400, 83])).
% 62.92/40.58 tff(402,plain,
% 62.92/40.58 (((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2)))))) | (~(sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12)) | (~(le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11)))) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_I2_7($sum(1, I!12), J!15, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), P!11))), -1)))))) | ((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2)))))),
% 62.92/40.58 inference(tautology,[status(thm)],[])).
% 62.92/40.58 tff(403,plain,
% 62.92/40.58 ((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))),
% 62.92/40.58 inference(unit_resolution,[status(thm)],[402, 401])).
% 62.92/40.58 tff(404,plain,
% 62.92/40.58 (sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))),
% 62.92/40.58 inference(and_elim,[status(thm)],[54])).
% 62.92/40.58 tff(405,plain,
% 62.92/40.58 ((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2)))))) | (~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))),
% 62.92/40.58 inference(tautology,[status(thm)],[])).
% 62.92/40.58 tff(406,plain,
% 62.92/40.58 ((~((~sorted_sub2(P!11, tb2t3(mk_array(elt1, A!10, t2tb5(A3!14))), J!15, $sum(1, I!12))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2)))))) | ![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))),
% 62.92/40.58 inference(unit_resolution,[status(thm)],[405, 404])).
% 62.92/40.58 tff(407,plain,
% 62.92/40.58 (![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))),
% 62.92/40.58 inference(unit_resolution,[status(thm)],[406, 403])).
% 62.92/40.58 tff(408,plain,
% 62.92/40.58 (((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | ((~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | $lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1))) <=> ((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | $lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1))),
% 62.92/40.58 inference(rewrite,[status(thm)],[])).
% 62.92/40.58 tff(409,plain,
% 62.92/40.58 (((~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | $lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) <=> ((~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | $lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1))),
% 62.92/40.58 inference(rewrite,[status(thm)],[])).
% 62.92/40.58 tff(410,plain,
% 62.92/40.58 ($greatereq($sum($product(-1, I!12), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))), 1) <=> $lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)),
% 62.92/40.58 inference(rewrite,[status(thm)],[])).
% 62.92/40.58 tff(411,plain,
% 62.92/40.58 ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)) = $sum($product(-1, I!12), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.58 inference(rewrite,[status(thm)],[])).
% 62.92/40.58 tff(412,plain,
% 62.92/40.58 ($greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 1) <=> $greatereq($sum($product(-1, I!12), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))), 1)),
% 62.92/40.58 inference(monotonicity,[status(thm)],[411])).
% 62.92/40.58 tff(413,plain,
% 62.92/40.58 ($greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 1) <=> $lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)),
% 62.92/40.58 inference(transitivity,[status(thm)],[412, 410])).
% 62.92/40.58 tff(414,plain,
% 62.92/40.58 ((~$greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 0)) <=> (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))),
% 62.92/40.58 inference(rewrite,[status(thm)],[])).
% 62.92/40.58 tff(415,plain,
% 62.92/40.58 ((~$lesseq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) <=> (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))),
% 62.92/40.58 inference(rewrite,[status(thm)],[])).
% 62.92/40.58 tff(416,plain,
% 62.92/40.58 (((~$lesseq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 0)) | $greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) <=> ((~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | $lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))),
% 62.92/40.58 inference(monotonicity,[status(thm)],[415, 414, 413])).
% 62.92/40.58 tff(417,plain,
% 62.92/40.58 (((~$lesseq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 0)) | $greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) <=> ((~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | $lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1))),
% 62.92/40.58 inference(transitivity,[status(thm)],[416, 409])).
% 62.92/40.58 tff(418,plain,
% 62.92/40.58 (((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | ((~$lesseq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 0)) | $greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))) <=> ((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | ((~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | $lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)))),
% 62.92/40.58 inference(monotonicity,[status(thm)],[417])).
% 62.92/40.58 tff(419,plain,
% 62.92/40.58 (((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | ((~$lesseq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 0)) | $greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))) <=> ((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | $lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1))),
% 62.92/40.59 inference(transitivity,[status(thm)],[418, 408])).
% 62.92/40.59 tff(420,plain,
% 62.92/40.59 ((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | ((~$lesseq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 0)) | $greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))),
% 62.92/40.59 inference(quant_inst,[status(thm)],[])).
% 62.92/40.59 tff(421,plain,
% 62.92/40.59 ((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | $lesseq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)),
% 62.92/40.59 inference(modus_ponens,[status(thm)],[420, 419])).
% 62.92/40.59 tff(422,plain,
% 62.92/40.59 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[421, 407, 289, 394])).
% 62.92/40.59 tff(423,plain,
% 62.92/40.59 ($false),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[422, 390, 388])).
% 62.92/40.59 tff(424,plain,($greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)), inference(lemma,lemma(discharge,[]))).
% 62.92/40.59 tff(425,plain,
% 62.92/40.59 ($greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[424, 282, 280, 255])).
% 62.92/40.59 tff(426,assumption,($greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)), introduced(assumption)).
% 62.92/40.59 tff(427,plain,
% 62.92/40.59 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) = 0)),
% 62.92/40.59 inference(quant_inst,[status(thm)],[])).
% 62.92/40.59 tff(428,plain,
% 62.92/40.59 ($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) = 0),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[427, 117])).
% 62.92/40.59 tff(429,plain,
% 62.92/40.59 ((~($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) = 0)) | $lesseq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))), 0)),
% 62.92/40.59 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.59 tff(430,plain,
% 62.92/40.59 ($lesseq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))), 0)),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[429, 428])).
% 62.92/40.59 tff(431,plain,
% 62.92/40.59 ((~($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) = 0)) | $greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))), 0)),
% 62.92/40.59 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.59 tff(432,plain,
% 62.92/40.59 ($greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))), 0)),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[431, 428])).
% 62.92/40.59 tff(433,plain,
% 62.92/40.59 (J!15 = tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.59 inference(theory_lemma,[status(thm)],[432, 430, 426, 281])).
% 62.92/40.59 tff(434,plain,
% 62.92/40.59 (tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = J!15),
% 62.92/40.59 inference(symmetry,[status(thm)],[433])).
% 62.92/40.59 tff(435,plain,
% 62.92/40.59 (tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.59 inference(monotonicity,[status(thm)],[278])).
% 62.92/40.59 tff(436,plain,
% 62.92/40.59 (tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.59 inference(symmetry,[status(thm)],[435])).
% 62.92/40.59 tff(437,plain,
% 62.92/40.59 (tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11) = tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.59 inference(theory_lemma,[status(thm)],[125, 121])).
% 62.92/40.59 tff(438,plain,
% 62.92/40.59 (tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11) = J!15),
% 62.92/40.59 inference(transitivity,[status(thm)],[437, 436, 434])).
% 62.92/40.59 tff(439,plain,
% 62.92/40.59 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), J!15)),
% 62.92/40.59 inference(monotonicity,[status(thm)],[265, 438])).
% 62.92/40.59 tff(440,plain,
% 62.92/40.59 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))),
% 62.92/40.59 inference(transitivity,[status(thm)],[439, 251, 242])).
% 62.92/40.59 tff(441,plain,
% 62.92/40.59 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))),
% 62.92/40.59 inference(monotonicity,[status(thm)],[440])).
% 62.92/40.59 tff(442,plain,
% 62.92/40.59 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.59 inference(symmetry,[status(thm)],[441])).
% 62.92/40.59 tff(443,plain,
% 62.92/40.59 (((~$greatereq(J!15, 0)) | (~$greatereq(J!15, 1)) | (~(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(J!15)))) | (~(get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 1) | $greatereq($sum(J!15, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | (~![K: $int] : ((~$greatereq(K, 0)) | ($sum(K, $product(-1, J!15)) = -1) | (get(elt1, int, t2tb5(A3!14), t2tb(K)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(K))) | $greatereq($sum(K, $product(-1, length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))))), 0) | ($sum(K, $product(-1, J!15)) = 0)))) | (get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))))),
% 62.92/40.59 inference(tautology,[status(thm)],[])).
% 62.92/40.59 tff(444,plain,
% 62.92/40.59 (get(elt1, int, t2tb5(A3!14), t2tb(J!15)) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15)))),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[443, 239])).
% 62.92/40.59 tff(445,plain,
% 62.92/40.59 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))),
% 62.92/40.59 inference(symmetry,[status(thm)],[444])).
% 62.92/40.59 tff(446,plain,
% 62.92/40.59 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(t2tb($sum(-1, J!15)))) = t2tb($sum(-1, J!15)))),
% 62.92/40.59 inference(quant_inst,[status(thm)],[])).
% 62.92/40.59 tff(447,plain,
% 62.92/40.59 (t2tb(tb2t(t2tb($sum(-1, J!15)))) = t2tb($sum(-1, J!15))),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[446, 276])).
% 62.92/40.59 tff(448,plain,
% 62.92/40.59 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb($sum(-1, J!15))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb($sum(-1, J!15)))),
% 62.92/40.59 inference(monotonicity,[status(thm)],[447])).
% 62.92/40.59 tff(449,plain,
% 62.92/40.59 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tb2t(t2tb($sum(-1, J!15)))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb($sum(-1, J!15))))))),
% 62.92/40.59 inference(quant_inst,[status(thm)],[])).
% 62.92/40.59 tff(450,plain,
% 62.92/40.59 (get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tb2t(t2tb($sum(-1, J!15)))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb($sum(-1, J!15)))))),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[449, 249])).
% 62.92/40.59 tff(451,plain,
% 62.92/40.59 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 1)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 1))),
% 62.92/40.59 inference(rewrite,[status(thm)],[])).
% 62.92/40.59 tff(452,plain,
% 62.92/40.59 (($sum(-1, $sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15)))))) = 0) <=> ($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 1)),
% 62.92/40.59 inference(rewrite,[status(thm)],[])).
