TSTP Solution File: SWW676_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW676_1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 20:59:37 EDT 2022
% Result : Theorem 9.55s 6.31s
% Output : Proof 9.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW676_1 : TPTP v8.1.0. Released v6.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 20:57:25 EDT 2022
% 0.20/0.34 % CPUTime :
% 0.20/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.34 Usage: tptp [options] [-file:]file
% 0.20/0.34 -h, -? prints this message.
% 0.20/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.34 -m, -model generate model.
% 0.20/0.34 -p, -proof generate proof.
% 0.20/0.34 -c, -core generate unsat core of named formulas.
% 0.20/0.34 -st, -statistics display statistics.
% 0.20/0.34 -t:timeout set timeout (in second).
% 0.20/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.34 -<param>:<value> configuration parameter and value.
% 0.20/0.34 -o:<output-file> file to place output in.
% 9.55/6.31 % SZS status Theorem
% 9.55/6.31 % SZS output start Proof
% 9.55/6.31 tff(div2_type, type, (
% 9.55/6.31 div2: $int > $int)).
% 9.55/6.31 tff(tptp_fun_U_5_type, type, (
% 9.55/6.31 tptp_fun_U_5: $int)).
% 9.55/6.31 tff(tptp_fun_L_6_type, type, (
% 9.55/6.31 tptp_fun_L_6: $int)).
% 9.55/6.31 tff(tptp_fun__select__Array_Int_Int__Int__Int__type, type, (
% 9.55/6.31 tptp_fun__select__Array_Int_Int__Int__Int_: ( 'Array[Int,Int]' * $int ) > $int)).
% 9.55/6.31 tff(tptp_fun_A_4_type, type, (
% 9.55/6.31 tptp_fun_A_4: 'Array[Int,Int]')).
% 9.55/6.31 tff(tptp_fun_E_3_type, type, (
% 9.55/6.31 tptp_fun_E_3: $int)).
% 9.55/6.31 tff(tptp_fun_I_12_type, type, (
% 9.55/6.31 tptp_fun_I_12: $int)).
% 9.55/6.31 tff(tptp_fun_I_11_type, type, (
% 9.55/6.31 tptp_fun_I_11: $int)).
% 9.55/6.31 tff(tptp_fun_U_6_10_type, type, (
% 9.55/6.31 tptp_fun_U_6_10: $int)).
% 9.55/6.31 tff(tptp_fun_M_2_7_type, type, (
% 9.55/6.31 tptp_fun_M_2_7: $int)).
% 9.55/6.31 tff(tptp_fun_I_9_type, type, (
% 9.55/6.31 tptp_fun_I_9: $int)).
% 9.55/6.31 tff(tptp_fun_L_4_8_type, type, (
% 9.55/6.31 tptp_fun_L_4_8: $int)).
% 9.55/6.31 tff(sorted_type, type, (
% 9.55/6.31 sorted: ( 'Array[Int,Int]' * $int * $int ) > $o)).
% 9.55/6.31 tff(length_type, type, (
% 9.55/6.31 length: 'Array[Int,Int]' > $int)).
% 9.55/6.31 tff(tptp_fun_I_2_type, type, (
% 9.55/6.31 tptp_fun_I_2: ( $int * $int * 'Array[Int,Int]' ) > $int)).
% 9.55/6.31 tff(tptp_fun_J_1_type, type, (
% 9.55/6.31 tptp_fun_J_1: ( $int * $int * 'Array[Int,Int]' ) > $int)).
% 9.55/6.31 tff(1,assumption,(~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)), introduced(assumption)).
% 9.55/6.31 tff(2,assumption,(~$lesseq($sum(L!6, $product(-1, U!5)), 0)), introduced(assumption)).
% 9.55/6.31 tff(3,plain,
% 9.55/6.31 (((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))))))) | $lesseq($sum(L!6, $product(-1, U!5)), 0)),
% 9.55/6.31 inference(tautology,[status(thm)],[])).
% 9.55/6.31 tff(4,plain,
% 9.55/6.31 ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))))))),
% 9.55/6.31 inference(unit_resolution,[status(thm)],[3, 2])).
% 9.55/6.31 tff(5,plain,
% 9.55/6.31 (((~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))))))))) | (~((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))))) <=> ((~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))))))))) | (~((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)))))),
% 9.55/6.31 inference(rewrite,[status(thm)],[])).
% 9.55/6.31 tff(6,plain,
% 9.55/6.31 (($lesseq($sum(L!6, $product(-1, I!12)), 0) & $greatereq($sum(U!5, $product(-1, I!12)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) <=> (~((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))))),
% 9.55/6.31 inference(rewrite,[status(thm)],[])).
% 9.55/6.31 tff(7,plain,
% 9.55/6.31 (($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))))))) <=> (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))))))))),
% 9.55/6.31 inference(rewrite,[status(thm)],[])).
% 9.55/6.31 tff(8,plain,
% 9.55/6.31 (((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))) <=> ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))))))),
% 9.55/6.31 inference(rewrite,[status(thm)],[])).
% 9.55/6.31 tff(9,plain,
% 9.55/6.31 (($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))) <=> ($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))))))),
% 9.55/6.31 inference(monotonicity,[status(thm)],[8])).
% 9.55/6.31 tff(10,plain,
% 9.55/6.31 (($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))) <=> (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))))))))),
% 9.55/6.31 inference(transitivity,[status(thm)],[9, 7])).
% 9.55/6.31 tff(11,plain,
% 9.55/6.31 ((($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))) | ($lesseq($sum(L!6, $product(-1, I!12)), 0) & $greatereq($sum(U!5, $product(-1, I!12)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) <=> ((~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))))))))) | (~((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)))))),
% 9.55/6.31 inference(monotonicity,[status(thm)],[10, 6])).
% 9.55/6.31 tff(12,plain,
% 9.55/6.31 ((($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))) | ($lesseq($sum(L!6, $product(-1, I!12)), 0) & $greatereq($sum(U!5, $product(-1, I!12)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) <=> ((~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))))))))) | (~((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)))))),
% 9.55/6.31 inference(transitivity,[status(thm)],[11, 5])).
% 9.55/6.31 tff(13,plain,
% 9.55/6.31 ((($greatereq(L!6, 0) & (~$lesseq($sum(length(A!4), $product(-1, U!5)), 0)) & sorted(A!4, 0, $sum(-1, length(A!4)))) & ((($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))) | ($lesseq($sum(L!6, $product(-1, I!12)), 0) & $greatereq($sum(U!5, $product(-1, I!12)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) & (![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))) <=> ($greatereq(L!6, 0) & (~$lesseq($sum(length(A!4), $product(-1, U!5)), 0)) & sorted(A!4, 0, $sum(-1, length(A!4))) & (($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))) | ($lesseq($sum(L!6, $product(-1, I!12)), 0) & $greatereq($sum(U!5, $product(-1, I!12)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) & (![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))),
% 9.55/6.32 inference(rewrite,[status(thm)],[])).
% 9.55/6.32 tff(14,plain,
% 9.55/6.32 (((($greatereq($sum(U!5, $product(-1, L!6)), 0) & ((~$greatereq($sum(U!5, $product(-1, L!6)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(U!5, L!6)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & ($lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $lesseq($sum(I!9, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & ($greatereq($sum(I!11, $product(-1, L!6)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))) | ($greatereq($sum(I!12, $product(-1, L!6)), 0) & $lesseq($sum(I!12, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) & (((~$greatereq($sum(U!5, $product(-1, L!6)), 0)) | ((~(~$greatereq($sum(U!5, $product(-1, L!6)), 0))) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(U!5, L!6)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ((~(~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0))) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) <=> ((($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))) | ($lesseq($sum(L!6, $product(-1, I!12)), 0) & $greatereq($sum(U!5, $product(-1, I!12)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) & (![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))),
% 9.55/6.32 inference(rewrite,[status(thm)],[])).
% 9.55/6.32 tff(15,plain,
% 9.55/6.32 ((~(~($greatereq(L!6, 0) & (~$lesseq($sum(length(A!4), $product(-1, U!5)), 0)) & sorted(A!4, 0, $sum(-1, length(A!4)))))) <=> ($greatereq(L!6, 0) & (~$lesseq($sum(length(A!4), $product(-1, U!5)), 0)) & sorted(A!4, 0, $sum(-1, length(A!4))))),
% 9.55/6.32 inference(rewrite,[status(thm)],[])).
% 9.55/6.32 tff(16,plain,
% 9.55/6.32 ((~($greatereq(L!6, 0) & (~$greatereq($sum(U!5, $product(-1, length(A!4))), 0)) & sorted(A!4, 0, $sum(-1, length(A!4))))) <=> (~($greatereq(L!6, 0) & (~$lesseq($sum(length(A!4), $product(-1, U!5)), 0)) & sorted(A!4, 0, $sum(-1, length(A!4)))))),
% 9.55/6.32 inference(rewrite,[status(thm)],[])).
% 9.55/6.32 tff(17,plain,
% 9.55/6.32 ((~(~($greatereq(L!6, 0) & (~$greatereq($sum(U!5, $product(-1, length(A!4))), 0)) & sorted(A!4, 0, $sum(-1, length(A!4)))))) <=> (~(~($greatereq(L!6, 0) & (~$lesseq($sum(length(A!4), $product(-1, U!5)), 0)) & sorted(A!4, 0, $sum(-1, length(A!4))))))),
% 9.55/6.32 inference(monotonicity,[status(thm)],[16])).
% 9.55/6.32 tff(18,plain,
% 9.55/6.32 ((~(~($greatereq(L!6, 0) & (~$greatereq($sum(U!5, $product(-1, length(A!4))), 0)) & sorted(A!4, 0, $sum(-1, length(A!4)))))) <=> ($greatereq(L!6, 0) & (~$lesseq($sum(length(A!4), $product(-1, U!5)), 0)) & sorted(A!4, 0, $sum(-1, length(A!4))))),
% 9.55/6.32 inference(transitivity,[status(thm)],[17, 15])).
% 9.55/6.32 tff(19,plain,
% 9.55/6.32 (((~(~($greatereq(L!6, 0) & (~$greatereq($sum(U!5, $product(-1, length(A!4))), 0)) & sorted(A!4, 0, $sum(-1, length(A!4)))))) & ((($greatereq($sum(U!5, $product(-1, L!6)), 0) & ((~$greatereq($sum(U!5, $product(-1, L!6)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(U!5, L!6)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & ($lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $lesseq($sum(I!9, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & ($greatereq($sum(I!11, $product(-1, L!6)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))) | ($greatereq($sum(I!12, $product(-1, L!6)), 0) & $lesseq($sum(I!12, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) & (((~$greatereq($sum(U!5, $product(-1, L!6)), 0)) | ((~(~$greatereq($sum(U!5, $product(-1, L!6)), 0))) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(U!5, L!6)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ((~(~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0))) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))) <=> (($greatereq(L!6, 0) & (~$lesseq($sum(length(A!4), $product(-1, U!5)), 0)) & sorted(A!4, 0, $sum(-1, length(A!4)))) & ((($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))) | ($lesseq($sum(L!6, $product(-1, I!12)), 0) & $greatereq($sum(U!5, $product(-1, I!12)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) & (![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.55/6.32 inference(monotonicity,[status(thm)],[18, 14])).
% 9.55/6.32 tff(20,plain,
% 9.55/6.32 (((~(~($greatereq(L!6, 0) & (~$greatereq($sum(U!5, $product(-1, length(A!4))), 0)) & sorted(A!4, 0, $sum(-1, length(A!4)))))) & ((($greatereq($sum(U!5, $product(-1, L!6)), 0) & ((~$greatereq($sum(U!5, $product(-1, L!6)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(U!5, L!6)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & ($lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $lesseq($sum(I!9, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & ($greatereq($sum(I!11, $product(-1, L!6)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))) | ($greatereq($sum(I!12, $product(-1, L!6)), 0) & $lesseq($sum(I!12, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) & (((~$greatereq($sum(U!5, $product(-1, L!6)), 0)) | ((~(~$greatereq($sum(U!5, $product(-1, L!6)), 0))) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(U!5, L!6)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ((~(~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0))) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))) <=> ($greatereq(L!6, 0) & (~$lesseq($sum(length(A!4), $product(-1, U!5)), 0)) & sorted(A!4, 0, $sum(-1, length(A!4))) & (($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))) | ($lesseq($sum(L!6, $product(-1, I!12)), 0) & $greatereq($sum(U!5, $product(-1, I!12)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) & (![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))),
% 9.55/6.32 inference(transitivity,[status(thm)],[19, 13])).