% 62.92/40.59 tff(453,plain,
% 62.92/40.59 ($sum($sum(-1, J!15), $product(-1, tb2t(t2tb($sum(-1, J!15))))) = $sum(-1, $sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))))),
% 62.92/40.59 inference(rewrite,[status(thm)],[])).
% 62.92/40.59 tff(454,plain,
% 62.92/40.59 (($sum($sum(-1, J!15), $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 0) <=> ($sum(-1, $sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15)))))) = 0)),
% 62.92/40.59 inference(monotonicity,[status(thm)],[453])).
% 62.92/40.59 tff(455,plain,
% 62.92/40.59 (($sum($sum(-1, J!15), $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 0) <=> ($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 1)),
% 62.92/40.59 inference(transitivity,[status(thm)],[454, 452])).
% 62.92/40.59 tff(456,plain,
% 62.92/40.59 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(-1, J!15), $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 1))),
% 62.92/40.59 inference(monotonicity,[status(thm)],[455])).
% 62.92/40.59 tff(457,plain,
% 62.92/40.59 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(-1, J!15), $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 1))),
% 62.92/40.59 inference(transitivity,[status(thm)],[456, 451])).
% 62.92/40.59 tff(458,plain,
% 62.92/40.59 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum($sum(-1, J!15), $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 0)),
% 62.92/40.59 inference(quant_inst,[status(thm)],[])).
% 62.92/40.59 tff(459,plain,
% 62.92/40.59 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 1)),
% 62.92/40.59 inference(modus_ponens,[status(thm)],[458, 457])).
% 62.92/40.59 tff(460,plain,
% 62.92/40.59 ($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 1),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[459, 117])).
% 62.92/40.59 tff(461,plain,
% 62.92/40.59 ((~($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 1)) | $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 1)),
% 62.92/40.59 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.59 tff(462,plain,
% 62.92/40.59 ($lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 1)),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[461, 460])).
% 62.92/40.59 tff(463,plain,
% 62.92/40.59 ((~($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))) = 1)) | $greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 1)),
% 62.92/40.59 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.59 tff(464,plain,
% 62.92/40.59 ($greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 1)),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[463, 460])).
% 62.92/40.59 tff(465,plain,
% 62.92/40.59 ($sum(-1, J!15) = tb2t(t2tb($sum(-1, J!15)))),
% 62.92/40.59 inference(theory_lemma,[status(thm)],[464, 462])).
% 62.92/40.59 tff(466,plain,
% 62.92/40.59 ($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1) | (~$lesseq($sum(J!15, $product(-1, J1!18)), 1)) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$lesseq($sum(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))),
% 62.92/40.59 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.59 tff(467,plain,
% 62.92/40.59 ($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[466, 100, 348, 58])).
% 62.92/40.59 tff(468,assumption,($greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)), introduced(assumption)).
% 62.92/40.59 tff(469,plain,
% 62.92/40.59 ($sum(-1, J!15) = tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.59 inference(theory_lemma,[status(thm)],[468, 467])).
% 62.92/40.59 tff(470,plain,
% 62.92/40.59 (tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = $sum(-1, J!15)),
% 62.92/40.59 inference(symmetry,[status(thm)],[469])).
% 62.92/40.59 tff(471,plain,
% 62.92/40.59 (tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11) = tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.59 inference(theory_lemma,[status(thm)],[286, 348])).
% 62.92/40.59 tff(472,plain,
% 62.92/40.59 (tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11) = tb2t(t2tb($sum(-1, J!15)))),
% 62.92/40.59 inference(transitivity,[status(thm)],[471, 470, 465])).
% 62.92/40.59 tff(473,plain,
% 62.92/40.59 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tb2t(t2tb($sum(-1, J!15))))),
% 62.92/40.59 inference(monotonicity,[status(thm)],[265, 472])).
% 62.92/40.59 tff(474,plain,
% 62.92/40.59 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))),
% 62.92/40.59 inference(transitivity,[status(thm)],[473, 450, 448, 445])).
% 62.92/40.59 tff(475,plain,
% 62.92/40.59 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 62.92/40.59 inference(monotonicity,[status(thm)],[474])).
% 62.92/40.59 tff(476,plain,
% 62.92/40.59 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.59 inference(symmetry,[status(thm)],[475])).
% 62.92/40.59 tff(477,plain,
% 62.92/40.59 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))) <=> le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.59 inference(monotonicity,[status(thm)],[476, 442])).
% 62.92/40.59 tff(478,plain,
% 62.92/40.59 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))),
% 62.92/40.59 inference(symmetry,[status(thm)],[477])).
% 62.92/40.59 tff(479,plain,
% 62.92/40.59 ((~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) <=> (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))))),
% 62.92/40.59 inference(monotonicity,[status(thm)],[478])).
% 62.92/40.59 tff(480,plain,
% 62.92/40.59 (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))),
% 62.92/40.59 inference(modus_ponens,[status(thm)],[387, 479])).
% 62.92/40.59 tff(481,plain,
% 62.92/40.59 (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))),
% 62.92/40.59 inference(and_elim,[status(thm)],[54])).
% 62.92/40.59 tff(482,plain,
% 62.92/40.59 (^[P: param, X: elt, Y: elt] : refl((le(P, Y, X) | le(P, X, Y)) <=> (le(P, Y, X) | le(P, X, Y)))),
% 62.92/40.59 inference(bind,[status(th)],[])).
% 62.92/40.59 tff(483,plain,
% 62.92/40.59 (![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y)) <=> ![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))),
% 62.92/40.59 inference(quant_intro,[status(thm)],[482])).
% 62.92/40.59 tff(484,plain,
% 62.92/40.59 (![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y)) <=> ![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))),
% 62.92/40.59 inference(rewrite,[status(thm)],[])).
% 62.92/40.59 tff(485,plain,
% 62.92/40.59 (^[P: param, X: elt, Y: elt] : rewrite(((~le(P, X, Y)) => le(P, Y, X)) <=> (le(P, Y, X) | le(P, X, Y)))),
% 62.92/40.59 inference(bind,[status(th)],[])).
% 62.92/40.59 tff(486,plain,
% 62.92/40.59 (![P: param, X: elt, Y: elt] : ((~le(P, X, Y)) => le(P, Y, X)) <=> ![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))),
% 62.92/40.59 inference(quant_intro,[status(thm)],[485])).
% 62.92/40.59 tff(487,axiom,(![P: param, X: elt, Y: elt] : ((~le(P, X, Y)) => le(P, Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','le_asym')).
% 62.92/40.59 tff(488,plain,
% 62.92/40.59 (![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))),
% 62.92/40.59 inference(modus_ponens,[status(thm)],[487, 486])).
% 62.92/40.59 tff(489,plain,
% 62.92/40.59 (![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))),
% 62.92/40.59 inference(modus_ponens,[status(thm)],[488, 484])).
% 62.92/40.59 tff(490,plain,(
% 62.92/40.59 ![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))),
% 62.92/40.59 inference(skolemize,[status(sab)],[489])).
% 62.92/40.59 tff(491,plain,
% 62.92/40.59 (![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))),
% 62.92/40.59 inference(modus_ponens,[status(thm)],[490, 483])).
% 62.92/40.59 tff(492,plain,
% 62.92/40.59 (((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))) <=> ((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))),
% 62.92/40.59 inference(rewrite,[status(thm)],[])).
% 62.92/40.59 tff(493,plain,
% 62.92/40.59 ((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))),
% 62.92/40.59 inference(quant_inst,[status(thm)],[])).
% 62.92/40.59 tff(494,plain,
% 62.92/40.59 ((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))),
% 62.92/40.59 inference(modus_ponens,[status(thm)],[493, 492])).
% 62.92/40.59 tff(495,plain,
% 62.92/40.59 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[494, 491, 481])).
% 62.92/40.59 tff(496,plain,
% 62.92/40.59 ($false),
% 62.92/40.59 inference(unit_resolution,[status(thm)],[495, 480])).
% 62.92/40.59 tff(497,plain,((~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1))), inference(lemma,lemma(discharge,[]))).
% 62.92/40.60 tff(498,plain,
% 62.92/40.60 (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.92/40.60 inference(unit_resolution,[status(thm)],[497, 425, 281])).
% 62.92/40.60 tff(499,plain,
% 62.92/40.60 (~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.92/40.60 inference(unit_resolution,[status(thm)],[294, 498])).
% 62.92/40.60 tff(500,plain,
% 62.92/40.60 (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.60 inference(unit_resolution,[status(thm)],[322, 499, 255, 280])).
% 62.92/40.60 tff(501,plain,
% 62.92/40.60 (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.92/40.60 inference(transitivity,[status(thm)],[500, 279, 270, 267])).
% 62.92/40.60 tff(502,plain,
% 62.92/40.60 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[501])).
% 62.92/40.60 tff(503,plain,
% 62.92/40.60 (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15))))) = get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[447])).
% 62.92/40.60 tff(504,plain,
% 62.92/40.60 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[503])).
% 62.92/40.60 tff(505,plain,
% 62.92/40.60 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) <=> le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[504, 502])).
% 62.92/40.60 tff(506,plain,
% 62.92/40.60 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))),
% 62.92/40.60 inference(symmetry,[status(thm)],[505])).
% 62.92/40.60 tff(507,plain,
% 62.92/40.60 ((~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) <=> (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[506])).
% 62.92/40.60 tff(508,plain,
% 62.92/40.60 ($sum(-1, J!15) = tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.60 inference(theory_lemma,[status(thm)],[425, 467])).
% 62.92/40.60 tff(509,plain,
% 62.92/40.60 (tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = $sum(-1, J!15)),
% 62.92/40.60 inference(symmetry,[status(thm)],[508])).
% 62.92/40.60 tff(510,plain,
% 62.92/40.60 (tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11) = tb2t(t2tb($sum(-1, J!15)))),
% 62.92/40.60 inference(transitivity,[status(thm)],[471, 509, 465])).
% 62.92/40.60 tff(511,plain,
% 62.92/40.60 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), tb2t(t2tb($sum(-1, J!15))))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[265, 510])).
% 62.92/40.60 tff(512,plain,
% 62.92/40.60 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))),
% 62.92/40.60 inference(transitivity,[status(thm)],[511, 450, 448, 445])).
% 62.92/40.60 tff(513,plain,
% 62.92/40.60 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[512])).
% 62.92/40.60 tff(514,plain,
% 62.92/40.60 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.60 inference(symmetry,[status(thm)],[513])).
% 62.92/40.60 tff(515,plain,
% 62.92/40.60 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[514])).
% 62.92/40.60 tff(516,plain,
% 62.92/40.60 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.60 inference(symmetry,[status(thm)],[515])).
% 62.92/40.60 tff(517,plain,
% 62.92/40.60 ((~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) <=> (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[516])).
% 62.92/40.60 tff(518,plain,
% 62.92/40.60 (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.60 inference(modus_ponens,[status(thm)],[387, 517])).
% 62.92/40.60 tff(519,plain,
% 62.92/40.60 (^[P: param, X: elt, Y: elt, Z: elt] : refl((le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z))) <=> (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z))))),
% 62.92/40.60 inference(bind,[status(th)],[])).
% 62.92/40.60 tff(520,plain,
% 62.92/40.60 (![P: param, X: elt, Y: elt, Z: elt] : (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z))) <=> ![P: param, X: elt, Y: elt, Z: elt] : (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z)))),
% 62.92/40.60 inference(quant_intro,[status(thm)],[519])).
% 62.92/40.60 tff(521,plain,
% 62.92/40.60 (^[P: param, X: elt, Y: elt, Z: elt] : trans(monotonicity(trans(monotonicity(rewrite((le(P, X, Y) & le(P, Y, Z)) <=> (~((~le(P, X, Y)) | (~le(P, Y, Z))))), ((~(le(P, X, Y) & le(P, Y, Z))) <=> (~(~((~le(P, X, Y)) | (~le(P, Y, Z))))))), rewrite((~(~((~le(P, X, Y)) | (~le(P, Y, Z))))) <=> ((~le(P, X, Y)) | (~le(P, Y, Z)))), ((~(le(P, X, Y) & le(P, Y, Z))) <=> ((~le(P, X, Y)) | (~le(P, Y, Z))))), (((~(le(P, X, Y) & le(P, Y, Z))) | le(P, X, Z)) <=> (((~le(P, X, Y)) | (~le(P, Y, Z))) | le(P, X, Z)))), rewrite((((~le(P, X, Y)) | (~le(P, Y, Z))) | le(P, X, Z)) <=> (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z)))), (((~(le(P, X, Y) & le(P, Y, Z))) | le(P, X, Z)) <=> (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z)))))),
% 62.92/40.60 inference(bind,[status(th)],[])).
% 62.92/40.60 tff(522,plain,
% 62.92/40.60 (![P: param, X: elt, Y: elt, Z: elt] : ((~(le(P, X, Y) & le(P, Y, Z))) | le(P, X, Z)) <=> ![P: param, X: elt, Y: elt, Z: elt] : (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z)))),
% 62.92/40.60 inference(quant_intro,[status(thm)],[521])).
% 62.92/40.60 tff(523,plain,
% 62.92/40.60 (![P: param, X: elt, Y: elt, Z: elt] : ((~(le(P, X, Y) & le(P, Y, Z))) | le(P, X, Z)) <=> ![P: param, X: elt, Y: elt, Z: elt] : ((~(le(P, X, Y) & le(P, Y, Z))) | le(P, X, Z))),
% 62.92/40.60 inference(rewrite,[status(thm)],[])).
% 62.92/40.60 tff(524,plain,
% 62.92/40.60 (^[P: param, X: elt, Y: elt, Z: elt] : rewrite(((le(P, X, Y) & le(P, Y, Z)) => le(P, X, Z)) <=> ((~(le(P, X, Y) & le(P, Y, Z))) | le(P, X, Z)))),
% 62.92/40.60 inference(bind,[status(th)],[])).
% 62.92/40.60 tff(525,plain,
% 62.92/40.60 (![P: param, X: elt, Y: elt, Z: elt] : ((le(P, X, Y) & le(P, Y, Z)) => le(P, X, Z)) <=> ![P: param, X: elt, Y: elt, Z: elt] : ((~(le(P, X, Y) & le(P, Y, Z))) | le(P, X, Z))),
% 62.92/40.60 inference(quant_intro,[status(thm)],[524])).
% 62.92/40.60 tff(526,axiom,(![P: param, X: elt, Y: elt, Z: elt] : ((le(P, X, Y) & le(P, Y, Z)) => le(P, X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','le_trans')).
% 62.92/40.60 tff(527,plain,
% 62.92/40.60 (![P: param, X: elt, Y: elt, Z: elt] : ((~(le(P, X, Y) & le(P, Y, Z))) | le(P, X, Z))),
% 62.92/40.60 inference(modus_ponens,[status(thm)],[526, 525])).
% 62.92/40.60 tff(528,plain,
% 62.92/40.60 (![P: param, X: elt, Y: elt, Z: elt] : ((~(le(P, X, Y) & le(P, Y, Z))) | le(P, X, Z))),
% 62.92/40.60 inference(modus_ponens,[status(thm)],[527, 523])).
% 62.92/40.60 tff(529,plain,(
% 62.92/40.60 ![P: param, X: elt, Y: elt, Z: elt] : ((~(le(P, X, Y) & le(P, Y, Z))) | le(P, X, Z))),
% 62.92/40.60 inference(skolemize,[status(sab)],[528])).
% 62.92/40.60 tff(530,plain,
% 62.92/40.60 (![P: param, X: elt, Y: elt, Z: elt] : (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z)))),
% 62.92/40.60 inference(modus_ponens,[status(thm)],[529, 522])).
% 62.92/40.60 tff(531,plain,
% 62.92/40.60 (![P: param, X: elt, Y: elt, Z: elt] : (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z)))),
% 62.92/40.60 inference(modus_ponens,[status(thm)],[530, 520])).
% 62.92/40.60 tff(532,plain,
% 62.92/40.60 (((~![P: param, X: elt, Y: elt, Z: elt] : (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z)))) | (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) | (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) <=> ((~![P: param, X: elt, Y: elt, Z: elt] : (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z)))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) | (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))),
% 62.92/40.60 inference(rewrite,[status(thm)],[])).
% 62.92/40.60 tff(533,plain,
% 62.92/40.60 ((~![P: param, X: elt, Y: elt, Z: elt] : (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z)))) | (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) | (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))),
% 62.92/40.60 inference(quant_inst,[status(thm)],[])).
% 62.92/40.60 tff(534,plain,
% 62.92/40.60 ((~![P: param, X: elt, Y: elt, Z: elt] : (le(P, X, Z) | (~le(P, X, Y)) | (~le(P, Y, Z)))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) | (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.60 inference(modus_ponens,[status(thm)],[533, 532])).
% 62.92/40.60 tff(535,plain,
% 62.92/40.60 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.60 inference(unit_resolution,[status(thm)],[534, 531, 495])).
% 62.92/40.60 tff(536,plain,
% 62.92/40.60 (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.60 inference(unit_resolution,[status(thm)],[535, 518])).
% 62.92/40.60 tff(537,plain,
% 62.92/40.60 (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))),
% 62.92/40.60 inference(modus_ponens,[status(thm)],[536, 507])).
% 62.92/40.60 tff(538,plain,
% 62.92/40.60 ($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1) | $greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.92/40.60 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.60 tff(539,plain,
% 62.92/40.60 ($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)),
% 62.92/40.60 inference(unit_resolution,[status(thm)],[538, 498])).
% 62.92/40.60 tff(540,plain,
% 62.92/40.60 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(J!15)) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[207])).
% 62.92/40.60 tff(541,plain,
% 62.92/40.60 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), J!15) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(J!15)))),
% 62.92/40.60 inference(quant_inst,[status(thm)],[])).
% 62.92/40.60 tff(542,plain,
% 62.92/40.60 (get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), J!15) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(J!15))),
% 62.92/40.60 inference(unit_resolution,[status(thm)],[541, 249])).
% 62.92/40.60 tff(543,plain,
% 62.92/40.60 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15) = get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), J!15)),
% 62.92/40.60 inference(monotonicity,[status(thm)],[330])).
% 62.92/40.60 tff(544,plain,
% 62.92/40.60 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))),
% 62.92/40.60 inference(transitivity,[status(thm)],[543, 542, 540])).
% 62.92/40.60 tff(545,plain,
% 62.92/40.60 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15)) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[544])).
% 62.92/40.60 tff(546,plain,
% 62.92/40.60 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(tb2t(t2tb($sum(-1, J!15))))) = get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[207, 447])).
% 62.92/40.60 tff(547,plain,
% 62.92/40.60 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), tb2t(t2tb($sum(-1, J!15)))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(tb2t(t2tb($sum(-1, J!15))))))),
% 62.92/40.60 inference(quant_inst,[status(thm)],[])).
% 62.92/40.60 tff(548,plain,
% 62.92/40.60 (get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), tb2t(t2tb($sum(-1, J!15)))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), t2tb(tb2t(t2tb($sum(-1, J!15)))))),
% 62.92/40.60 inference(unit_resolution,[status(thm)],[547, 249])).
% 62.92/40.60 tff(549,plain,
% 62.92/40.60 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15)))) = get1(elt1, mk_array(elt1, A!10, t2tb5(A3!14)), tb2t(t2tb($sum(-1, J!15))))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[330])).
% 62.92/40.60 tff(550,plain,
% 62.92/40.60 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15)))) = get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))),
% 62.92/40.60 inference(transitivity,[status(thm)],[549, 548, 546])).
% 62.92/40.60 tff(551,plain,
% 62.92/40.60 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[550])).