% 9.55/6.32 tff(21,plain,
% 9.55/6.32 ((~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($greatereq(L, 0) & (~$greatereq($sum(U, $product(-1, length(A))), 0)) & sorted(A, 0, $sum(-1, length(A))))) | (($greatereq($sum(U, $product(-1, L)), 0) & ((~$greatereq($sum(U, $product(-1, L)), 0)) | ?[M_2: $int] : (($sum(M_2, $product(-1, div2($sum(U, L)))) = 0) & (($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) = 0) | (($lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0) | ?[L_4: $int] : (($sum(M_2, $product(-1, L_4)) = -1) & ?[I: $int] : ($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0)))) & ((~$lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0)) | ?[U_6: $int] : (($sum(M_2, $product(-1, U_6)) = 1) & ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0))))))))) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0))))) <=> (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($greatereq(L, 0) & (~$greatereq($sum(U, $product(-1, length(A))), 0)) & sorted(A, 0, $sum(-1, length(A))))) | (($greatereq($sum(U, $product(-1, L)), 0) & ((~$greatereq($sum(U, $product(-1, L)), 0)) | ?[M_2: $int] : (($sum(M_2, $product(-1, div2($sum(U, L)))) = 0) & (($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) = 0) | (($lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0) | ?[L_4: $int] : (($sum(M_2, $product(-1, L_4)) = -1) & ?[I: $int] : ($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0)))) & ((~$lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0)) | ?[U_6: $int] : (($sum(M_2, $product(-1, U_6)) = 1) & ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0))))))))) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0)))))),
% 9.55/6.32 inference(rewrite,[status(thm)],[])).
% 9.55/6.32 tff(22,plain,
% 9.55/6.32 ((~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($greatereq(L, 0) & (~$lesseq($sum(length(A), $product(-1, U)), 0)) & sorted(A, 0, $sum(-1, length(A))))) | (($lesseq($sum(L, $product(-1, U)), 0) & ((~$lesseq($sum(L, $product(-1, U)), 0)) | ?[M_2: $int] : (($sum(M_2, $product(-1, div2($sum(L, U)))) = 0) & (($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2), $product(-1, E)) = 0) | (($lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0) | ?[L_4: $int] : (($sum(L_4, $product(-1, M_2)) = 1) & ?[I: $int] : ($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, E)) = 0)))) & ((~$lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0)) | ?[U_6: $int] : (($sum(U_6, $product(-1, M_2)) = -1) & ?[I: $int] : ($lesseq($sum(L, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U_6)), 0) & ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, E)) = 0))))))))) <=> ?[I: $int] : ($lesseq($sum(L, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, E)) = 0))))) <=> (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($greatereq(L, 0) & (~$greatereq($sum(U, $product(-1, length(A))), 0)) & sorted(A, 0, $sum(-1, length(A))))) | (($greatereq($sum(U, $product(-1, L)), 0) & ((~$greatereq($sum(U, $product(-1, L)), 0)) | ?[M_2: $int] : (($sum(M_2, $product(-1, div2($sum(U, L)))) = 0) & (($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) = 0) | (($lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0) | ?[L_4: $int] : (($sum(M_2, $product(-1, L_4)) = -1) & ?[I: $int] : ($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0)))) & ((~$lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0)) | ?[U_6: $int] : (($sum(M_2, $product(-1, U_6)) = 1) & ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0))))))))) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0)))))),
% 9.55/6.32 inference(rewrite,[status(thm)],[])).
% 9.55/6.32 tff(23,plain,
% 9.55/6.32 ((~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($lesseq(0, L) & (~$lesseq(length(A), U)) & sorted(A, 0, $sum(-1, length(A))))) | (($lesseq(L, U) & ((~$lesseq(L, U)) | ?[M_2: $int] : ((M_2 = div2($sum(L, U))) & ((tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E) | (($lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2)) | ?[L_4: $int] : ((L_4 = $sum(1, M_2)) & ?[I: $int] : ($lesseq(L_4, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))) & ((~$lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) | ?[U_6: $int] : ((U_6 = $sum(-1, M_2)) & ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U_6) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))))))) <=> ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))) <=> (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($greatereq(L, 0) & (~$lesseq($sum(length(A), $product(-1, U)), 0)) & sorted(A, 0, $sum(-1, length(A))))) | (($lesseq($sum(L, $product(-1, U)), 0) & ((~$lesseq($sum(L, $product(-1, U)), 0)) | ?[M_2: $int] : (($sum(M_2, $product(-1, div2($sum(L, U)))) = 0) & (($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2), $product(-1, E)) = 0) | (($lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0) | ?[L_4: $int] : (($sum(L_4, $product(-1, M_2)) = 1) & ?[I: $int] : ($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, E)) = 0)))) & ((~$lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0)) | ?[U_6: $int] : (($sum(U_6, $product(-1, M_2)) = -1) & ?[I: $int] : ($lesseq($sum(L, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U_6)), 0) & ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, E)) = 0))))))))) <=> ?[I: $int] : ($lesseq($sum(L, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, E)) = 0)))))),
% 9.55/6.32 inference(rewrite,[status(thm)],[])).
% 9.55/6.32 tff(24,plain,
% 9.55/6.32 ((~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($lesseq(0, L) & (~$lesseq(length(A), U)) & sorted(A, 0, $sum(-1, length(A))))) | (($lesseq(L, U) & ((~$lesseq(L, U)) | ?[M_2: $int] : ((M_2 = div2($sum(L, U))) & ((tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E) | (($lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2)) | ?[L_4: $int] : ((L_4 = $sum(1, M_2)) & ?[I: $int] : ($lesseq(L_4, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))) & ((~$lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) | ?[U_6: $int] : ((U_6 = $sum(-1, M_2)) & ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U_6) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))))))) <=> ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))) <=> (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($lesseq(0, L) & (~$lesseq(length(A), U)) & sorted(A, 0, $sum(-1, length(A))))) | (($lesseq(L, U) & ((~$lesseq(L, U)) | ?[M_2: $int] : ((M_2 = div2($sum(L, U))) & ((tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E) | (($lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2)) | ?[L_4: $int] : ((L_4 = $sum(1, M_2)) & ?[I: $int] : ($lesseq(L_4, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))) & ((~$lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) | ?[U_6: $int] : ((U_6 = $sum(-1, M_2)) & ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U_6) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))))))) <=> ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))))),
% 9.55/6.32 inference(rewrite,[status(thm)],[])).
% 9.55/6.32 tff(25,plain,
% 9.55/6.32 ((~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((($lesseq(0, L) & $less(U, length(A))) & sorted(A, 0, $difference(length(A), 1))) => ((($greater(L, U) => $false) & ((~$greater(L, U)) => ?[M_2: $int] : (((M_2 = div2($sum(L, U))) & ((tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E) => $true)) & ((~(tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E)) => (($less(tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2), E) => ?[L_4: $int] : ((L_4 = $sum(M_2, 1)) & ?[I: $int] : (($lesseq(L_4, I) & $lesseq(I, U)) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))) & ((~$less(tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2), E)) => ?[U_6: $int] : ((U_6 = $difference(M_2, 1)) & ?[I: $int] : (($lesseq(L, I) & $lesseq(I, U_6)) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))))))) <=> ?[I: $int] : (($lesseq(L, I) & $lesseq(I, U)) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))) <=> (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($lesseq(0, L) & (~$lesseq(length(A), U)) & sorted(A, 0, $sum(-1, length(A))))) | (($lesseq(L, U) & ((~$lesseq(L, U)) | ?[M_2: $int] : ((M_2 = div2($sum(L, U))) & ((tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E) | (($lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2)) | ?[L_4: $int] : ((L_4 = $sum(1, M_2)) & ?[I: $int] : ($lesseq(L_4, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))) & ((~$lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) | ?[U_6: $int] : ((U_6 = $sum(-1, M_2)) & ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U_6) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))))))) <=> ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))))),
% 9.55/6.32 inference(rewrite,[status(thm)],[])).
% 9.55/6.32 tff(26,axiom,(~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((($lesseq(0, L) & $less(U, length(A))) & sorted(A, 0, $difference(length(A), 1))) => ((($greater(L, U) => $false) & ((~$greater(L, U)) => ?[M_2: $int] : (((M_2 = div2($sum(L, U))) & ((tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E) => $true)) & ((~(tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E)) => (($less(tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2), E) => ?[L_4: $int] : ((L_4 = $sum(M_2, 1)) & ?[I: $int] : (($lesseq(L_4, I) & $lesseq(I, U)) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))) & ((~$less(tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2), E)) => ?[U_6: $int] : ((U_6 = $difference(M_2, 1)) & ?[I: $int] : (($lesseq(L, I) & $lesseq(I, U_6)) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))))))) <=> ?[I: $int] : (($lesseq(L, I) & $lesseq(I, U)) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','formula_007')).
% 9.55/6.32 tff(27,plain,
% 9.55/6.32 (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($lesseq(0, L) & (~$lesseq(length(A), U)) & sorted(A, 0, $sum(-1, length(A))))) | (($lesseq(L, U) & ((~$lesseq(L, U)) | ?[M_2: $int] : ((M_2 = div2($sum(L, U))) & ((tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E) | (($lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2)) | ?[L_4: $int] : ((L_4 = $sum(1, M_2)) & ?[I: $int] : ($lesseq(L_4, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))) & ((~$lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) | ?[U_6: $int] : ((U_6 = $sum(-1, M_2)) & ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U_6) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))))))) <=> ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))),
% 9.55/6.32 inference(modus_ponens,[status(thm)],[26, 25])).
% 9.55/6.32 tff(28,plain,
% 9.55/6.32 (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($lesseq(0, L) & (~$lesseq(length(A), U)) & sorted(A, 0, $sum(-1, length(A))))) | (($lesseq(L, U) & ((~$lesseq(L, U)) | ?[M_2: $int] : ((M_2 = div2($sum(L, U))) & ((tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E) | (($lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2)) | ?[L_4: $int] : ((L_4 = $sum(1, M_2)) & ?[I: $int] : ($lesseq(L_4, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))) & ((~$lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) | ?[U_6: $int] : ((U_6 = $sum(-1, M_2)) & ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U_6) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))))))) <=> ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))),
% 9.55/6.32 inference(modus_ponens,[status(thm)],[27, 24])).
% 9.55/6.32 tff(29,plain,
% 9.55/6.32 (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($lesseq(0, L) & (~$lesseq(length(A), U)) & sorted(A, 0, $sum(-1, length(A))))) | (($lesseq(L, U) & ((~$lesseq(L, U)) | ?[M_2: $int] : ((M_2 = div2($sum(L, U))) & ((tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E) | (($lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2)) | ?[L_4: $int] : ((L_4 = $sum(1, M_2)) & ?[I: $int] : ($lesseq(L_4, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))) & ((~$lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) | ?[U_6: $int] : ((U_6 = $sum(-1, M_2)) & ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U_6) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))))))) <=> ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))),
% 9.55/6.32 inference(modus_ponens,[status(thm)],[28, 24])).
% 9.55/6.32 tff(30,plain,
% 9.55/6.32 (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($lesseq(0, L) & (~$lesseq(length(A), U)) & sorted(A, 0, $sum(-1, length(A))))) | (($lesseq(L, U) & ((~$lesseq(L, U)) | ?[M_2: $int] : ((M_2 = div2($sum(L, U))) & ((tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2) = E) | (($lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2)) | ?[L_4: $int] : ((L_4 = $sum(1, M_2)) & ?[I: $int] : ($lesseq(L_4, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E)))) & ((~$lesseq(E, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) | ?[U_6: $int] : ((U_6 = $sum(-1, M_2)) & ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U_6) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))))))) <=> ?[I: $int] : ($lesseq(L, I) & $lesseq(I, U) & (tptp_fun__select__Array_Int_Int__Int__Int_(A, I) = E))))),
% 9.55/6.32 inference(modus_ponens,[status(thm)],[29, 24])).
% 9.55/6.32 tff(31,plain,
% 9.55/6.32 (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($greatereq(L, 0) & (~$lesseq($sum(length(A), $product(-1, U)), 0)) & sorted(A, 0, $sum(-1, length(A))))) | (($lesseq($sum(L, $product(-1, U)), 0) & ((~$lesseq($sum(L, $product(-1, U)), 0)) | ?[M_2: $int] : (($sum(M_2, $product(-1, div2($sum(L, U)))) = 0) & (($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2), $product(-1, E)) = 0) | (($lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0) | ?[L_4: $int] : (($sum(L_4, $product(-1, M_2)) = 1) & ?[I: $int] : ($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, E)) = 0)))) & ((~$lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0)) | ?[U_6: $int] : (($sum(U_6, $product(-1, M_2)) = -1) & ?[I: $int] : ($lesseq($sum(L, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U_6)), 0) & ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, E)) = 0))))))))) <=> ?[I: $int] : ($lesseq($sum(L, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, E)) = 0))))),
% 9.55/6.32 inference(modus_ponens,[status(thm)],[30, 23])).