% 62.92/40.60 tff(552,plain,
% 62.92/40.60 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))) <=> le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[551, 545])).
% 62.92/40.60 tff(553,plain,
% 62.92/40.60 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) <=> le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15)))),
% 62.92/40.60 inference(symmetry,[status(thm)],[552])).
% 62.92/40.60 tff(554,plain,
% 62.92/40.60 ((~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) <=> (~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))))),
% 62.92/40.60 inference(monotonicity,[status(thm)],[553])).
% 62.92/40.60 tff(555,plain,
% 62.92/40.60 (~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15)))),
% 62.92/40.60 inference(modus_ponens,[status(thm)],[481, 554])).
% 62.92/40.60 tff(556,plain,
% 62.92/40.60 ($greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 1))),
% 62.92/40.60 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.60 tff(557,plain,
% 62.92/40.60 ($greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)),
% 62.92/40.60 inference(unit_resolution,[status(thm)],[556, 464])).
% 62.92/40.60 tff(558,plain,
% 62.92/40.60 ($greatereq($sum(I!12, $product(-1, J!15)), 0)),
% 62.92/40.60 inference(and_elim,[status(thm)],[54])).
% 62.92/40.60 tff(559,plain,
% 62.92/40.60 ((~$lesseq($sum(I!12, $product(-1, J!15)), -1)) | (~$greatereq($sum(I!12, $product(-1, J!15)), 0))),
% 62.92/40.60 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.60 tff(560,plain,
% 62.92/40.60 (~$lesseq($sum(I!12, $product(-1, J!15)), -1)),
% 62.92/40.60 inference(unit_resolution,[status(thm)],[559, 558])).
% 62.92/40.60 tff(561,plain,
% 62.92/40.60 (((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | ($lesseq($sum(I!12, $product(-1, J!15)), -1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)))) <=> ((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | $lesseq($sum(I!12, $product(-1, J!15)), -1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)))),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(562,plain,
% 62.92/40.61 (((~$greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)) | $lesseq($sum(I!12, $product(-1, J!15)), -1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15)))) <=> ($lesseq($sum(I!12, $product(-1, J!15)), -1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)))),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(563,plain,
% 62.92/40.61 ($greatereq($sum($product(-1, I!12), J!15), 1) <=> $lesseq($sum(I!12, $product(-1, J!15)), -1)),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(564,plain,
% 62.92/40.61 ($sum(J!15, $product(-1, I!12)) = $sum($product(-1, I!12), J!15)),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(565,plain,
% 62.92/40.61 ($greatereq($sum(J!15, $product(-1, I!12)), 1) <=> $greatereq($sum($product(-1, I!12), J!15), 1)),
% 62.92/40.61 inference(monotonicity,[status(thm)],[564])).
% 62.92/40.61 tff(566,plain,
% 62.92/40.61 ($greatereq($sum(J!15, $product(-1, I!12)), 1) <=> $lesseq($sum(I!12, $product(-1, J!15)), -1)),
% 62.92/40.61 inference(transitivity,[status(thm)],[565, 563])).
% 62.92/40.61 tff(567,plain,
% 62.92/40.61 ((~$greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) <=> (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0))),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(568,plain,
% 62.92/40.61 ((~$lesseq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) <=> (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0))),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(569,plain,
% 62.92/40.61 (((~$lesseq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) | (~$greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) | $greatereq($sum(J!15, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15)))) <=> ((~$greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)) | $lesseq($sum(I!12, $product(-1, J!15)), -1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))))),
% 62.92/40.61 inference(monotonicity,[status(thm)],[568, 567, 566])).
% 62.92/40.61 tff(570,plain,
% 62.92/40.61 (((~$lesseq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) | (~$greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) | $greatereq($sum(J!15, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15)))) <=> ($lesseq($sum(I!12, $product(-1, J!15)), -1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)))),
% 62.92/40.61 inference(transitivity,[status(thm)],[569, 562])).
% 62.92/40.61 tff(571,plain,
% 62.92/40.61 (((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | ((~$lesseq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) | (~$greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) | $greatereq($sum(J!15, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))))) <=> ((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | ($lesseq($sum(I!12, $product(-1, J!15)), -1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0))))),
% 62.92/40.61 inference(monotonicity,[status(thm)],[570])).
% 62.92/40.61 tff(572,plain,
% 62.92/40.61 (((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | ((~$lesseq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) | (~$greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) | $greatereq($sum(J!15, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))))) <=> ((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | $lesseq($sum(I!12, $product(-1, J!15)), -1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)))),
% 62.92/40.61 inference(transitivity,[status(thm)],[571, 561])).
% 62.92/40.61 tff(573,plain,
% 62.92/40.61 ((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | ((~$lesseq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) | (~$greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0)) | $greatereq($sum(J!15, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))))),
% 62.92/40.61 inference(quant_inst,[status(thm)],[])).
% 62.92/40.61 tff(574,plain,
% 62.92/40.61 ((~![I1: $int, I2: $int] : ((~$lesseq($sum(I1, $product(-1, I2)), 0)) | (~$greatereq($sum(I1, $product(-1, J!15)), 0)) | $greatereq($sum(I2, $product(-1, I!12)), 1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I1)), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), I2))))) | $lesseq($sum(I!12, $product(-1, J!15)), -1) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0))),
% 62.92/40.61 inference(modus_ponens,[status(thm)],[573, 572])).
% 62.92/40.61 tff(575,plain,
% 62.92/40.61 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), tb2t(t2tb($sum(-1, J!15))))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A3!14)))), J!15))) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0))),
% 62.92/40.61 inference(unit_resolution,[status(thm)],[574, 407, 560, 557])).
% 62.92/40.61 tff(576,plain,
% 62.92/40.61 (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)),
% 62.92/40.61 inference(unit_resolution,[status(thm)],[575, 555])).
% 62.92/40.61 tff(577,assumption,(~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)), introduced(assumption)).
% 62.92/40.61 tff(578,plain,
% 62.92/40.61 ($false),
% 62.92/40.61 inference(theory_lemma,[status(thm)],[462, 296, 577])).
% 62.92/40.61 tff(579,plain,($greatereq(tb2t(t2tb($sum(-1, J!15))), 0)), inference(lemma,lemma(discharge,[]))).
% 62.92/40.61 tff(580,plain,
% 62.92/40.61 (^[K1: $int, K2: $int] : refl(((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0))) <=> ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0))))),
% 62.92/40.61 inference(bind,[status(th)],[])).
% 62.92/40.61 tff(581,plain,
% 62.92/40.61 (![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0))) <=> ![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))),
% 62.92/40.61 inference(quant_intro,[status(thm)],[580])).
% 62.92/40.61 tff(582,plain,
% 62.92/40.61 (^[K1: $int, K2: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0)) <=> (~((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0))))), ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) <=> (~(~((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0))))))), rewrite((~(~((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0))))) <=> ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))), ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) <=> ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0))))), (((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))) <=> (((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))))), rewrite((((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))) <=> ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))), (((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))) <=> ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))))),
% 62.92/40.61 inference(bind,[status(th)],[])).
% 62.92/40.61 tff(583,plain,
% 62.92/40.61 (![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2))))) <=> ![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))),
% 62.92/40.61 inference(quant_intro,[status(thm)],[582])).
% 62.92/40.61 tff(584,plain,
% 62.92/40.61 (![K1: $int, K2: $int] : ((~($greatereq(K1, 0) & (~$greatereq($sum(K1, $product(-1, J!15)), 0)) & $greatereq($sum(K2, $product(-1, J!15)), 1) & $lesseq($sum(K2, $product(-1, I!12)), 0))) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))))),
% 62.92/40.61 inference(and_elim,[status(thm)],[54])).
% 62.92/40.61 tff(585,plain,
% 62.92/40.61 (![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))),
% 62.92/40.61 inference(modus_ponens,[status(thm)],[584, 583])).
% 62.92/40.61 tff(586,plain,
% 62.92/40.61 (![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))),
% 62.92/40.61 inference(modus_ponens,[status(thm)],[585, 581])).
% 62.92/40.61 tff(587,plain,
% 62.92/40.61 (((~![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))) | ((~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)) | (~$greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))))) <=> ((~![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))) | (~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)) | (~$greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))))),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(588,plain,
% 62.92/40.61 (((~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)) | (~$greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))) <=> ((~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)) | (~$greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))))),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(589,plain,
% 62.92/40.61 ((~$lesseq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 0)) <=> (~$greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(590,plain,
% 62.92/40.61 ((~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 1)) <=> (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1))),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(591,plain,
% 62.92/40.61 ($greatereq($sum($product(-1, J!15), tb2t(t2tb($sum(-1, J!15)))), 0) <=> $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(592,plain,
% 62.92/40.61 ($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)) = $sum($product(-1, J!15), tb2t(t2tb($sum(-1, J!15))))),
% 62.92/40.61 inference(rewrite,[status(thm)],[])).
% 62.92/40.61 tff(593,plain,
% 62.92/40.61 ($greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0) <=> $greatereq($sum($product(-1, J!15), tb2t(t2tb($sum(-1, J!15)))), 0)),
% 62.92/40.61 inference(monotonicity,[status(thm)],[592])).
% 62.92/40.61 tff(594,plain,
% 62.92/40.61 ($greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0) <=> $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0)),
% 62.92/40.61 inference(transitivity,[status(thm)],[593, 591])).
% 62.92/40.61 tff(595,plain,
% 62.92/40.61 (((~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 1)) | (~$lesseq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 0))) <=> ((~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)) | (~$greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)))),
% 62.92/40.61 inference(monotonicity,[status(thm)],[594, 590, 589])).
% 62.92/40.61 tff(596,plain,
% 62.92/40.61 (((~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 1)) | (~$lesseq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 0))) <=> ((~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)) | (~$greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))))),
% 62.92/40.61 inference(transitivity,[status(thm)],[595, 588])).
% 62.92/40.61 tff(597,plain,
% 62.92/40.61 (((~![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))) | ((~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 1)) | (~$lesseq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 0)))) <=> ((~![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))) | ((~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)) | (~$greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))))),
% 62.92/40.61 inference(monotonicity,[status(thm)],[596])).
% 62.92/40.61 tff(598,plain,
% 62.92/40.61 (((~![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))) | ((~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 1)) | (~$lesseq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 0)))) <=> ((~![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))) | (~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)) | (~$greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))))),
% 62.92/40.61 inference(transitivity,[status(thm)],[597, 587])).
% 62.92/40.61 tff(599,plain,
% 62.92/40.61 ((~![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))) | ((~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $greatereq($sum(tb2t(t2tb($sum(-1, J!15))), $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) | (~$greatereq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, J!15)), 1)) | (~$lesseq($sum(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), $product(-1, I!12)), 0)))),
% 62.92/40.61 inference(quant_inst,[status(thm)],[])).
% 62.92/40.61 tff(600,plain,
% 62.92/40.61 ((~![K1: $int, K2: $int] : ((~$greatereq(K1, 0)) | $greatereq($sum(K1, $product(-1, J!15)), 0) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K1))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(K2)))) | (~$greatereq($sum(K2, $product(-1, J!15)), 1)) | (~$lesseq($sum(K2, $product(-1, I!12)), 0)))) | (~$greatereq(tb2t(t2tb($sum(-1, J!15))), 0)) | $lesseq($sum(J!15, $product(-1, tb2t(t2tb($sum(-1, J!15))))), 0) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)) | (~$greatereq($sum(I!12, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))),
% 62.92/40.62 inference(modus_ponens,[status(thm)],[599, 598])).
% 62.92/40.62 tff(601,plain,
% 62.92/40.62 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))),
% 62.92/40.62 inference(unit_resolution,[status(thm)],[600, 586, 579, 576, 392, 539])).
% 62.92/40.62 tff(602,plain,
% 62.92/40.62 ($false),
% 62.92/40.62 inference(unit_resolution,[status(thm)],[601, 537])).
% 62.92/40.62 tff(603,plain,(($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))), inference(lemma,lemma(discharge,[]))).
% 62.92/40.62 tff(604,plain,
% 62.92/40.62 ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0),
% 62.92/40.62 inference(unit_resolution,[status(thm)],[603, 257, 255, 254])).
% 62.92/40.62 tff(605,plain,
% 62.92/40.62 ((~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)) | $lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.92/40.62 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.62 tff(606,plain,
% 62.92/40.62 ($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.92/40.62 inference(unit_resolution,[status(thm)],[605, 604])).
% 62.92/40.62 tff(607,plain,
% 62.92/40.62 ((~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)) | $greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.92/40.62 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.62 tff(608,plain,
% 62.92/40.62 ($greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.92/40.62 inference(unit_resolution,[status(thm)],[607, 604])).
% 62.92/40.62 tff(609,plain,
% 62.92/40.62 (J!15 = tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.62 inference(theory_lemma,[status(thm)],[608, 606])).
% 62.92/40.62 tff(610,plain,
% 62.92/40.62 (tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = J!15),
% 62.92/40.62 inference(symmetry,[status(thm)],[609])).
% 62.92/40.62 tff(611,plain,
% 62.92/40.62 (tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11) = J!15),
% 62.92/40.62 inference(transitivity,[status(thm)],[471, 610])).
% 62.92/40.62 tff(612,plain,
% 62.92/40.62 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), J!15)),
% 62.92/40.62 inference(monotonicity,[status(thm)],[265, 611])).
% 62.92/40.62 tff(613,plain,
% 62.92/40.62 (tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)),
% 62.92/40.62 inference(symmetry,[status(thm)],[471])).
% 62.92/40.62 tff(614,assumption,(~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)), introduced(assumption)).
% 62.92/40.62 tff(615,plain,
% 62.92/40.62 (~($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 0)),
% 62.92/40.62 inference(unit_resolution,[status(thm)],[294, 614])).
% 62.92/40.62 tff(616,plain,
% 62.92/40.62 (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.62 inference(unit_resolution,[status(thm)],[322, 615, 255, 280])).
% 62.92/40.62 tff(617,plain,
% 62.92/40.62 (get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.92/40.62 inference(transitivity,[status(thm)],[616, 279, 270, 267])).
% 62.92/40.62 tff(618,plain,
% 62.92/40.62 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.62 inference(monotonicity,[status(thm)],[617])).
% 62.92/40.62 tff(619,assumption,($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)), introduced(assumption)).
% 62.92/40.62 tff(620,assumption,($greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)), introduced(assumption)).
% 62.92/40.62 tff(621,plain,
% 62.92/40.62 (J!15 = tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.62 inference(theory_lemma,[status(thm)],[620, 619])).
% 62.92/40.62 tff(622,plain,
% 62.92/40.62 (tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = J!15),
% 62.92/40.62 inference(symmetry,[status(thm)],[621])).
% 62.92/40.62 tff(623,plain,
% 62.92/40.62 (tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11) = J!15),
% 62.92/40.62 inference(transitivity,[status(thm)],[471, 622])).
% 62.92/40.62 tff(624,plain,
% 62.92/40.62 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get1(elt1, mk_array(elt1, A!10, t2tb5(A5!17)), J!15)),
% 62.92/40.62 inference(monotonicity,[status(thm)],[265, 623])).
% 62.92/40.62 tff(625,plain,
% 62.92/40.62 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))),
% 62.92/40.62 inference(transitivity,[status(thm)],[624, 251, 242])).
% 62.92/40.62 tff(626,plain,
% 62.92/40.62 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))),
% 62.92/40.62 inference(monotonicity,[status(thm)],[625])).
% 62.92/40.62 tff(627,plain,
% 62.92/40.62 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.62 inference(symmetry,[status(thm)],[626])).
% 62.92/40.62 tff(628,plain,
% 62.92/40.62 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.62 inference(transitivity,[status(thm)],[504, 627])).
% 62.92/40.62 tff(629,plain,
% 62.92/40.62 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))) <=> le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.62 inference(monotonicity,[status(thm)],[628, 618])).
% 62.92/40.62 tff(630,plain,
% 62.92/40.62 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))),
% 62.92/40.62 inference(symmetry,[status(thm)],[629])).
% 62.92/40.62 tff(631,plain,
% 62.92/40.62 ((~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) <=> (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))))),
% 62.92/40.62 inference(monotonicity,[status(thm)],[630])).
% 62.92/40.62 tff(632,plain,
% 62.92/40.62 (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))),
% 62.92/40.62 inference(modus_ponens,[status(thm)],[387, 631])).
% 62.92/40.62 tff(633,plain,
% 62.92/40.62 ($lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), -1)),
% 62.92/40.62 inference(unit_resolution,[status(thm)],[538, 614])).
% 62.92/40.62 tff(634,plain,
% 62.92/40.62 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb($sum(-1, J!15)))))), tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))))),
% 62.92/40.62 inference(unit_resolution,[status(thm)],[600, 586, 579, 576, 392, 633])).
% 62.92/40.62 tff(635,plain,
% 62.92/40.62 ($false),
% 62.92/40.62 inference(unit_resolution,[status(thm)],[634, 632])).
% 62.92/40.62 tff(636,plain,($greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$lesseq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0) | ($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = 1)), inference(lemma,lemma(discharge,[]))).
% 62.92/40.62 tff(637,plain,
% 62.92/40.62 ($greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)),
% 62.92/40.62 inference(unit_resolution,[status(thm)],[636, 608, 606, 255, 257])).
% 62.92/40.62 tff(638,plain,
% 62.92/40.62 (J!15 = tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.62 inference(theory_lemma,[status(thm)],[432, 430, 637, 254])).
% 62.92/40.62 tff(639,plain,
% 62.92/40.62 (tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) = J!15),
% 62.92/40.62 inference(symmetry,[status(thm)],[638])).
% 62.92/40.62 tff(640,plain,
% 62.92/40.62 (tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t(t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.62 inference(monotonicity,[status(thm)],[324])).
% 62.92/40.62 tff(641,plain,
% 62.92/40.62 (tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11) = tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)),
% 62.92/40.62 inference(transitivity,[status(thm)],[437, 640, 639, 609, 613])).
% 62.92/40.62 tff(642,plain,
% 62.92/40.62 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.92/40.62 inference(monotonicity,[status(thm)],[641])).
% 62.92/40.62 tff(643,plain,
% 62.92/40.62 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))),
% 62.92/40.62 inference(transitivity,[status(thm)],[642, 612, 251, 242])).
% 62.92/40.62 tff(644,plain,
% 62.92/40.62 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))),
% 62.92/40.62 inference(monotonicity,[status(thm)],[643])).
% 62.92/40.62 tff(645,plain,
% 62.92/40.62 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.62 inference(symmetry,[status(thm)],[644])).
% 62.92/40.62 tff(646,plain,
% 62.92/40.62 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))),
% 62.92/40.62 inference(transitivity,[status(thm)],[612, 251, 242])).
% 62.92/40.62 tff(647,plain,
% 62.92/40.62 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))),
% 62.92/40.62 inference(monotonicity,[status(thm)],[646])).
% 62.92/40.62 tff(648,plain,
% 62.92/40.62 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.62 inference(transitivity,[status(thm)],[647, 645])).
% 62.92/40.62 tff(649,plain,
% 62.92/40.62 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.62 inference(symmetry,[status(thm)],[647])).
% 62.92/40.62 tff(650,plain,
% 62.92/40.62 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.62 inference(transitivity,[status(thm)],[644, 649])).
% 62.92/40.62 tff(651,plain,
% 62.92/40.62 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.62 inference(monotonicity,[status(thm)],[650, 648])).