% 9.55/6.32 tff(32,plain,
% 9.55/6.32 (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($greatereq(L, 0) & (~$greatereq($sum(U, $product(-1, length(A))), 0)) & sorted(A, 0, $sum(-1, length(A))))) | (($greatereq($sum(U, $product(-1, L)), 0) & ((~$greatereq($sum(U, $product(-1, L)), 0)) | ?[M_2: $int] : (($sum(M_2, $product(-1, div2($sum(U, L)))) = 0) & (($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) = 0) | (($lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0) | ?[L_4: $int] : (($sum(M_2, $product(-1, L_4)) = -1) & ?[I: $int] : ($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0)))) & ((~$lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0)) | ?[U_6: $int] : (($sum(M_2, $product(-1, U_6)) = 1) & ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0))))))))) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0))))),
% 9.55/6.32 inference(modus_ponens,[status(thm)],[31, 22])).
% 9.55/6.32 tff(33,plain,
% 9.55/6.32 (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($greatereq(L, 0) & (~$greatereq($sum(U, $product(-1, length(A))), 0)) & sorted(A, 0, $sum(-1, length(A))))) | (($greatereq($sum(U, $product(-1, L)), 0) & ((~$greatereq($sum(U, $product(-1, L)), 0)) | ?[M_2: $int] : (($sum(M_2, $product(-1, div2($sum(U, L)))) = 0) & (($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) = 0) | (($lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0) | ?[L_4: $int] : (($sum(M_2, $product(-1, L_4)) = -1) & ?[I: $int] : ($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0)))) & ((~$lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0)) | ?[U_6: $int] : (($sum(M_2, $product(-1, U_6)) = 1) & ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0))))))))) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0))))),
% 9.55/6.32 inference(modus_ponens,[status(thm)],[32, 21])).
% 9.55/6.32 tff(34,plain,
% 9.55/6.32 (~![L: $int, U: $int, A: 'Array[Int,Int]', E: $int] : ((~($greatereq(L, 0) & (~$greatereq($sum(U, $product(-1, length(A))), 0)) & sorted(A, 0, $sum(-1, length(A))))) | (($greatereq($sum(U, $product(-1, L)), 0) & ((~$greatereq($sum(U, $product(-1, L)), 0)) | ?[M_2: $int] : (($sum(M_2, $product(-1, div2($sum(U, L)))) = 0) & (($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))) = 0) | (($lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0) | ?[L_4: $int] : (($sum(M_2, $product(-1, L_4)) = -1) & ?[I: $int] : ($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0)))) & ((~$lesseq($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, M_2))), 0)) | ?[U_6: $int] : (($sum(M_2, $product(-1, U_6)) = 1) & ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0))))))))) <=> ?[I: $int] : ($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, U)), 0) & ($sum(E, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))) = 0))))),
% 9.55/6.32 inference(modus_ponens,[status(thm)],[33, 21])).
% 9.55/6.32 tff(35,plain,
% 9.55/6.32 ($greatereq(L!6, 0) & (~$lesseq($sum(length(A!4), $product(-1, U!5)), 0)) & sorted(A!4, 0, $sum(-1, length(A!4))) & (($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))) | ($lesseq($sum(L!6, $product(-1, I!12)), 0) & $greatereq($sum(U!5, $product(-1, I!12)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) & (![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))),
% 9.55/6.32 inference(modus_ponens,[status(thm)],[34, 20])).
% 9.55/6.32 tff(36,plain,
% 9.55/6.32 (($lesseq($sum(L!6, $product(-1, U!5)), 0) & ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0) & (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (($sum(M_2!7, $product(-1, L_4!8)) = -1) & $lesseq($sum(L_4!8, $product(-1, I!9)), 0) & $greatereq($sum(U!5, $product(-1, I!9)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) & ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (($sum(M_2!7, $product(-1, U_6!10)) = 1) & $lesseq($sum(L!6, $product(-1, I!11)), 0) & $greatereq($sum(U_6!10, $product(-1, I!11)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))) | ($lesseq($sum(L!6, $product(-1, I!12)), 0) & $greatereq($sum(U!5, $product(-1, I!12)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))),
% 9.55/6.32 inference(and_elim,[status(thm)],[35])).
% 9.55/6.32 tff(37,plain,
% 9.55/6.32 ((~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))))))))) | (~((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))))),
% 9.55/6.32 inference(modus_ponens,[status(thm)],[36, 12])).
% 9.55/6.32 tff(38,plain,
% 9.55/6.32 (~((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)))),
% 9.55/6.32 inference(unit_resolution,[status(thm)],[37, 4])).
% 9.55/6.32 tff(39,plain,
% 9.55/6.32 (((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) | $lesseq($sum(L!6, $product(-1, I!12)), 0)),
% 9.55/6.32 inference(tautology,[status(thm)],[])).
% 9.55/6.32 tff(40,plain,
% 9.55/6.32 ($lesseq($sum(L!6, $product(-1, I!12)), 0)),
% 9.55/6.32 inference(unit_resolution,[status(thm)],[39, 38])).
% 9.55/6.32 tff(41,plain,
% 9.55/6.32 (((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) | $greatereq($sum(U!5, $product(-1, I!12)), 0)),
% 9.55/6.32 inference(tautology,[status(thm)],[])).
% 9.55/6.32 tff(42,plain,
% 9.55/6.32 ($greatereq($sum(U!5, $product(-1, I!12)), 0)),
% 9.55/6.32 inference(unit_resolution,[status(thm)],[41, 38])).
% 9.55/6.32 tff(43,assumption,($lesseq($sum(L!6, $product(-1, I!12)), 0)), introduced(assumption)).
% 9.55/6.32 tff(44,assumption,($greatereq($sum(U!5, $product(-1, I!12)), 0)), introduced(assumption)).
% 9.55/6.32 tff(45,plain,
% 9.55/6.32 ($false),
% 9.55/6.32 inference(theory_lemma,[status(thm)],[44, 2, 43])).
% 9.55/6.32 tff(46,plain,($lesseq($sum(L!6, $product(-1, U!5)), 0) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~$lesseq($sum(L!6, $product(-1, I!12)), 0))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.32 tff(47,plain,
% 9.55/6.32 ($false),
% 9.55/6.32 inference(unit_resolution,[status(thm)],[46, 42, 40, 2])).
% 9.55/6.32 tff(48,plain,($lesseq($sum(L!6, $product(-1, U!5)), 0)), inference(lemma,lemma(discharge,[]))).
% 9.55/6.32 tff(49,assumption,(~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0)), introduced(assumption)).
% 9.55/6.32 tff(50,assumption,((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2)), introduced(assumption)).
% 9.55/6.32 tff(51,plain,
% 9.55/6.32 (^[A: $int, Res: $int] : refl(((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0)) <=> ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0)))),
% 9.55/6.32 inference(bind,[status(th)],[])).
% 9.55/6.32 tff(52,plain,
% 9.55/6.32 (![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0)) <=> ![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))),
% 9.55/6.32 inference(quant_intro,[status(thm)],[51])).
% 9.55/6.32 tff(53,plain,
% 9.55/6.32 (^[A: $int, Res: $int] : rewrite((($greatereq($sum(A, $product(-2, Res)), 0) & (~$greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0)) <=> ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0)))),
% 9.55/6.32 inference(bind,[status(th)],[])).
% 9.55/6.32 tff(54,plain,
% 9.55/6.32 (![A: $int, Res: $int] : (($greatereq($sum(A, $product(-2, Res)), 0) & (~$greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0)) <=> ![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))),
% 9.55/6.32 inference(quant_intro,[status(thm)],[53])).
% 9.55/6.32 tff(55,plain,
% 9.55/6.32 (^[A: $int, Res: $int] : rewrite((($lesseq($sum($product(2, Res), $product(-1, A)), 0) & (~$lesseq($sum($product(2, Res), $product(-1, A)), -2))) <=> ($sum(div2(A), $product(-1, Res)) = 0)) <=> (($greatereq($sum(A, $product(-2, Res)), 0) & (~$greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0)))),
% 9.55/6.32 inference(bind,[status(th)],[])).
% 9.55/6.32 tff(56,plain,
% 9.55/6.32 (![A: $int, Res: $int] : (($lesseq($sum($product(2, Res), $product(-1, A)), 0) & (~$lesseq($sum($product(2, Res), $product(-1, A)), -2))) <=> ($sum(div2(A), $product(-1, Res)) = 0)) <=> ![A: $int, Res: $int] : (($greatereq($sum(A, $product(-2, Res)), 0) & (~$greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))),
% 9.55/6.32 inference(quant_intro,[status(thm)],[55])).
% 9.55/6.32 tff(57,plain,
% 9.55/6.32 (^[A: $int, Res: $int] : rewrite((($lesseq($product(2, Res), A) & (~$lesseq($product(2, Res), $sum(-2, A)))) <=> (div2(A) = Res)) <=> (($lesseq($sum($product(2, Res), $product(-1, A)), 0) & (~$lesseq($sum($product(2, Res), $product(-1, A)), -2))) <=> ($sum(div2(A), $product(-1, Res)) = 0)))),
% 9.55/6.32 inference(bind,[status(th)],[])).
% 9.55/6.32 tff(58,plain,
% 9.55/6.32 (![A: $int, Res: $int] : (($lesseq($product(2, Res), A) & (~$lesseq($product(2, Res), $sum(-2, A)))) <=> (div2(A) = Res)) <=> ![A: $int, Res: $int] : (($lesseq($sum($product(2, Res), $product(-1, A)), 0) & (~$lesseq($sum($product(2, Res), $product(-1, A)), -2))) <=> ($sum(div2(A), $product(-1, Res)) = 0))),
% 9.55/6.32 inference(quant_intro,[status(thm)],[57])).
% 9.55/6.32 tff(59,plain,
% 9.55/6.32 (![A: $int, Res: $int] : (($lesseq($product(2, Res), A) & (~$lesseq($product(2, Res), $sum(-2, A)))) <=> (div2(A) = Res)) <=> ![A: $int, Res: $int] : (($lesseq($product(2, Res), A) & (~$lesseq($product(2, Res), $sum(-2, A)))) <=> (div2(A) = Res))),
% 9.55/6.32 inference(rewrite,[status(thm)],[])).
% 9.55/6.32 tff(60,plain,
% 9.55/6.32 (^[A: $int, Res: $int] : rewrite((($lesseq($product(2, Res), A) & $greater($product(2, $sum(Res, 1)), A)) <=> (div2(A) = Res)) <=> (($lesseq($product(2, Res), A) & (~$lesseq($product(2, Res), $sum(-2, A)))) <=> (div2(A) = Res)))),
% 9.55/6.32 inference(bind,[status(th)],[])).
% 9.55/6.32 tff(61,plain,
% 9.55/6.32 (![A: $int, Res: $int] : (($lesseq($product(2, Res), A) & $greater($product(2, $sum(Res, 1)), A)) <=> (div2(A) = Res)) <=> ![A: $int, Res: $int] : (($lesseq($product(2, Res), A) & (~$lesseq($product(2, Res), $sum(-2, A)))) <=> (div2(A) = Res))),
% 9.55/6.32 inference(quant_intro,[status(thm)],[60])).
% 9.55/6.32 tff(62,axiom,(![A: $int, Res: $int] : (($lesseq($product(2, Res), A) & $greater($product(2, $sum(Res, 1)), A)) <=> (div2(A) = Res))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','formula_004')).
% 9.55/6.32 tff(63,plain,
% 9.55/6.32 (![A: $int, Res: $int] : (($lesseq($product(2, Res), A) & (~$lesseq($product(2, Res), $sum(-2, A)))) <=> (div2(A) = Res))),
% 9.55/6.33 inference(modus_ponens,[status(thm)],[62, 61])).
% 9.55/6.33 tff(64,plain,
% 9.55/6.33 (![A: $int, Res: $int] : (($lesseq($product(2, Res), A) & (~$lesseq($product(2, Res), $sum(-2, A)))) <=> (div2(A) = Res))),
% 9.55/6.33 inference(modus_ponens,[status(thm)],[63, 59])).
% 9.55/6.33 tff(65,plain,
% 9.55/6.33 (![A: $int, Res: $int] : (($lesseq($sum($product(2, Res), $product(-1, A)), 0) & (~$lesseq($sum($product(2, Res), $product(-1, A)), -2))) <=> ($sum(div2(A), $product(-1, Res)) = 0))),
% 9.55/6.33 inference(modus_ponens,[status(thm)],[64, 58])).
% 9.55/6.33 tff(66,plain,
% 9.55/6.33 (![A: $int, Res: $int] : (($greatereq($sum(A, $product(-2, Res)), 0) & (~$greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))),
% 9.55/6.33 inference(modus_ponens,[status(thm)],[65, 56])).
% 9.55/6.33 tff(67,plain,(
% 9.55/6.33 ![A: $int, Res: $int] : (($greatereq($sum(A, $product(-2, Res)), 0) & (~$greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))),
% 9.55/6.33 inference(skolemize,[status(sab)],[66])).
% 9.55/6.33 tff(68,plain,
% 9.55/6.33 (![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))),
% 9.55/6.33 inference(modus_ponens,[status(thm)],[67, 54])).
% 9.55/6.33 tff(69,plain,
% 9.55/6.33 (![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))),
% 9.55/6.33 inference(modus_ponens,[status(thm)],[68, 52])).