% 62.92/40.62 tff(652,plain,
% 62.92/40.62 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.62 inference(symmetry,[status(thm)],[651])).
% 62.92/40.62 tff(653,plain,
% 62.92/40.62 ((~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) <=> (~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.62 inference(monotonicity,[status(thm)],[652])).
% 62.92/40.62 tff(654,plain,
% 62.92/40.62 (~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.62 inference(modus_ponens,[status(thm)],[387, 653])).
% 62.92/40.62 tff(655,plain,
% 62.92/40.62 (((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) <=> ((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.62 inference(rewrite,[status(thm)],[])).
% 62.92/40.62 tff(656,plain,
% 62.92/40.62 ((le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) <=> (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.63 inference(rewrite,[status(thm)],[])).
% 62.92/40.63 tff(657,plain,
% 62.92/40.63 (((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) <=> ((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))),
% 62.92/40.63 inference(monotonicity,[status(thm)],[656])).
% 62.92/40.63 tff(658,plain,
% 62.92/40.63 (((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) <=> ((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.63 inference(transitivity,[status(thm)],[657, 655])).
% 62.92/40.63 tff(659,plain,
% 62.92/40.63 ((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.63 inference(quant_inst,[status(thm)],[])).
% 62.92/40.63 tff(660,plain,
% 62.92/40.63 ((~![P: param, X: elt, Y: elt] : (le(P, Y, X) | le(P, X, Y))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.63 inference(modus_ponens,[status(thm)],[659, 658])).
% 62.92/40.63 tff(661,plain,
% 62.92/40.63 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.63 inference(unit_resolution,[status(thm)],[660, 491, 387])).
% 62.92/40.63 tff(662,plain,
% 62.92/40.63 ($false),
% 62.92/40.63 inference(unit_resolution,[status(thm)],[661, 654])).
% 62.92/40.63 tff(663,plain,($greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1) | $lesseq($sum(length(elt1, mk_array(elt1, A!10, t2tb5(A3!14))), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)), inference(lemma,lemma(discharge,[]))).
% 62.92/40.63 tff(664,plain,
% 62.92/40.63 ($greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)),
% 62.92/40.63 inference(unit_resolution,[status(thm)],[663, 146])).
% 62.92/40.63 tff(665,plain,
% 62.92/40.63 ((~$lesseq($sum(J!15, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)) | (~$lesseq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0))),
% 62.92/40.63 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.63 tff(666,plain,
% 62.92/40.63 (~$lesseq($sum(J!15, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.92/40.63 inference(unit_resolution,[status(thm)],[665, 664, 121])).
% 62.92/40.63 tff(667,plain,
% 62.92/40.63 ($greatereq($sum($sum(-1, J!15), $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0) | $lesseq($sum(J!15, $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.92/40.63 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.63 tff(668,plain,
% 62.92/40.63 ($greatereq($sum($sum(-1, J!15), $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.92/40.63 inference(unit_resolution,[status(thm)],[667, 666])).
% 62.92/40.63 tff(669,plain,
% 62.92/40.63 (($sum(-1, J!15) = tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) | (~$lesseq($sum($sum(-1, J!15), $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum($sum(-1, J!15), $product(-1, tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0))),
% 62.92/40.63 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.63 tff(670,plain,
% 62.92/40.63 ($sum(-1, J!15) = tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)),
% 62.92/40.63 inference(unit_resolution,[status(thm)],[669, 668, 104])).
% 62.92/40.63 tff(671,assumption,($sum(-1, J!15) = tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)), introduced(assumption)).
% 62.92/40.63 tff(672,plain,
% 62.92/40.63 (tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11) = $sum(-1, J!15)),
% 62.92/40.63 inference(symmetry,[status(thm)],[671])).
% 62.92/40.63 tff(673,plain,
% 62.92/40.63 (tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)),
% 62.92/40.63 inference(symmetry,[status(thm)],[437])).
% 62.92/40.63 tff(674,plain,
% 62.92/40.63 (tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t(t2tb($sum(-1, J!15)))),
% 62.92/40.63 inference(transitivity,[status(thm)],[673, 672, 465])).
% 62.92/40.63 tff(675,plain,
% 62.92/40.63 (t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = t2tb(tb2t(t2tb($sum(-1, J!15))))),
% 62.92/40.63 inference(monotonicity,[status(thm)],[674])).
% 62.92/40.63 tff(676,plain,
% 62.92/40.63 (t2tb(tb2t(t2tb($sum(-1, J!15)))) = t2tb(tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.63 inference(symmetry,[status(thm)],[675])).
% 62.92/40.63 tff(677,plain,
% 62.92/40.63 (t2tb($sum(-1, J!15)) = t2tb(tb2t(t2tb($sum(-1, J!15))))),
% 62.92/40.63 inference(symmetry,[status(thm)],[447])).
% 62.92/40.63 tff(678,plain,
% 62.92/40.63 (t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.92/40.63 inference(transitivity,[status(thm)],[677, 676, 278])).
% 62.92/40.63 tff(679,assumption,(~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))), introduced(assumption)).
% 62.92/40.63 tff(680,plain,
% 62.92/40.63 ($false),
% 62.92/40.63 inference(unit_resolution,[status(thm)],[679, 678])).
% 62.92/40.63 tff(681,plain,((~($sum(-1, J!15) = tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) | (t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))), inference(lemma,lemma(discharge,[]))).
% 62.92/40.63 tff(682,plain,
% 62.92/40.63 (t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.92/40.63 inference(unit_resolution,[status(thm)],[681, 670])).
% 62.92/40.63 tff(683,plain,
% 62.92/40.63 (^[A: ty, B: ty, X: uni, X1: uni] : refl(sort(B, get(B, A, X, X1)) <=> sort(B, get(B, A, X, X1)))),
% 62.92/40.63 inference(bind,[status(th)],[])).
% 62.92/40.63 tff(684,plain,
% 62.92/40.63 (![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1)) <=> ![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))),
% 62.92/40.63 inference(quant_intro,[status(thm)],[683])).
% 62.92/40.63 tff(685,plain,
% 62.92/40.63 (![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1)) <=> ![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))),
% 62.92/40.63 inference(rewrite,[status(thm)],[])).
% 62.92/40.63 tff(686,axiom,(![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','get_sort2')).
% 62.92/40.63 tff(687,plain,
% 62.92/40.63 (![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))),
% 62.92/40.63 inference(modus_ponens,[status(thm)],[686, 685])).
% 62.92/40.63 tff(688,plain,(
% 62.92/40.63 ![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))),
% 62.92/40.63 inference(skolemize,[status(sab)],[687])).
% 62.92/40.63 tff(689,plain,
% 62.92/40.63 (![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))),
% 62.92/40.63 inference(modus_ponens,[status(thm)],[688, 684])).
% 62.92/40.63 tff(690,plain,
% 62.92/40.63 ((~![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))) | sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 62.92/40.63 inference(quant_inst,[status(thm)],[])).
% 62.92/40.63 tff(691,plain,
% 62.92/40.63 (sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 62.92/40.63 inference(unit_resolution,[status(thm)],[690, 689])).
% 62.92/40.63 tff(692,plain,
% 62.92/40.63 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : refl(((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1))))),
% 62.92/40.63 inference(bind,[status(th)],[])).
% 62.92/40.63 tff(693,plain,
% 62.92/40.63 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))),
% 62.92/40.63 inference(quant_intro,[status(thm)],[692])).
% 62.92/40.63 tff(694,plain,
% 62.92/40.63 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))),
% 62.92/40.63 inference(rewrite,[status(thm)],[])).
% 62.92/40.63 tff(695,plain,
% 62.92/40.63 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : trans(monotonicity(rewrite(((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)) <=> ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))), ((sort(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> (sort(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))))), rewrite((sort(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))), ((sort(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))))),
% 62.92/40.63 inference(bind,[status(th)],[])).
% 62.92/40.63 tff(696,plain,
% 62.92/40.63 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))),
% 62.92/40.63 inference(quant_intro,[status(thm)],[695])).
% 62.92/40.63 tff(697,axiom,(![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','select_eq')).
% 62.92/40.63 tff(698,plain,
% 62.92/40.63 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))),
% 62.92/40.63 inference(modus_ponens,[status(thm)],[697, 696])).
% 62.92/40.63 tff(699,plain,
% 62.92/40.63 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))),
% 62.92/40.63 inference(modus_ponens,[status(thm)],[698, 694])).
% 62.92/40.63 tff(700,plain,(
% 62.92/40.63 ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))),
% 62.92/40.63 inference(skolemize,[status(sab)],[699])).
% 62.92/40.63 tff(701,plain,
% 62.92/40.63 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))),
% 62.92/40.63 inference(modus_ponens,[status(thm)],[700, 693])).
% 62.92/40.63 tff(702,plain,
% 62.92/40.63 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.63 inference(rewrite,[status(thm)],[])).
% 62.92/40.63 tff(703,plain,
% 62.92/40.63 (((get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) <=> ((~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.63 inference(rewrite,[status(thm)],[])).
% 62.92/40.63 tff(704,plain,
% 62.92/40.63 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))),
% 62.92/40.63 inference(monotonicity,[status(thm)],[703])).
% 62.92/40.63 tff(705,plain,
% 62.92/40.63 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.63 inference(transitivity,[status(thm)],[704, 702])).
% 62.92/40.63 tff(706,plain,
% 62.92/40.63 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))),
% 62.92/40.63 inference(quant_inst,[status(thm)],[])).
% 62.92/40.63 tff(707,plain,
% 62.92/40.64 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.64 inference(modus_ponens,[status(thm)],[706, 705])).
% 62.92/40.64 tff(708,plain,
% 62.92/40.64 ((get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[707, 701, 691])).
% 62.92/40.64 tff(709,plain,
% 62.92/40.64 (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[708, 682])).
% 62.92/40.64 tff(710,plain,
% 62.92/40.64 (A4!16 = tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))),
% 62.92/40.64 inference(and_elim,[status(thm)],[54])).