% 9.55/6.33 tff(70,plain,
% 9.55/6.33 (((~![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))) | (~((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2)))) <=> ((~![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))) | (~((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2))))),
% 9.55/6.33 inference(rewrite,[status(thm)],[])).
% 9.55/6.33 tff(71,plain,
% 9.55/6.33 (((~((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2))) <=> $true) <=> (~((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2)))),
% 9.55/6.33 inference(rewrite,[status(thm)],[])).
% 9.55/6.33 tff(72,plain,
% 9.55/6.33 ((0 = 0) <=> $true),
% 9.55/6.33 inference(rewrite,[status(thm)],[])).
% 9.55/6.33 tff(73,plain,
% 9.55/6.33 ($sum(div2($sum(L!6, U!5)), $product(-1, div2($sum(L!6, U!5)))) = 0),
% 9.55/6.33 inference(rewrite,[status(thm)],[])).
% 9.55/6.33 tff(74,plain,
% 9.55/6.33 (($sum(div2($sum(L!6, U!5)), $product(-1, div2($sum(L!6, U!5)))) = 0) <=> (0 = 0)),
% 9.55/6.33 inference(monotonicity,[status(thm)],[73])).
% 9.55/6.33 tff(75,plain,
% 9.55/6.33 (($sum(div2($sum(L!6, U!5)), $product(-1, div2($sum(L!6, U!5)))) = 0) <=> $true),
% 9.55/6.33 inference(transitivity,[status(thm)],[74, 72])).
% 9.55/6.33 tff(76,plain,
% 9.55/6.33 ((~((~$greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 0)) | $greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 2))) <=> (~((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2)))),
% 9.55/6.33 inference(rewrite,[status(thm)],[])).
% 9.55/6.33 tff(77,plain,
% 9.55/6.33 (((~((~$greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 0)) | $greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 2))) <=> ($sum(div2($sum(L!6, U!5)), $product(-1, div2($sum(L!6, U!5)))) = 0)) <=> ((~((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2))) <=> $true)),
% 9.55/6.33 inference(monotonicity,[status(thm)],[76, 75])).
% 9.55/6.33 tff(78,plain,
% 9.55/6.33 (((~((~$greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 0)) | $greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 2))) <=> ($sum(div2($sum(L!6, U!5)), $product(-1, div2($sum(L!6, U!5)))) = 0)) <=> (~((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2)))),
% 9.55/6.33 inference(transitivity,[status(thm)],[77, 71])).
% 9.55/6.33 tff(79,plain,
% 9.55/6.33 (((~![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))) | ((~((~$greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 0)) | $greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 2))) <=> ($sum(div2($sum(L!6, U!5)), $product(-1, div2($sum(L!6, U!5)))) = 0))) <=> ((~![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))) | (~((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2))))),
% 9.55/6.33 inference(monotonicity,[status(thm)],[78])).
% 9.55/6.33 tff(80,plain,
% 9.55/6.33 (((~![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))) | ((~((~$greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 0)) | $greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 2))) <=> ($sum(div2($sum(L!6, U!5)), $product(-1, div2($sum(L!6, U!5)))) = 0))) <=> ((~![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))) | (~((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2))))),
% 9.55/6.33 inference(transitivity,[status(thm)],[79, 70])).
% 9.55/6.33 tff(81,plain,
% 9.55/6.33 ((~![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))) | ((~((~$greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 0)) | $greatereq($sum($sum(L!6, U!5), $product(-2, div2($sum(L!6, U!5)))), 2))) <=> ($sum(div2($sum(L!6, U!5)), $product(-1, div2($sum(L!6, U!5)))) = 0))),
% 9.55/6.33 inference(quant_inst,[status(thm)],[])).
% 9.55/6.33 tff(82,plain,
% 9.55/6.33 ((~![A: $int, Res: $int] : ((~((~$greatereq($sum(A, $product(-2, Res)), 0)) | $greatereq($sum(A, $product(-2, Res)), 2))) <=> ($sum(Res, $product(-1, div2(A))) = 0))) | (~((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2)))),
% 9.55/6.33 inference(modus_ponens,[status(thm)],[81, 80])).
% 9.55/6.33 tff(83,plain,
% 9.55/6.33 ($false),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[82, 69, 50])).
% 9.55/6.33 tff(84,plain,(~((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.33 tff(85,plain,
% 9.55/6.33 (((~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2)) | (~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2))),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(86,plain,
% 9.55/6.33 (~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 2)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[85, 84])).
% 9.55/6.33 tff(87,plain,
% 9.55/6.33 ($false),
% 9.55/6.33 inference(theory_lemma,[status(thm)],[86, 49, 48])).
% 9.55/6.33 tff(88,plain,($lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0)), inference(lemma,lemma(discharge,[]))).
% 9.55/6.33 tff(89,plain,
% 9.55/6.33 ($greatereq(L!6, 0)),
% 9.55/6.33 inference(and_elim,[status(thm)],[35])).
% 9.55/6.33 tff(90,plain,
% 9.55/6.33 ((~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$greatereq(L!6, 0)) | $greatereq(div2($sum(L!6, U!5)), 0)),
% 9.55/6.33 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.33 tff(91,plain,
% 9.55/6.33 ((~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0)) | $greatereq(div2($sum(L!6, U!5)), 0)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[90, 89])).
% 9.55/6.33 tff(92,plain,
% 9.55/6.33 ($greatereq(div2($sum(L!6, U!5)), 0)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[91, 88])).
% 9.55/6.33 tff(93,assumption,(~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))))), introduced(assumption)).
% 9.55/6.33 tff(94,plain,
% 9.55/6.33 (((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))) | ($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(95,plain,
% 9.55/6.33 ($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[94, 93])).
% 9.55/6.33 tff(96,plain,
% 9.55/6.33 ((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | $greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.33 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.33 tff(97,plain,
% 9.55/6.33 ($greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[96, 95])).
% 9.55/6.33 tff(98,plain,
% 9.55/6.33 ($greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1) | (~$greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0))),
% 9.55/6.33 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.33 tff(99,plain,
% 9.55/6.33 ($greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[98, 97])).
% 9.55/6.33 tff(100,plain,
% 9.55/6.33 ((~$lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1)) | (~$greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0))),
% 9.55/6.33 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.33 tff(101,plain,
% 9.55/6.33 (~$lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[100, 97])).
% 9.55/6.33 tff(102,plain,
% 9.55/6.33 (((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))) | (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(103,plain,
% 9.55/6.33 (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[102, 93])).
% 9.55/6.33 tff(104,assumption,(~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)), introduced(assumption)).
% 9.55/6.33 tff(105,plain,
% 9.55/6.33 ((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | $lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.33 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.33 tff(106,plain,
% 9.55/6.33 ($lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[105, 95])).
% 9.55/6.33 tff(107,plain,
% 9.55/6.33 ((~$greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 1)) | (~$lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0))),
% 9.55/6.33 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.33 tff(108,plain,
% 9.55/6.33 (~$greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 1)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[107, 106])).
% 9.55/6.33 tff(109,assumption,(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))), introduced(assumption)).
% 9.55/6.33 tff(110,assumption,($lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)), introduced(assumption)).
% 9.55/6.33 tff(111,plain,
% 9.55/6.33 ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0))),
% 9.55/6.33 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.33 tff(112,plain,
% 9.55/6.33 (~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[111, 104, 110])).
% 9.55/6.33 tff(113,assumption,((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))), introduced(assumption)).
% 9.55/6.33 tff(114,assumption,(~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)), introduced(assumption)).
% 9.55/6.33 tff(115,plain,
% 9.55/6.33 ((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | $lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))))),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(116,plain,
% 9.55/6.33 (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[115, 114, 113])).
% 9.55/6.33 tff(117,plain,
% 9.55/6.33 ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0)) | $lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)),
% 9.55/6.33 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.33 tff(118,plain,
% 9.55/6.33 (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[117, 114])).
% 9.55/6.33 tff(119,plain,
% 9.55/6.33 ((~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))) | ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(120,plain,
% 9.55/6.33 (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[119, 118, 109])).
% 9.55/6.33 tff(121,plain,
% 9.55/6.33 (((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(122,plain,
% 9.55/6.33 ($false),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[121, 120, 116])).
% 9.55/6.33 tff(123,plain,($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.33 tff(124,plain,
% 9.55/6.33 (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[123, 112, 109])).
% 9.55/6.33 tff(125,plain,
% 9.55/6.33 (((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) | $lesseq($sum(L_4!8, $product(-1, I!9)), 0)),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(126,plain,
% 9.55/6.33 ($lesseq($sum(L_4!8, $product(-1, I!9)), 0)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[125, 124])).
% 9.55/6.33 tff(127,assumption,($greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1)), introduced(assumption)).
% 9.55/6.33 tff(128,plain,
% 9.55/6.33 (((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) | ($sum(M_2!7, $product(-1, L_4!8)) = -1)),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(129,plain,
% 9.55/6.33 ($sum(M_2!7, $product(-1, L_4!8)) = -1),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[128, 124])).
% 9.55/6.33 tff(130,plain,
% 9.55/6.33 ((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | $lesseq($sum(M_2!7, $product(-1, L_4!8)), -1)),
% 9.55/6.33 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.33 tff(131,plain,
% 9.55/6.33 ($lesseq($sum(M_2!7, $product(-1, L_4!8)), -1)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[130, 129])).
% 9.55/6.33 tff(132,plain,
% 9.55/6.33 ($lesseq($sum(L!6, $product(-1, I!9)), 0) | (~$lesseq($sum(M_2!7, $product(-1, L_4!8)), -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1)) | (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0))),
% 9.55/6.33 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.33 tff(133,plain,
% 9.55/6.33 ($lesseq($sum(L!6, $product(-1, I!9)), 0) | (~$lesseq($sum(M_2!7, $product(-1, L_4!8)), -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1))),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[132, 88])).
% 9.55/6.33 tff(134,plain,
% 9.55/6.33 ($lesseq($sum(L!6, $product(-1, I!9)), 0)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[133, 131, 127, 126])).
% 9.55/6.33 tff(135,assumption,(~$lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1)), introduced(assumption)).
% 9.55/6.33 tff(136,assumption,(~$greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 1)), introduced(assumption)).
% 9.55/6.33 tff(137,plain,
% 9.55/6.33 (((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) | $greatereq($sum(U!5, $product(-1, I!9)), 0)),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(138,plain,
% 9.55/6.33 ($greatereq($sum(U!5, $product(-1, I!9)), 0)),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[137, 124])).
% 9.55/6.33 tff(139,plain,
% 9.55/6.33 (((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))) | ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(140,plain,
% 9.55/6.33 ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[139, 124])).
% 9.55/6.33 tff(141,assumption,(![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))), introduced(assumption)).
% 9.55/6.33 tff(142,assumption,($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0), introduced(assumption)).
% 9.55/6.33 tff(143,assumption,($greatereq($sum(U!5, $product(-1, I!9)), 0)), introduced(assumption)).
% 9.55/6.33 tff(144,assumption,($lesseq($sum(L_4!8, $product(-1, I!9)), 0)), introduced(assumption)).
% 9.55/6.33 tff(145,plain,
% 9.55/6.33 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))) | ((~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))),
% 9.55/6.33 inference(rewrite,[status(thm)],[])).
% 9.55/6.33 tff(146,plain,
% 9.55/6.33 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0))) <=> ((~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))),
% 9.55/6.33 inference(rewrite,[status(thm)],[])).
% 9.55/6.33 tff(147,plain,
% 9.55/6.33 ((~$greatereq($sum(I!9, $product(-1, L_4!8)), 0)) <=> (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0))),
% 9.55/6.33 inference(rewrite,[status(thm)],[])).
% 9.55/6.33 tff(148,plain,
% 9.55/6.33 ((~$lesseq($sum(I!9, $product(-1, U!5)), 0)) <=> (~$greatereq($sum(U!5, $product(-1, I!9)), 0))),
% 9.55/6.33 inference(rewrite,[status(thm)],[])).
% 9.55/6.33 tff(149,plain,
% 9.55/6.33 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(I!9, $product(-1, U!5)), 0)) | (~$greatereq($sum(I!9, $product(-1, L_4!8)), 0))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)))),
% 9.55/6.33 inference(monotonicity,[status(thm)],[148, 147])).
% 9.55/6.33 tff(150,plain,
% 9.55/6.33 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(I!9, $product(-1, U!5)), 0)) | (~$greatereq($sum(I!9, $product(-1, L_4!8)), 0))) <=> ((~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))),
% 9.55/6.33 inference(transitivity,[status(thm)],[149, 146])).
% 9.55/6.33 tff(151,plain,
% 9.55/6.33 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(I!9, $product(-1, U!5)), 0)) | (~$greatereq($sum(I!9, $product(-1, L_4!8)), 0)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))) | ((~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))))),
% 9.55/6.33 inference(monotonicity,[status(thm)],[150])).
% 9.55/6.33 tff(152,plain,
% 9.55/6.33 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(I!9, $product(-1, U!5)), 0)) | (~$greatereq($sum(I!9, $product(-1, L_4!8)), 0)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))),
% 9.55/6.33 inference(transitivity,[status(thm)],[151, 145])).
% 9.55/6.33 tff(153,plain,
% 9.55/6.33 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(I!9, $product(-1, U!5)), 0)) | (~$greatereq($sum(I!9, $product(-1, L_4!8)), 0)))),
% 9.55/6.33 inference(quant_inst,[status(thm)],[])).
% 9.55/6.33 tff(154,plain,
% 9.55/6.33 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))),
% 9.55/6.33 inference(modus_ponens,[status(thm)],[153, 152])).
% 9.55/6.33 tff(155,plain,
% 9.55/6.33 ($false),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[154, 144, 143, 142, 141])).
% 9.55/6.33 tff(156,plain,((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.33 tff(157,plain,
% 9.55/6.33 (~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[156, 140, 138, 126])).
% 9.55/6.33 tff(158,assumption,((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))), introduced(assumption)).
% 9.55/6.33 tff(159,plain,
% 9.55/6.33 (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))) | $lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(160,plain,
% 9.55/6.33 ((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))),
% 9.55/6.33 inference(unit_resolution,[status(thm)],[159, 104])).
% 9.55/6.33 tff(161,plain,
% 9.55/6.33 ((~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))) | (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))),
% 9.55/6.33 inference(tautology,[status(thm)],[])).
% 9.55/6.33 tff(162,plain,
% 9.55/6.33 (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))),
% 9.55/6.34 inference(unit_resolution,[status(thm)],[161, 160, 158])).
% 9.55/6.34 tff(163,plain,
% 9.55/6.34 (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0)))))) | ![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))),
% 9.55/6.34 inference(tautology,[status(thm)],[])).
% 9.55/6.34 tff(164,plain,
% 9.55/6.34 (![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))),
% 9.55/6.34 inference(unit_resolution,[status(thm)],[163, 162])).
% 9.55/6.34 tff(165,plain,
% 9.55/6.34 ((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | $greatereq($sum(M_2!7, $product(-1, L_4!8)), -1)),
% 9.55/6.34 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.34 tff(166,plain,
% 9.55/6.34 ($greatereq($sum(M_2!7, $product(-1, L_4!8)), -1)),
% 9.55/6.34 inference(unit_resolution,[status(thm)],[165, 129])).
% 9.55/6.34 tff(167,plain,
% 9.55/6.34 ($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1),
% 9.55/6.34 inference(theory_lemma,[status(thm)],[166, 131, 135, 136])).
% 9.55/6.34 tff(168,assumption,($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1), introduced(assumption)).
% 9.55/6.34 tff(169,assumption,(~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))), introduced(assumption)).
% 9.55/6.34 tff(170,assumption,(![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))), introduced(assumption)).
% 9.55/6.34 tff(171,plain,
% 9.55/6.34 (((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ((~($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0))))) <=> ((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | (~($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0))))),
% 9.55/6.34 inference(rewrite,[status(thm)],[])).
% 9.55/6.34 tff(172,plain,
% 9.55/6.34 (((~($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4!8, $product(-1, I)), 0)))) <=> ((~($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0))))),
% 9.55/6.34 inference(rewrite,[status(thm)],[])).
% 9.55/6.34 tff(173,plain,
% 9.55/6.34 (((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ((~($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4!8, $product(-1, I)), 0))))) <=> ((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ((~($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))))),
% 9.55/6.34 inference(monotonicity,[status(thm)],[172])).
% 9.55/6.34 tff(174,plain,
% 9.55/6.34 (((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ((~($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4!8, $product(-1, I)), 0))))) <=> ((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | (~($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0))))),
% 9.55/6.34 inference(transitivity,[status(thm)],[173, 171])).
% 9.55/6.34 tff(175,plain,
% 9.55/6.34 ((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ((~($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4!8, $product(-1, I)), 0))))),
% 9.55/6.34 inference(quant_inst,[status(thm)],[])).
% 9.55/6.34 tff(176,plain,
% 9.55/6.34 ((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | (~($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))),
% 9.55/6.34 inference(modus_ponens,[status(thm)],[175, 174])).
% 9.55/6.34 tff(177,plain,
% 9.55/6.34 ($false),
% 9.55/6.34 inference(unit_resolution,[status(thm)],[176, 170, 169, 168])).
% 9.55/6.34 tff(178,plain,((~($sum(L_4!8, $product(-1, div2($sum(L!6, U!5)))) = 1)) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, L_4!8)), 0)))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.34 tff(179,plain,
% 9.55/6.34 ($false),
% 9.55/6.34 inference(unit_resolution,[status(thm)],[178, 167, 164, 157])).
% 9.55/6.34 tff(180,plain,($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | $lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1) | $greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 1) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))) | (~$lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.34 tff(181,plain,
% 9.55/6.34 (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))),
% 9.55/6.34 inference(unit_resolution,[status(thm)],[180, 104, 136, 109, 135, 110])).
% 9.55/6.34 tff(182,plain,
% 9.55/6.34 ((($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))) | ((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))),
% 9.55/6.34 inference(tautology,[status(thm)],[])).
% 9.55/6.34 tff(183,plain,
% 9.55/6.34 (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))),
% 9.55/6.34 inference(unit_resolution,[status(thm)],[182, 181])).
% 9.55/6.34 tff(184,plain,
% 9.55/6.34 (((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))) <=> ((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.55/6.34 inference(rewrite,[status(thm)],[])).
% 9.55/6.34 tff(185,plain,
% 9.55/6.34 (($false | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))) <=> (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))),
% 9.55/6.34 inference(rewrite,[status(thm)],[])).
% 9.55/6.34 tff(186,plain,
% 9.55/6.34 ((~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0) | (~![L_4: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0)) | (~![U_6: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))) <=> (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))),
% 9.55/6.34 inference(rewrite,[status(thm)],[])).
% 9.55/6.34 tff(187,plain,
% 9.55/6.34 ((~$true) <=> $false),
% 9.55/6.34 inference(rewrite,[status(thm)],[])).
% 9.55/6.34 tff(188,plain,
% 9.55/6.34 ($sum(0, div2($sum(L!6, U!5))) = div2($sum(L!6, U!5))),
% 9.55/6.34 inference(rewrite,[status(thm)],[])).
% 9.55/6.34 tff(189,plain,
% 9.55/6.34 ($product(-1, $product(-1, div2($sum(L!6, U!5)))) = div2($sum(L!6, U!5))),
% 9.55/6.34 inference(rewrite,[status(thm)],[])).
% 9.55/6.34 tff(190,plain,
% 9.55/6.34 ($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))) = $sum(0, div2($sum(L!6, U!5)))),
% 9.55/6.34 inference(monotonicity,[status(thm)],[189])).
% 9.55/6.34 tff(191,plain,
% 9.55/6.34 ($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))) = div2($sum(L!6, U!5))),
% 9.55/6.34 inference(transitivity,[status(thm)],[190, 188])).
% 9.55/6.34 tff(192,plain,
% 9.55/6.34 ($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = $sum(div2($sum(L!6, U!5)), $product(-1, div2($sum(L!6, U!5))))),
% 9.55/6.34 inference(monotonicity,[status(thm)],[191])).
% 9.55/6.34 tff(193,plain,
% 9.55/6.34 ($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 0),
% 9.55/6.34 inference(transitivity,[status(thm)],[192, 73])).
% 9.55/6.34 tff(194,plain,
% 9.55/6.34 (($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 0) <=> (0 = 0)),
% 9.55/6.34 inference(monotonicity,[status(thm)],[193])).
% 9.55/6.34 tff(195,plain,
% 9.55/6.34 (($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 0) <=> $true),
% 9.55/6.34 inference(transitivity,[status(thm)],[194, 72])).
% 9.55/6.34 tff(196,plain,
% 9.55/6.34 ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 0)) <=> (~$true)),
% 9.55/6.34 inference(monotonicity,[status(thm)],[195])).
% 9.55/6.34 tff(197,plain,
% 9.55/6.34 ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 0)) <=> $false),
% 9.55/6.34 inference(transitivity,[status(thm)],[196, 187])).
% 9.55/6.34 tff(198,plain,
% 9.55/6.34 (((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0) | (~![L_4: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0)) | (~![U_6: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))) <=> ($false | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.55/6.34 inference(monotonicity,[status(thm)],[197, 186])).
% 9.55/6.34 tff(199,plain,
% 9.55/6.34 (((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0) | (~![L_4: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0)) | (~![U_6: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))) <=> (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))),
% 9.55/6.34 inference(transitivity,[status(thm)],[198, 185])).
% 9.55/6.34 tff(200,plain,
% 9.55/6.34 (((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0) | (~![L_4: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0)) | (~![U_6: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) <=> ((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.55/6.34 inference(monotonicity,[status(thm)],[199])).
% 9.55/6.34 tff(201,plain,
% 9.55/6.34 (((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0) | (~![L_4: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0)) | (~![U_6: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) <=> ((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.55/6.34 inference(transitivity,[status(thm)],[200, 184])).
% 9.55/6.34 tff(202,plain,
% 9.55/6.34 ((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0) | (~![L_4: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, $sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5)))))))), 0)) | (~![U_6: $int] : ((~($sum($sum(0, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.55/6.35 inference(quant_inst,[status(thm)],[])).
% 9.55/6.35 tff(203,plain,
% 9.55/6.35 ((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))),
% 9.55/6.35 inference(modus_ponens,[status(thm)],[202, 201])).
% 9.55/6.35 tff(204,plain,
% 9.55/6.35 (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.55/6.35 inference(unit_resolution,[status(thm)],[203, 183])).
% 9.55/6.35 tff(205,plain,
% 9.55/6.35 (((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))))) | ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.55/6.35 inference(tautology,[status(thm)],[])).
% 9.55/6.35 tff(206,plain,
% 9.55/6.35 ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))))),
% 9.55/6.35 inference(unit_resolution,[status(thm)],[205, 204])).
% 9.55/6.35 tff(207,plain,
% 9.55/6.35 (((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))))))) <=> ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))))))),
% 9.55/6.35 inference(rewrite,[status(thm)],[])).
% 9.55/6.35 tff(208,plain,
% 9.55/6.35 ((![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))))))) <=> ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))))))),
% 9.55/6.35 inference(rewrite,[status(thm)],[])).
% 9.55/6.35 tff(209,plain,
% 9.55/6.35 (($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) <=> (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))))))),
% 9.55/6.35 inference(rewrite,[status(thm)],[])).
% 9.55/6.35 tff(210,plain,
% 9.55/6.35 (^[M_2: $int] : rewrite(((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))) <=> ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))))),
% 9.55/6.35 inference(bind,[status(th)],[])).
% 9.55/6.35 tff(211,plain,
% 9.55/6.35 (![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))) <=> ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.55/6.35 inference(quant_intro,[status(thm)],[210])).
% 9.55/6.35 tff(212,plain,
% 9.55/6.35 (($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))) <=> ($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))))),
% 9.55/6.35 inference(monotonicity,[status(thm)],[211])).
% 9.55/6.35 tff(213,plain,
% 9.55/6.35 (($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))) <=> (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))))))),
% 9.55/6.35 inference(transitivity,[status(thm)],[212, 209])).
% 9.55/6.35 tff(214,plain,
% 9.55/6.35 (^[I: $int] : trans(monotonicity(rewrite(($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) <=> (~((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))))), ((~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) <=> (~(~((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))))))), rewrite((~(~((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))), ((~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))))),
% 9.55/6.35 inference(bind,[status(th)],[])).
% 9.55/6.35 tff(215,plain,
% 9.55/6.35 (![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) <=> ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))),
% 9.55/6.35 inference(quant_intro,[status(thm)],[214])).
% 9.55/6.35 tff(216,plain,
% 9.55/6.35 ((![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))) <=> (![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))))))),
% 9.55/6.35 inference(monotonicity,[status(thm)],[215, 213])).
% 9.55/6.35 tff(217,plain,
% 9.55/6.35 ((![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))) <=> ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))))))),
% 9.55/6.35 inference(transitivity,[status(thm)],[216, 208])).
% 9.55/6.35 tff(218,plain,
% 9.55/6.35 (![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ($lesseq($sum(L!6, $product(-1, U!5)), 0) & ![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0)) & (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) & ![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : (~($lesseq($sum(L_4, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, U!5)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) & ![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : (~($greatereq($sum(I, $product(-1, L!6)), 0) & $greatereq($sum(U_6, $product(-1, I)), 0) & ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))),
% 9.55/6.35 inference(and_elim,[status(thm)],[35])).
% 9.55/6.35 tff(219,plain,
% 9.55/6.35 ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))))))),
% 9.55/6.35 inference(modus_ponens,[status(thm)],[218, 217])).