% 62.92/40.64 tff(711,plain,
% 62.92/40.64 (t2tb5(A4!16) = t2tb5(tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))))),
% 62.92/40.64 inference(monotonicity,[status(thm)],[710])).
% 62.92/40.64 tff(712,plain,
% 62.92/40.64 (t2tb5(tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) = t2tb5(A4!16)),
% 62.92/40.64 inference(symmetry,[status(thm)],[711])).
% 62.92/40.64 tff(713,plain,
% 62.92/40.64 (^[A: ty, B: ty, X: uni, X1: uni, X2: uni] : refl(sort(map(A, B), set(B, A, X, X1, X2)) <=> sort(map(A, B), set(B, A, X, X1, X2)))),
% 62.92/40.64 inference(bind,[status(th)],[])).
% 62.92/40.64 tff(714,plain,
% 62.92/40.64 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))),
% 62.92/40.64 inference(quant_intro,[status(thm)],[713])).
% 62.92/40.64 tff(715,plain,
% 62.92/40.64 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))),
% 62.92/40.64 inference(rewrite,[status(thm)],[])).
% 62.92/40.64 tff(716,axiom,(![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','set_sort2')).
% 62.92/40.64 tff(717,plain,
% 62.92/40.64 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))),
% 62.92/40.64 inference(modus_ponens,[status(thm)],[716, 715])).
% 62.92/40.64 tff(718,plain,(
% 62.92/40.64 ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))),
% 62.92/40.64 inference(skolemize,[status(sab)],[717])).
% 62.92/40.64 tff(719,plain,
% 62.92/40.64 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))),
% 62.92/40.64 inference(modus_ponens,[status(thm)],[718, 714])).
% 62.92/40.64 tff(720,plain,
% 62.92/40.64 ((~![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))) | sort(map(int, elt1), set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))),
% 62.92/40.64 inference(quant_inst,[status(thm)],[])).
% 62.92/40.64 tff(721,plain,
% 62.92/40.64 (sort(map(int, elt1), set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[720, 719])).
% 62.92/40.64 tff(722,plain,
% 62.92/40.64 (^[J: uni] : refl(((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J)) <=> ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J)))),
% 62.92/40.64 inference(bind,[status(th)],[])).
% 62.92/40.64 tff(723,plain,
% 62.92/40.64 (![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J)) <=> ![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))),
% 62.92/40.64 inference(quant_intro,[status(thm)],[722])).
% 62.92/40.64 tff(724,plain,
% 62.92/40.64 (![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J)) <=> ![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))),
% 62.92/40.64 inference(rewrite,[status(thm)],[])).
% 62.92/40.64 tff(725,plain,
% 62.92/40.64 (^[J: uni] : rewrite((sort(map(int, elt1), J) => (t2tb5(tb2t5(J)) = J)) <=> ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J)))),
% 62.92/40.64 inference(bind,[status(th)],[])).
% 62.92/40.64 tff(726,plain,
% 62.92/40.64 (![J: uni] : (sort(map(int, elt1), J) => (t2tb5(tb2t5(J)) = J)) <=> ![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))),
% 62.92/40.64 inference(quant_intro,[status(thm)],[725])).
% 62.92/40.64 tff(727,axiom,(![J: uni] : (sort(map(int, elt1), J) => (t2tb5(tb2t5(J)) = J))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR5')).
% 62.92/40.64 tff(728,plain,
% 62.92/40.64 (![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))),
% 62.92/40.64 inference(modus_ponens,[status(thm)],[727, 726])).
% 62.92/40.64 tff(729,plain,
% 62.92/40.64 (![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))),
% 62.92/40.64 inference(modus_ponens,[status(thm)],[728, 724])).
% 62.92/40.64 tff(730,plain,(
% 62.92/40.64 ![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))),
% 62.92/40.64 inference(skolemize,[status(sab)],[729])).
% 62.92/40.64 tff(731,plain,
% 62.92/40.64 (![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))),
% 62.92/40.64 inference(modus_ponens,[status(thm)],[730, 723])).
% 62.92/40.64 tff(732,plain,
% 62.92/40.64 (((~![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort(map(int, elt1), set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) | (t2tb5(tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) = set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))))) <=> ((~![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))) | (~sort(map(int, elt1), set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) | (t2tb5(tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) = set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))))),
% 62.92/40.64 inference(rewrite,[status(thm)],[])).
% 62.92/40.64 tff(733,plain,
% 62.92/40.64 ((~![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort(map(int, elt1), set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) | (t2tb5(tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) = set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))))),
% 62.92/40.64 inference(quant_inst,[status(thm)],[])).
% 62.92/40.64 tff(734,plain,
% 62.92/40.64 ((~![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))) | (~sort(map(int, elt1), set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) | (t2tb5(tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) = set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))),
% 62.92/40.64 inference(modus_ponens,[status(thm)],[733, 732])).
% 62.92/40.64 tff(735,plain,
% 62.92/40.64 (t2tb5(tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))))) = set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[734, 731, 721])).
% 62.92/40.64 tff(736,plain,
% 62.92/40.64 (set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))) = t2tb5(tb2t5(set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15))))))),
% 62.92/40.64 inference(symmetry,[status(thm)],[735])).
% 62.92/40.64 tff(737,plain,
% 62.92/40.64 (set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))) = t2tb5(A4!16)),
% 62.92/40.64 inference(transitivity,[status(thm)],[736, 712])).
% 62.92/40.64 tff(738,plain,
% 62.92/40.64 (set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))) = set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 62.92/40.64 inference(monotonicity,[status(thm)],[737])).
% 62.92/40.64 tff(739,plain,
% 62.92/40.64 (set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))) = set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 62.92/40.64 inference(symmetry,[status(thm)],[738])).
% 62.92/40.64 tff(740,plain,
% 62.92/40.64 ((~![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))) | sort(map(int, elt1), set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))),
% 62.92/40.64 inference(quant_inst,[status(thm)],[])).
% 62.92/40.64 tff(741,plain,
% 62.92/40.64 (sort(map(int, elt1), set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[740, 719])).
% 62.92/40.64 tff(742,plain,
% 62.92/40.64 (((~![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort(map(int, elt1), set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) | (t2tb5(tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) = set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))) <=> ((~![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))) | (~sort(map(int, elt1), set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) | (t2tb5(tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) = set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))),
% 62.92/40.64 inference(rewrite,[status(thm)],[])).
% 62.92/40.64 tff(743,plain,
% 62.92/40.64 ((~![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))) | ((~sort(map(int, elt1), set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) | (t2tb5(tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) = set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))),
% 62.92/40.64 inference(quant_inst,[status(thm)],[])).
% 62.92/40.64 tff(744,plain,
% 62.92/40.64 ((~![J: uni] : ((~sort(map(int, elt1), J)) | (t2tb5(tb2t5(J)) = J))) | (~sort(map(int, elt1), set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) | (t2tb5(tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) = set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))),
% 62.92/40.64 inference(modus_ponens,[status(thm)],[743, 742])).
% 62.92/40.64 tff(745,plain,
% 62.92/40.64 (t2tb5(tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) = set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[744, 731, 741])).
% 62.92/40.64 tff(746,plain,
% 62.92/40.64 (A5!17 = tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))),
% 62.92/40.64 inference(and_elim,[status(thm)],[54])).
% 62.92/40.64 tff(747,plain,
% 62.92/40.64 (t2tb5(A5!17) = t2tb5(tb2t5(set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))),
% 62.92/40.64 inference(monotonicity,[status(thm)],[746])).
% 62.92/40.64 tff(748,plain,
% 62.92/40.64 (t2tb5(A5!17) = set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 62.92/40.64 inference(transitivity,[status(thm)],[747, 745])).
% 62.92/40.64 tff(749,plain,
% 62.92/40.64 (sort(map(int, elt1), t2tb5(A5!17)) <=> sort(map(int, elt1), set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))))),
% 62.92/40.64 inference(monotonicity,[status(thm)],[748])).
% 62.92/40.64 tff(750,plain,
% 62.92/40.64 (sort(map(int, elt1), set(elt1, int, t2tb5(A4!16), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) <=> sort(map(int, elt1), t2tb5(A5!17))),
% 62.92/40.64 inference(symmetry,[status(thm)],[749])).
% 62.92/40.64 tff(751,plain,
% 62.92/40.64 (sort(map(int, elt1), t2tb5(A5!17))),
% 62.92/40.64 inference(modus_ponens,[status(thm)],[741, 750])).
% 62.92/40.64 tff(752,plain,
% 62.92/40.64 (((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | ((~sort(map(int, elt1), t2tb5(A5!17))) | (elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))) = t2tb5(A5!17)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | (~sort(map(int, elt1), t2tb5(A5!17))) | (elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))) = t2tb5(A5!17)))),
% 62.92/40.64 inference(rewrite,[status(thm)],[])).
% 62.92/40.64 tff(753,plain,
% 62.92/40.64 ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | ((~sort(map(int, elt1), t2tb5(A5!17))) | (elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))) = t2tb5(A5!17)))),
% 62.92/40.64 inference(quant_inst,[status(thm)],[])).
% 62.92/40.64 tff(754,plain,
% 62.92/40.64 ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | (~sort(map(int, elt1), t2tb5(A5!17))) | (elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))) = t2tb5(A5!17))),
% 62.92/40.64 inference(modus_ponens,[status(thm)],[753, 752])).
% 62.92/40.64 tff(755,plain,
% 62.92/40.64 ((~sort(map(int, elt1), t2tb5(A5!17))) | (elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))) = t2tb5(A5!17))),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[754, 202])).
% 62.92/40.64 tff(756,plain,
% 62.92/40.64 (elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))) = t2tb5(A5!17)),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[755, 751])).
% 62.92/40.64 tff(757,plain,
% 62.92/40.64 (elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))) = set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 62.92/40.64 inference(transitivity,[status(thm)],[756, 747, 745, 739])).