% 9.55/6.35 tff(220,plain,
% 9.55/6.35 ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))))))),
% 9.55/6.35 inference(modus_ponens,[status(thm)],[219, 207])).
% 9.55/6.35 tff(221,plain,
% 9.55/6.35 (![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0))) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))))))),
% 9.55/6.35 inference(unit_resolution,[status(thm)],[220, 48])).
% 9.55/6.35 tff(222,plain,
% 9.55/6.35 (![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))),
% 9.55/6.35 inference(unit_resolution,[status(thm)],[221, 206])).
% 9.55/6.35 tff(223,plain,
% 9.55/6.35 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!9)), 0)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!9)), 0)))),
% 9.55/6.35 inference(rewrite,[status(thm)],[])).
% 9.55/6.35 tff(224,plain,
% 9.55/6.35 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0))) <=> ((~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!9)), 0)))),
% 9.55/6.35 inference(rewrite,[status(thm)],[])).
% 9.55/6.35 tff(225,plain,
% 9.55/6.35 ((~$greatereq($sum(I!9, $product(-1, L!6)), 0)) <=> (~$lesseq($sum(L!6, $product(-1, I!9)), 0))),
% 9.55/6.35 inference(rewrite,[status(thm)],[])).
% 9.55/6.35 tff(226,plain,
% 9.55/6.35 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$greatereq($sum(I!9, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!9, $product(-1, U!5)), 0))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)))),
% 9.55/6.35 inference(monotonicity,[status(thm)],[225, 148])).
% 9.55/6.35 tff(227,plain,
% 9.55/6.35 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$greatereq($sum(I!9, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!9, $product(-1, U!5)), 0))) <=> ((~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!9)), 0)))),
% 9.55/6.35 inference(transitivity,[status(thm)],[226, 224])).
% 9.55/6.35 tff(228,plain,
% 9.55/6.35 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$greatereq($sum(I!9, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!9, $product(-1, U!5)), 0)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!9)), 0))))),
% 9.55/6.35 inference(monotonicity,[status(thm)],[227])).
% 9.55/6.35 tff(229,plain,
% 9.55/6.35 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$greatereq($sum(I!9, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!9, $product(-1, U!5)), 0)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!9)), 0)))),
% 9.55/6.35 inference(transitivity,[status(thm)],[228, 223])).
% 9.55/6.35 tff(230,plain,
% 9.55/6.35 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$greatereq($sum(I!9, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!9, $product(-1, U!5)), 0)))),
% 9.55/6.35 inference(quant_inst,[status(thm)],[])).
% 9.55/6.35 tff(231,plain,
% 9.55/6.35 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!9)), 0))),
% 9.55/6.35 inference(modus_ponens,[status(thm)],[230, 229])).
% 9.55/6.35 tff(232,plain,
% 9.55/6.35 ($false),
% 9.55/6.35 inference(unit_resolution,[status(thm)],[231, 138, 140, 222, 134])).
% 9.55/6.35 tff(233,plain,($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))) | $greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 1) | $lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1) | (~$lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.35 tff(234,plain,
% 9.55/6.35 (~$lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.55/6.35 inference(unit_resolution,[status(thm)],[233, 108, 104, 103, 101, 99])).
% 9.55/6.35 tff(235,assumption,($lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)), introduced(assumption)).
% 9.55/6.35 tff(236,plain,
% 9.55/6.35 (M_2!7 = div2($sum(L!6, U!5))),
% 9.55/6.35 inference(theory_lemma,[status(thm)],[135, 235])).
% 9.55/6.35 tff(237,plain,
% 9.55/6.35 (tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7) = tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5)))),
% 9.55/6.35 inference(monotonicity,[status(thm)],[236])).
% 9.55/6.35 tff(238,assumption,(~(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7) = tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), introduced(assumption)).
% 9.55/6.35 tff(239,plain,
% 9.55/6.35 ($false),
% 9.55/6.35 inference(unit_resolution,[status(thm)],[238, 237])).
% 9.55/6.35 tff(240,plain,((tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7) = tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5)))) | $lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1) | (~$lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.35 tff(241,plain,
% 9.55/6.35 (tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7) = tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5)))),
% 9.55/6.35 inference(unit_resolution,[status(thm)],[240, 101, 106])).
% 9.55/6.35 tff(242,plain,
% 9.55/6.35 ((~(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7) = tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.55/6.35 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.35 tff(243,plain,
% 9.55/6.35 ($false),
% 9.55/6.35 inference(unit_resolution,[status(thm)],[242, 241, 234])).
% 9.55/6.35 tff(244,plain,(((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))) | $lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)), inference(lemma,lemma(discharge,[]))).
% 9.55/6.36 tff(245,plain,
% 9.55/6.36 ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[244, 93])).
% 9.55/6.36 tff(246,plain,
% 9.55/6.36 (($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0)))))) | (~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))),
% 9.55/6.36 inference(tautology,[status(thm)],[])).
% 9.55/6.36 tff(247,plain,
% 9.55/6.36 ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0)))))),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[246, 245])).
% 9.55/6.36 tff(248,assumption,(~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 1)), introduced(assumption)).
% 9.55/6.36 tff(249,plain,
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% 9.55/6.36 inference(tautology,[status(thm)],[])).
% 9.55/6.36 tff(250,plain,
% 9.55/6.36 ($greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[249, 84])).
% 9.55/6.36 tff(251,assumption,(~$greatereq($sum(L!6, $product(-1, U!5)), 0)), introduced(assumption)).
% 9.55/6.36 tff(252,plain,
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% 9.55/6.36 inference(theory_lemma,[status(thm)],[248, 251, 250])).
% 9.55/6.36 tff(253,plain,($greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 1) | $greatereq($sum(L!6, $product(-1, U!5)), 0)), inference(lemma,lemma(discharge,[]))).
% 9.55/6.36 tff(254,plain,
% 9.55/6.36 ($greatereq($sum(L!6, $product(-1, U!5)), 0)),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[253, 248])).
% 9.55/6.36 tff(255,assumption,($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0), introduced(assumption)).
% 9.55/6.36 tff(256,plain,
% 9.55/6.36 ($greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[96, 255])).
% 9.55/6.36 tff(257,assumption,($lesseq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), -1)), introduced(assumption)).
% 9.55/6.36 tff(258,plain,
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% 9.55/6.36 tff(259,plain,
% 9.55/6.36 ($lesseq($sum(U!5, $product(-1, M_2!7)), -1) | $lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1) | (~$lesseq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), -1))),
% 9.55/6.36 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.36 tff(260,plain,
% 9.55/6.36 ($lesseq($sum(U!5, $product(-1, M_2!7)), -1)),
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% 9.55/6.36 tff(261,plain,
% 9.55/6.36 ((~$lesseq($sum(U!5, $product(-1, M_2!7)), -1)) | (~$greatereq($sum(L!6, $sum(U!5, $product(-2, div2($sum(L!6, U!5))))), 0)) | $greatereq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 1) | (~$lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0))),
% 9.55/6.36 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.36 tff(262,plain,
% 9.55/6.36 ((~$lesseq($sum(U!5, $product(-1, M_2!7)), -1)) | $greatereq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 1) | (~$lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0))),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[261, 250])).
% 9.55/6.36 tff(263,plain,
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% 9.55/6.36 tff(264,plain,
% 9.55/6.36 ((~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), -1)) | (~$greatereq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 1))),
% 9.55/6.36 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.36 tff(265,plain,
% 9.55/6.36 (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), -1)),
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% 9.55/6.36 tff(266,plain,
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% 9.55/6.36 tff(267,plain,((~$lesseq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), -1)) | (~$lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)) | $lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1)), inference(lemma,lemma(discharge,[]))).
% 9.55/6.36 tff(268,plain,
% 9.55/6.36 ($lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), -1)),
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% 9.55/6.36 tff(269,plain,
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% 9.55/6.36 inference(unit_resolution,[status(thm)],[100, 268, 256])).
% 9.55/6.36 tff(270,plain,((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~$lesseq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), -1))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.36 tff(271,plain,
% 9.55/6.36 (~$lesseq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), -1)),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[270, 95])).
% 9.55/6.36 tff(272,assumption,((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))), introduced(assumption)).
% 9.55/6.36 tff(273,assumption,(~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)), introduced(assumption)).
% 9.55/6.36 tff(274,plain,
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% 9.55/6.36 inference(unit_resolution,[status(thm)],[242, 241])).
% 9.55/6.36 tff(275,assumption,(~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))), introduced(assumption)).
% 9.55/6.36 tff(276,plain,
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% 9.55/6.36 ($sum(M_2!7, $product(-1, L_4!8)) = -1),
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% 9.55/6.36 tff(278,plain,
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% 9.55/6.36 tff(279,assumption,($greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)), introduced(assumption)).
% 9.55/6.36 tff(280,plain,
% 9.55/6.36 ($lesseq($sum(L_4!8, $product(-1, I!9)), 0)),
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% 9.55/6.36 tff(281,plain,
% 9.55/6.36 ((~$lesseq($sum(I!9, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$lesseq($sum(M_2!7, $product(-1, L_4!8)), -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0))),
% 9.55/6.36 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.36 tff(282,plain,
% 9.55/6.36 (~$lesseq($sum(I!9, $product(-1, div2($sum(L!6, U!5)))), 0)),
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% 9.55/6.36 tff(283,plain,
% 9.55/6.36 ($greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 1) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | $lesseq($sum(I!9, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.36 inference(theory_lemma,[status(thm)],[])).
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% 9.55/6.36 inference(tautology,[status(thm)],[])).
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% 9.55/6.36 inference(theory_lemma,[status(thm)],[])).
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% 9.55/6.36 inference(unit_resolution,[status(thm)],[221, 314])).
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% 9.55/6.36 inference(rewrite,[status(thm)],[])).
% 9.55/6.36 tff(317,plain,
% 9.55/6.36 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0)))),
% 9.55/6.36 inference(rewrite,[status(thm)],[])).
% 9.55/6.36 tff(318,plain,
% 9.55/6.36 ((~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, U!5)), 0)) <=> (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0))),
% 9.55/6.36 inference(rewrite,[status(thm)],[])).
% 9.55/6.36 tff(319,plain,
% 9.55/6.36 ((~$greatereq($sum(div2($sum(L!6, U!5)), $product(-1, L!6)), 0)) <=> (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0))),
% 9.55/6.36 inference(rewrite,[status(thm)],[])).
% 9.55/6.36 tff(320,plain,
% 9.55/6.36 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$greatereq($sum(div2($sum(L!6, U!5)), $product(-1, L!6)), 0)) | (~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, U!5)), 0))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)))),
% 9.55/6.36 inference(monotonicity,[status(thm)],[319, 318])).
% 9.55/6.36 tff(321,plain,
% 9.55/6.36 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$greatereq($sum(div2($sum(L!6, U!5)), $product(-1, L!6)), 0)) | (~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, U!5)), 0))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0)))),
% 9.55/6.36 inference(transitivity,[status(thm)],[320, 317])).
% 9.55/6.36 tff(322,plain,
% 9.55/6.36 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$greatereq($sum(div2($sum(L!6, U!5)), $product(-1, L!6)), 0)) | (~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, U!5)), 0)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0))))),
% 9.55/6.36 inference(monotonicity,[status(thm)],[321])).
% 9.55/6.36 tff(323,plain,
% 9.55/6.36 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$greatereq($sum(div2($sum(L!6, U!5)), $product(-1, L!6)), 0)) | (~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, U!5)), 0)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0)))),
% 9.55/6.36 inference(transitivity,[status(thm)],[322, 316])).
% 9.55/6.36 tff(324,plain,
% 9.55/6.36 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$greatereq($sum(div2($sum(L!6, U!5)), $product(-1, L!6)), 0)) | (~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, U!5)), 0)))),
% 9.55/6.36 inference(quant_inst,[status(thm)],[])).
% 9.55/6.36 tff(325,plain,
% 9.55/6.36 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0))),
% 9.55/6.36 inference(modus_ponens,[status(thm)],[324, 323])).
% 9.55/6.36 tff(326,plain,
% 9.55/6.36 ($false),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[325, 315, 310, 309, 88])).
% 9.55/6.36 tff(327,plain,((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)) | (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.36 tff(328,plain,
% 9.55/6.36 (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[327, 308])).
% 9.55/6.36 tff(329,plain,
% 9.55/6.36 ($lesseq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), -1) | $greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.36 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.36 tff(330,plain,
% 9.55/6.36 ($false),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[329, 328, 271])).
% 9.55/6.36 tff(331,plain,(((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))) | $greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 1) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.36 tff(332,plain,
% 9.55/6.36 (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[331, 93, 248])).
% 9.55/6.36 tff(333,assumption,(~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))), introduced(assumption)).
% 9.55/6.36 tff(334,plain,
% 9.55/6.36 (((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))) | ($sum(M_2!7, $product(-1, U_6!10)) = 1)),
% 9.55/6.36 inference(tautology,[status(thm)],[])).
% 9.55/6.36 tff(335,plain,
% 9.55/6.36 ($sum(M_2!7, $product(-1, U_6!10)) = 1),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[334, 333])).
% 9.55/6.36 tff(336,plain,
% 9.55/6.36 ((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | $greatereq($sum(M_2!7, $product(-1, U_6!10)), 1)),
% 9.55/6.36 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.36 tff(337,plain,
% 9.55/6.36 ($greatereq($sum(M_2!7, $product(-1, U_6!10)), 1)),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[336, 335])).
% 9.55/6.36 tff(338,assumption,(~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), -1)), introduced(assumption)).
% 9.55/6.36 tff(339,plain,
% 9.55/6.36 (((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))) | $lesseq($sum(L!6, $product(-1, I!11)), 0)),
% 9.55/6.36 inference(tautology,[status(thm)],[])).
% 9.55/6.36 tff(340,plain,
% 9.55/6.36 ($lesseq($sum(L!6, $product(-1, I!11)), 0)),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[339, 333])).
% 9.55/6.36 tff(341,plain,
% 9.55/6.36 (((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))) | $greatereq($sum(U_6!10, $product(-1, I!11)), 0)),
% 9.55/6.36 inference(tautology,[status(thm)],[])).
% 9.55/6.36 tff(342,plain,
% 9.55/6.36 ($greatereq($sum(U_6!10, $product(-1, I!11)), 0)),
% 9.55/6.36 inference(unit_resolution,[status(thm)],[341, 333])).
% 9.55/6.36 tff(343,assumption,($greatereq($sum(U_6!10, $product(-1, I!11)), 0)), introduced(assumption)).
% 9.55/6.36 tff(344,assumption,($lesseq($sum(L!6, $product(-1, I!11)), 0)), introduced(assumption)).
% 9.55/6.36 tff(345,assumption,($greatereq($sum(M_2!7, $product(-1, U_6!10)), 1)), introduced(assumption)).
% 9.55/6.36 tff(346,plain,
% 9.55/6.36 ($false),
% 9.55/6.36 inference(theory_lemma,[status(thm)],[345, 235, 344, 338, 343])).
% 9.55/6.36 tff(347,plain,($lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), -1) | (~$greatereq($sum(M_2!7, $product(-1, U_6!10)), 1)) | (~$lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.37 tff(348,plain,
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% 9.55/6.37 inference(unit_resolution,[status(thm)],[347, 342, 340, 235, 338, 337])).
% 9.55/6.37 tff(349,plain,(((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))) | (~$lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)) | $lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), -1)), inference(lemma,lemma(discharge,[]))).
% 9.55/6.37 tff(350,plain,
% 9.55/6.37 ($lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), -1)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[349, 332, 106])).
% 9.55/6.37 tff(351,plain,
% 9.55/6.37 ($greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[329, 271])).
% 9.55/6.37 tff(352,plain,
% 9.55/6.37 ((~$greatereq($sum(L!6, $product(-1, U!5)), 0)) | (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), -1))),
% 9.55/6.37 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.37 tff(353,plain,
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% 9.55/6.37 inference(unit_resolution,[status(thm)],[352, 351, 350, 254])).
% 9.55/6.37 tff(354,plain,(((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))) | $greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 1)), inference(lemma,lemma(discharge,[]))).
% 9.55/6.37 tff(355,plain,
% 9.55/6.37 ($greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 1)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[354, 93])).
% 9.55/6.37 tff(356,plain,
% 9.55/6.37 ((~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 1)) | $greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.37 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.37 tff(357,plain,
% 9.55/6.37 ($greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[356, 355])).
% 9.55/6.37 tff(358,plain,
% 9.55/6.37 (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[327, 357])).
% 9.55/6.37 tff(359,plain,
% 9.55/6.37 (~$greatereq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[305, 358, 245])).
% 9.55/6.37 tff(360,plain,
% 9.55/6.37 ($greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 1) | $lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.37 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.37 tff(361,plain,
% 9.55/6.37 ($lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[360, 136])).
% 9.55/6.37 tff(362,plain,
% 9.55/6.37 (tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7) = tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5)))),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[240, 101, 361])).
% 9.55/6.37 tff(363,plain,
% 9.55/6.37 ($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[301, 362])).
% 9.55/6.37 tff(364,plain,
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% 9.55/6.37 tff(365,plain,
% 9.55/6.37 (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[299, 364, 103])).
% 9.55/6.37 tff(366,plain,
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% 9.55/6.37 inference(unit_resolution,[status(thm)],[339, 365])).
% 9.55/6.37 tff(367,plain,
% 9.55/6.37 (((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))) | ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)),
% 9.55/6.37 inference(tautology,[status(thm)],[])).
% 9.55/6.37 tff(368,plain,
% 9.55/6.37 ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[367, 365])).
% 9.55/6.37 tff(369,plain,
% 9.55/6.37 ($sum(M_2!7, $product(-1, U_6!10)) = 1),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[334, 365])).
% 9.55/6.37 tff(370,plain,
% 9.55/6.37 ($greatereq($sum(M_2!7, $product(-1, U_6!10)), 1)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[336, 369])).
% 9.55/6.37 tff(371,plain,
% 9.55/6.37 ($greatereq($sum(U_6!10, $product(-1, I!11)), 0)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[341, 365])).
% 9.55/6.37 tff(372,assumption,($greatereq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), 0)), introduced(assumption)).
% 9.55/6.37 tff(373,plain,
% 9.55/6.37 ($false),
% 9.55/6.37 inference(theory_lemma,[status(thm)],[345, 235, 372, 343])).
% 9.55/6.37 tff(374,plain,((~$greatereq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$greatereq($sum(M_2!7, $product(-1, U_6!10)), 1)) | (~$lesseq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.37 tff(375,plain,
% 9.55/6.37 (~$greatereq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[374, 371, 361, 370])).
% 9.55/6.37 tff(376,assumption,($lesseq($sum(U!5, $product(-1, I!11)), 0)), introduced(assumption)).
% 9.55/6.37 tff(377,assumption,(~$greatereq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), 0)), introduced(assumption)).
% 9.55/6.37 tff(378,plain,
% 9.55/6.37 ($false),
% 9.55/6.37 inference(theory_lemma,[status(thm)],[309, 377, 376])).
% 9.55/6.37 tff(379,plain,((~$lesseq($sum(U!5, $product(-1, I!11)), 0)) | (~$greatereq($sum(U!5, $product(-1, div2($sum(L!6, U!5)))), 0)) | $greatereq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), 0)), inference(lemma,lemma(discharge,[]))).
% 9.55/6.37 tff(380,plain,
% 9.55/6.37 (~$lesseq($sum(U!5, $product(-1, I!11)), 0)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[379, 375, 357])).
% 9.55/6.37 tff(381,plain,
% 9.55/6.37 ($greatereq($sum(U!5, $product(-1, I!11)), 0) | $lesseq($sum(U!5, $product(-1, I!11)), 0)),
% 9.55/6.37 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.37 tff(382,plain,
% 9.55/6.37 ($greatereq($sum(U!5, $product(-1, I!11)), 0)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[381, 380])).
% 9.55/6.37 tff(383,assumption,($greatereq($sum(U!5, $product(-1, I!11)), 0)), introduced(assumption)).
% 9.55/6.37 tff(384,assumption,(![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))), introduced(assumption)).
% 9.55/6.37 tff(385,assumption,($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0), introduced(assumption)).
% 9.55/6.37 tff(386,plain,
% 9.55/6.37 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!11)), 0)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!11)), 0)))),
% 9.55/6.37 inference(rewrite,[status(thm)],[])).
% 9.55/6.37 tff(387,plain,
% 9.55/6.37 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!11)), 0))) <=> ((~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!11)), 0)))),
% 9.55/6.37 inference(rewrite,[status(thm)],[])).
% 9.55/6.37 tff(388,plain,
% 9.55/6.37 ((~$lesseq($sum(I!11, $product(-1, U!5)), 0)) <=> (~$greatereq($sum(U!5, $product(-1, I!11)), 0))),
% 9.55/6.37 inference(rewrite,[status(thm)],[])).
% 9.55/6.37 tff(389,plain,
% 9.55/6.37 ((~$greatereq($sum(I!11, $product(-1, L!6)), 0)) <=> (~$lesseq($sum(L!6, $product(-1, I!11)), 0))),
% 9.55/6.37 inference(rewrite,[status(thm)],[])).
% 9.55/6.37 tff(390,plain,
% 9.55/6.37 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(I!11, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!11, $product(-1, U!5)), 0))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!11)), 0)))),
% 9.55/6.37 inference(monotonicity,[status(thm)],[389, 388])).
% 9.55/6.37 tff(391,plain,
% 9.55/6.37 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(I!11, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!11, $product(-1, U!5)), 0))) <=> ((~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!11)), 0)))),
% 9.55/6.37 inference(transitivity,[status(thm)],[390, 387])).
% 9.55/6.37 tff(392,plain,
% 9.55/6.37 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(I!11, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!11, $product(-1, U!5)), 0)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!11)), 0))))),
% 9.55/6.37 inference(monotonicity,[status(thm)],[391])).
% 9.55/6.37 tff(393,plain,
% 9.55/6.37 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(I!11, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!11, $product(-1, U!5)), 0)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!11)), 0)))),
% 9.55/6.37 inference(transitivity,[status(thm)],[392, 386])).
% 9.55/6.37 tff(394,plain,
% 9.55/6.37 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(I!11, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!11, $product(-1, U!5)), 0)))),
% 9.55/6.37 inference(quant_inst,[status(thm)],[])).
% 9.55/6.37 tff(395,plain,
% 9.55/6.37 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!11)), 0))),
% 9.55/6.37 inference(modus_ponens,[status(thm)],[394, 393])).
% 9.55/6.37 tff(396,plain,
% 9.55/6.37 ($false),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[395, 344, 385, 384, 383])).
% 9.55/6.37 tff(397,plain,((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!11)), 0))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.37 tff(398,plain,
% 9.55/6.37 (~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[397, 382, 368, 366])).
% 9.55/6.37 tff(399,plain,
% 9.55/6.37 (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))))),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[221, 398])).
% 9.55/6.37 tff(400,plain,
% 9.55/6.37 (![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[205, 399])).
% 9.55/6.37 tff(401,plain,
% 9.55/6.37 (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[203, 400])).
% 9.55/6.37 tff(402,plain,
% 9.55/6.37 ((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[182, 401])).
% 9.55/6.37 tff(403,plain,
% 9.55/6.37 (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[161, 402, 247])).
% 9.55/6.37 tff(404,plain,
% 9.55/6.37 (((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))) | ![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))),
% 9.55/6.37 inference(tautology,[status(thm)],[])).
% 9.55/6.37 tff(405,plain,
% 9.55/6.37 (![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[404, 403])).
% 9.55/6.37 tff(406,assumption,(~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))), introduced(assumption)).
% 9.55/6.37 tff(407,assumption,(![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))), introduced(assumption)).
% 9.55/6.37 tff(408,plain,
% 9.55/6.37 (((~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) <=> ((~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1))))),
% 9.55/6.37 inference(rewrite,[status(thm)],[])).
% 9.55/6.37 tff(409,plain,
% 9.55/6.37 (($false | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) <=> ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.55/6.37 inference(rewrite,[status(thm)],[])).
% 9.55/6.37 tff(410,plain,
% 9.55/6.37 (^[I: $int] : trans(monotonicity(rewrite((~$greatereq($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)) <=> (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1))), (((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) <=> ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))), rewrite(((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))), (((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))))),
% 9.55/6.37 inference(bind,[status(th)],[])).
% 9.55/6.37 tff(411,plain,
% 9.55/6.37 (![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))) <=> ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.55/6.37 inference(quant_intro,[status(thm)],[410])).
% 9.55/6.37 tff(412,plain,
% 9.55/6.37 ((-1 = -1) <=> $true),
% 9.55/6.37 inference(rewrite,[status(thm)],[])).
% 9.55/6.37 tff(413,plain,
% 9.55/6.37 ($sum($sum(-1, div2($sum(L!6, U!5))), $product(-1, div2($sum(L!6, U!5)))) = -1),
% 9.55/6.37 inference(rewrite,[status(thm)],[])).
% 9.55/6.37 tff(414,plain,
% 9.55/6.37 ($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))) = $sum(-1, div2($sum(L!6, U!5)))),
% 9.55/6.37 inference(rewrite,[status(thm)],[])).
% 9.55/6.37 tff(415,plain,
% 9.55/6.37 ($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = $sum($sum(-1, div2($sum(L!6, U!5))), $product(-1, div2($sum(L!6, U!5))))),
% 9.55/6.37 inference(monotonicity,[status(thm)],[414])).
% 9.55/6.37 tff(416,plain,
% 9.55/6.37 ($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = -1),
% 9.55/6.37 inference(transitivity,[status(thm)],[415, 413])).