% 62.92/40.64 tff(758,plain,
% 62.92/40.64 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.64 inference(monotonicity,[status(thm)],[757])).
% 62.92/40.64 tff(759,plain,
% 62.92/40.64 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))),
% 62.92/40.64 inference(transitivity,[status(thm)],[266, 269, 758, 709])).
% 62.92/40.64 tff(760,plain,
% 62.92/40.64 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 62.92/40.64 inference(monotonicity,[status(thm)],[759])).
% 62.92/40.64 tff(761,plain,
% 62.92/40.64 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 62.92/40.64 inference(symmetry,[status(thm)],[760])).
% 62.92/40.64 tff(762,plain,
% 62.92/40.64 ($lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 1) | (~$lesseq($sum(J!15, $product(-1, J1!18)), 1)) | (~$lesseq($sum(J1!18, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0))),
% 62.92/40.64 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.64 tff(763,plain,
% 62.92/40.64 ($lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 1)),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[762, 100, 58])).
% 62.92/40.64 tff(764,plain,
% 62.92/40.64 ($lesseq($sum($sum(-1, J!15), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0) | (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 1))),
% 62.92/40.64 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.64 tff(765,plain,
% 62.92/40.64 ($lesseq($sum($sum(-1, J!15), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[764, 763])).
% 62.92/40.64 tff(766,plain,
% 62.92/40.64 ((~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum(J!15, $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 1)) | (~$lesseq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tb2t(t2tb(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), 0)) | (~$greatereq($sum(tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0))),
% 62.92/40.64 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.64 tff(767,plain,
% 62.92/40.64 (~$lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[766, 664, 98, 121])).
% 62.92/40.64 tff(768,plain,
% 62.92/40.64 ($greatereq($sum($sum(-1, J!15), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0) | $lesseq($sum(J!15, $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.92/40.64 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.64 tff(769,plain,
% 62.92/40.64 ($greatereq($sum($sum(-1, J!15), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[768, 767])).
% 62.92/40.64 tff(770,plain,
% 62.92/40.64 (($sum(-1, J!15) = tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) | (~$lesseq($sum($sum(-1, J!15), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0)) | (~$greatereq($sum($sum(-1, J!15), $product(-1, tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), 0))),
% 62.92/40.64 inference(theory_lemma,[status(thm)],[])).
% 62.92/40.64 tff(771,plain,
% 62.92/40.64 ($sum(-1, J!15) = tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[770, 769, 765])).
% 62.92/40.64 tff(772,assumption,($sum(-1, J!15) = tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)), introduced(assumption)).
% 62.92/40.64 tff(773,plain,
% 62.92/40.64 (tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11) = $sum(-1, J!15)),
% 62.92/40.64 inference(symmetry,[status(thm)],[772])).
% 62.92/40.64 tff(774,plain,
% 62.92/40.64 (tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t(t2tb($sum(-1, J!15)))),
% 62.92/40.64 inference(transitivity,[status(thm)],[613, 773, 465])).
% 62.92/40.64 tff(775,plain,
% 62.92/40.64 (t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) = t2tb(tb2t(t2tb($sum(-1, J!15))))),
% 62.92/40.64 inference(monotonicity,[status(thm)],[774])).
% 62.92/40.64 tff(776,plain,
% 62.92/40.64 (t2tb(tb2t(t2tb($sum(-1, J!15)))) = t2tb(tb2t(t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.64 inference(symmetry,[status(thm)],[775])).
% 62.92/40.64 tff(777,plain,
% 62.92/40.64 (t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.92/40.64 inference(transitivity,[status(thm)],[677, 776, 340])).
% 62.92/40.64 tff(778,assumption,(~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))), introduced(assumption)).
% 62.92/40.64 tff(779,plain,
% 62.92/40.64 ($false),
% 62.92/40.64 inference(unit_resolution,[status(thm)],[778, 777])).
% 62.92/40.64 tff(780,plain,((~($sum(-1, J!15) = tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) | (t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))), inference(lemma,lemma(discharge,[]))).
% 62.92/40.65 tff(781,plain,
% 62.92/40.65 (t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))),
% 62.92/40.65 inference(unit_resolution,[status(thm)],[780, 771])).
% 62.92/40.65 tff(782,plain,
% 62.92/40.65 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.65 inference(rewrite,[status(thm)],[])).
% 62.92/40.65 tff(783,plain,
% 62.92/40.65 (((get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15))))) <=> ((~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.65 inference(rewrite,[status(thm)],[])).
% 62.92/40.65 tff(784,plain,
% 62.92/40.65 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))))),
% 62.92/40.65 inference(monotonicity,[status(thm)],[783])).
% 62.92/40.65 tff(785,plain,
% 62.92/40.65 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 62.92/40.65 inference(transitivity,[status(thm)],[784, 782])).
% 62.92/40.65 tff(786,plain,
% 62.92/40.65 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))))),
% 62.92/40.65 inference(quant_inst,[status(thm)],[])).
% 62.92/40.65 tff(787,plain,
% 62.92/40.65 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | (~sort(elt1, get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.65 inference(modus_ponens,[status(thm)],[786, 785])).
% 62.92/40.65 tff(788,plain,
% 62.92/40.65 ((get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))) | (~(t2tb($sum(-1, J!15)) = t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 62.92/40.65 inference(unit_resolution,[status(thm)],[787, 701, 691])).
% 62.92/40.65 tff(789,plain,
% 62.92/40.65 (get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))),
% 62.92/40.65 inference(unit_resolution,[status(thm)],[788, 781])).
% 62.92/40.65 tff(790,plain,
% 62.92/40.65 (get(elt1, int, elts(elt1, mk_array(elt1, A!10, t2tb5(A5!17))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 63.00/40.65 inference(monotonicity,[status(thm)],[757])).
% 63.00/40.65 tff(791,plain,
% 63.00/40.65 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))),
% 63.00/40.65 inference(transitivity,[status(thm)],[334, 337, 790, 789])).
% 63.00/40.65 tff(792,plain,
% 63.00/40.65 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 63.00/40.65 inference(monotonicity,[status(thm)],[791])).
% 63.00/40.65 tff(793,plain,
% 63.00/40.65 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 63.00/40.65 inference(transitivity,[status(thm)],[792, 761])).
% 63.00/40.65 tff(794,plain,
% 63.00/40.65 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 63.00/40.65 inference(monotonicity,[status(thm)],[760, 793])).
% 63.00/40.65 tff(795,plain,
% 63.00/40.65 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 63.00/40.65 inference(symmetry,[status(thm)],[794])).
% 63.00/40.65 tff(796,plain,
% 63.00/40.65 ((~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) <=> (~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 63.00/40.65 inference(monotonicity,[status(thm)],[795])).
% 63.00/40.65 tff(797,assumption,(get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))), introduced(assumption)).
% 63.00/40.65 tff(798,plain,
% 63.00/40.65 (get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)) = get(elt1, int, t2tb5(A3!14), t2tb(J!15))),
% 63.00/40.65 inference(transitivity,[status(thm)],[334, 337, 790, 797])).
% 63.00/40.65 tff(799,plain,
% 63.00/40.65 (tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15)))),
% 63.00/40.65 inference(monotonicity,[status(thm)],[798])).
% 63.00/40.65 tff(800,plain,
% 63.00/40.65 (tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))) = tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))),
% 63.00/40.65 inference(symmetry,[status(thm)],[799])).
% 63.00/40.65 tff(801,plain,
% 63.00/40.65 (le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 63.00/40.66 inference(monotonicity,[status(thm)],[800])).
% 63.00/40.66 tff(802,plain,
% 63.00/40.66 (le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))) <=> le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 63.00/40.66 inference(symmetry,[status(thm)],[801])).
% 63.00/40.66 tff(803,plain,
% 63.00/40.66 ((~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))) <=> (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))),
% 63.00/40.66 inference(monotonicity,[status(thm)],[802])).
% 63.00/40.66 tff(804,plain,
% 63.00/40.66 (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 63.00/40.66 inference(modus_ponens,[status(thm)],[387, 803])).
% 63.00/40.66 tff(805,assumption,(le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))), introduced(assumption)).
% 63.00/40.66 tff(806,plain,
% 63.00/40.66 ($false),
% 63.00/40.66 inference(unit_resolution,[status(thm)],[805, 804])).
% 63.00/40.66 tff(807,plain,((~(get(elt1, int, set(elt1, int, set(elt1, int, t2tb5(A3!14), t2tb(J!15), get(elt1, int, t2tb5(A3!14), t2tb($sum(-1, J!15)))), t2tb($sum(-1, J!15)), get(elt1, int, t2tb5(A3!14), t2tb(J!15))), t2tb(tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))) = get(elt1, int, t2tb5(A3!14), t2tb(J!15)))) | (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11)))))), inference(lemma,lemma(discharge,[]))).
% 63.00/40.66 tff(808,plain,
% 63.00/40.66 (~le(P!11, tb2t4(get(elt1, int, t2tb5(A3!14), t2tb(J!15))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 63.00/40.66 inference(unit_resolution,[status(thm)],[807, 789])).
% 63.00/40.66 tff(809,plain,
% 63.00/40.66 (~le(P!11, tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I2_7($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))), tb2t4(get1(elt1, t2tb3(tb2t3(mk_array(elt1, A!10, t2tb5(A5!17)))), tptp_fun_I1_8($sum(1, I!12), J1!18, tb2t3(mk_array(elt1, A!10, t2tb5(A5!17))), P!11))))),
% 63.00/40.66 inference(modus_ponens,[status(thm)],[808, 796])).
% 63.00/40.66 tff(810,plain,
% 63.00/40.66 ($false),
% 63.00/40.66 inference(unit_resolution,[status(thm)],[661, 809])).
% 63.00/40.66 % SZS output end Proof
%------------------------------------------------------------------------------