% 9.55/6.37 tff(417,plain,
% 9.55/6.37 (($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = -1) <=> (-1 = -1)),
% 9.55/6.37 inference(monotonicity,[status(thm)],[416])).
% 9.55/6.37 tff(418,plain,
% 9.55/6.37 (($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = -1) <=> $true),
% 9.55/6.37 inference(transitivity,[status(thm)],[417, 412])).
% 9.55/6.37 tff(419,plain,
% 9.55/6.37 ((~($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = -1)) <=> (~$true)),
% 9.55/6.37 inference(monotonicity,[status(thm)],[418])).
% 9.55/6.37 tff(420,plain,
% 9.55/6.37 ((~($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = -1)) <=> $false),
% 9.55/6.37 inference(transitivity,[status(thm)],[419, 187])).
% 9.55/6.37 tff(421,plain,
% 9.55/6.37 (((~($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))) <=> ($false | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1))))),
% 9.55/6.37 inference(monotonicity,[status(thm)],[420, 411])).
% 9.55/6.37 tff(422,plain,
% 9.55/6.37 (((~($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))) <=> ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.55/6.37 inference(transitivity,[status(thm)],[421, 409])).
% 9.55/6.37 tff(423,plain,
% 9.55/6.37 (((~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ((~($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) <=> ((~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1))))),
% 9.55/6.37 inference(monotonicity,[status(thm)],[422])).
% 9.55/6.37 tff(424,plain,
% 9.55/6.37 (((~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ((~($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) <=> ((~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1))))),
% 9.55/6.37 inference(transitivity,[status(thm)],[423, 408])).
% 9.55/6.37 tff(425,plain,
% 9.55/6.37 ((~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ((~($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum($sum(-1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))),
% 9.55/6.37 inference(quant_inst,[status(thm)],[])).
% 9.55/6.37 tff(426,plain,
% 9.55/6.37 ((~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.55/6.37 inference(modus_ponens,[status(thm)],[425, 424])).
% 9.55/6.37 tff(427,plain,
% 9.55/6.37 ($false),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[426, 407, 406])).
% 9.55/6.37 tff(428,plain,(![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1))) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.37 tff(429,plain,
% 9.55/6.37 (![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[428, 405])).
% 9.55/6.37 tff(430,plain,
% 9.55/6.37 ($lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~$greatereq($sum(M_2!7, $product(-1, U_6!10)), 1)) | $greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 1)),
% 9.55/6.37 inference(theory_lemma,[status(thm)],[])).
% 9.55/6.37 tff(431,plain,
% 9.55/6.37 ($lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1)),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[430, 371, 136, 370])).
% 9.55/6.37 tff(432,plain,
% 9.55/6.37 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | ((~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.55/6.37 inference(rewrite,[status(thm)],[])).
% 9.55/6.37 tff(433,plain,
% 9.55/6.37 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1))) <=> ((~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.55/6.37 inference(rewrite,[status(thm)],[])).
% 9.55/6.37 tff(434,plain,
% 9.55/6.37 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(I!11, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.55/6.37 inference(monotonicity,[status(thm)],[389])).
% 9.55/6.37 tff(435,plain,
% 9.55/6.37 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(I!11, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1))) <=> ((~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.55/6.37 inference(transitivity,[status(thm)],[434, 433])).
% 9.55/6.37 tff(436,plain,
% 9.55/6.37 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(I!11, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | ((~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1))))),
% 9.55/6.37 inference(monotonicity,[status(thm)],[435])).
% 9.55/6.37 tff(437,plain,
% 9.55/6.37 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(I!11, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.55/6.37 inference(transitivity,[status(thm)],[436, 432])).
% 9.55/6.37 tff(438,plain,
% 9.55/6.37 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$greatereq($sum(I!11, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.55/6.37 inference(quant_inst,[status(thm)],[])).
% 9.55/6.37 tff(439,plain,
% 9.55/6.37 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)) | (~$lesseq($sum(I!11, $product(-1, div2($sum(L!6, U!5)))), -1))),
% 9.55/6.37 inference(modus_ponens,[status(thm)],[438, 437])).
% 9.55/6.37 tff(440,plain,
% 9.55/6.37 ($false),
% 9.55/6.37 inference(unit_resolution,[status(thm)],[439, 366, 368, 431, 429])).
% 9.55/6.37 tff(441,plain,(((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))) | $greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 1)), inference(lemma,lemma(discharge,[]))).
% 9.55/6.38 tff(442,plain,
% 9.55/6.38 ($greatereq($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))), 1)),
% 9.55/6.38 inference(unit_resolution,[status(thm)],[441, 93])).
% 9.55/6.38 tff(443,plain,
% 9.55/6.38 ($false),
% 9.55/6.38 inference(unit_resolution,[status(thm)],[107, 106, 442])).
% 9.55/6.38 tff(444,plain,((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.38 tff(445,assumption,((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))), introduced(assumption)).
% 9.55/6.38 tff(446,assumption,(~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))))))))), introduced(assumption)).
% 9.55/6.38 tff(447,plain,
% 9.55/6.38 ($lesseq($sum(L!6, $product(-1, U!5)), 0)),
% 9.55/6.38 inference(unit_resolution,[status(thm)],[3, 446])).
% 9.55/6.38 tff(448,plain,
% 9.55/6.38 (((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))))))) | ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))))))),
% 9.55/6.38 inference(tautology,[status(thm)],[])).
% 9.55/6.38 tff(449,plain,
% 9.55/6.38 ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))))),
% 9.55/6.38 inference(unit_resolution,[status(thm)],[448, 446])).
% 9.55/6.38 tff(450,plain,
% 9.55/6.38 ((~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0)))))))))))))) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))))),
% 9.55/6.38 inference(tautology,[status(thm)],[])).
% 9.55/6.38 tff(451,plain,
% 9.55/6.38 ($false),
% 9.55/6.38 inference(unit_resolution,[status(thm)],[450, 449, 447, 445])).
% 9.55/6.38 tff(452,plain,(((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))))))) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))))), inference(lemma,lemma(discharge,[]))).
% 9.55/6.38 tff(453,plain,
% 9.55/6.38 ((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~((~($sum(M_2!7, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0) | (~((~($sum(M_2!7, $product(-1, L_4!8)) = -1)) | (~$lesseq($sum(L_4!8, $product(-1, I!9)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!9)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!9))) = 0)))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2!7))), 0)) | (~((~($sum(M_2!7, $product(-1, U_6!10)) = 1)) | (~$lesseq($sum(L!6, $product(-1, I!11)), 0)) | (~$greatereq($sum(U_6!10, $product(-1, I!11)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!11))) = 0))))))))))))))),
% 9.55/6.38 inference(unit_resolution,[status(thm)],[452, 444])).
% 9.55/6.38 tff(454,plain,
% 9.55/6.38 (~((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)))),
% 9.55/6.38 inference(unit_resolution,[status(thm)],[37, 453])).
% 9.55/6.38 tff(455,plain,
% 9.55/6.38 ($greatereq($sum(U!5, $product(-1, I!12)), 0)),
% 9.55/6.38 inference(unit_resolution,[status(thm)],[41, 454])).
% 9.55/6.38 tff(456,plain,
% 9.55/6.38 (~$lesseq($sum(length(A!4), $product(-1, U!5)), 0)),
% 9.55/6.38 inference(and_elim,[status(thm)],[35])).
% 9.55/6.38 tff(457,assumption,(~$greatereq($sum(length(A!4), $product(-1, I!12)), 1)), introduced(assumption)).
% 9.55/6.38 tff(458,plain,
% 9.55/6.38 ($false),
% 9.55/6.38 inference(theory_lemma,[status(thm)],[44, 457, 456])).
% 9.55/6.38 tff(459,plain,((~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | $greatereq($sum(length(A!4), $product(-1, I!12)), 1)), inference(lemma,lemma(discharge,[]))).
% 9.55/6.38 tff(460,plain,
% 9.55/6.38 ($greatereq($sum(length(A!4), $product(-1, I!12)), 1)),
% 9.55/6.38 inference(unit_resolution,[status(thm)],[459, 455])).
% 9.55/6.38 tff(461,plain,
% 9.55/6.38 (^[A: 'Array[Int,Int]', L: $int, U: $int] : refl((~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0)))))))) <=> (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0)))))))))),
% 9.55/6.38 inference(bind,[status(th)],[])).
% 9.55/6.38 tff(462,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0)))))))) <=> ![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))),
% 9.55/6.38 inference(quant_intro,[status(thm)],[461])).
% 9.55/6.38 tff(463,plain,
% 9.55/6.38 (^[A: 'Array[Int,Int]', L: $int, U: $int] : rewrite((~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0)))))))) <=> (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0)))))))))),
% 9.55/6.38 inference(bind,[status(th)],[])).
% 9.55/6.38 tff(464,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0)))))))) <=> ![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))),
% 9.55/6.38 inference(quant_intro,[status(thm)],[463])).
% 9.55/6.38 tff(465,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0)))))))) <=> ![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))),
% 9.55/6.38 inference(transitivity,[status(thm)],[464, 462])).
% 9.55/6.38 tff(466,plain,
% 9.55/6.38 (^[A: 'Array[Int,Int]', L: $int, U: $int] : trans(monotonicity(rewrite(((~sorted(A, L, U)) | ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0))) <=> ((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))), trans(monotonicity(rewrite((~((~($lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0) & (~$lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0)) & $greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0))) <=> (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))), ((sorted(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0) & (~$lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0)) & $greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0)))) <=> (sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))), rewrite((sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))) <=> (sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0)))))), ((sorted(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0) & (~$lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0)) & $greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0)))) <=> (sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, 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(~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0)))) & (sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0)))))))), rewrite((((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0)))) & (sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0)))))) <=> (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))), ((((~sorted(A, L, U)) | ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0))) & (sorted(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0) & (~$lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0)) & $greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0))))) <=> (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))))),
% 9.55/6.38 inference(bind,[status(th)],[])).
% 9.55/6.38 tff(467,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (((~sorted(A, L, U)) | ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0))) & (sorted(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0) & (~$lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0)) & $greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0))))) <=> ![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))),
% 9.55/6.38 inference(quant_intro,[status(thm)],[466])).
% 9.55/6.38 tff(468,plain,
% 9.55/6.38 (^[A: 'Array[Int,Int]', L: $int, U: $int] : rewrite((((~sorted(A, L, U)) | ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0))) & (sorted(A, L, U) | (~((~($greatereq($sum(tptp_fun_I_2(U, L, A), $product(-1, L)), 0) & (~$greatereq($sum(tptp_fun_I_2(U, L, A), $product(-1, tptp_fun_J_1(U, L, A))), 0)) & $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0))))) <=> (((~sorted(A, L, U)) | ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0))) & (sorted(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0) & (~$lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0)) & $greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0))))))),
% 9.55/6.38 inference(bind,[status(th)],[])).
% 9.55/6.38 tff(469,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (((~sorted(A, L, U)) | ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0))) & (sorted(A, L, U) | (~((~($greatereq($sum(tptp_fun_I_2(U, L, A), $product(-1, L)), 0) & (~$greatereq($sum(tptp_fun_I_2(U, L, A), $product(-1, tptp_fun_J_1(U, L, A))), 0)) & $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0))))) <=> ![A: 'Array[Int,Int]', L: $int, U: $int] : (((~sorted(A, L, U)) | ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0))) & (sorted(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0) & (~$lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0)) & $greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0)))))),
% 9.55/6.38 inference(quant_intro,[status(thm)],[468])).
% 9.55/6.38 tff(470,plain,
% 9.55/6.38 (^[A: 'Array[Int,Int]', L: $int, U: $int] : rewrite((sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, J))), 0))) <=> (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0))))),
% 9.55/6.38 inference(bind,[status(th)],[])).
% 9.55/6.38 tff(471,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, J))), 0))) <=> ![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0)))),
% 9.55/6.38 inference(quant_intro,[status(thm)],[470])).
% 9.55/6.38 tff(472,plain,
% 9.55/6.38 (^[A: 'Array[Int,Int]', L: $int, U: $int] : rewrite((sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq(L, I) & (~$lesseq(J, I)) & $lesseq(J, U))) | $lesseq(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), tptp_fun__select__Array_Int_Int__Int__Int_(A, J)))) <=> (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, J))), 0))))),
% 9.55/6.38 inference(bind,[status(th)],[])).
% 9.55/6.38 tff(473,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq(L, I) & (~$lesseq(J, I)) & $lesseq(J, U))) | $lesseq(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), tptp_fun__select__Array_Int_Int__Int__Int_(A, J)))) <=> ![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, J))), 0)))),
% 9.55/6.38 inference(quant_intro,[status(thm)],[472])).
% 9.55/6.38 tff(474,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq(L, I) & (~$lesseq(J, I)) & $lesseq(J, U))) | $lesseq(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), tptp_fun__select__Array_Int_Int__Int__Int_(A, J)))) <=> ![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq(L, I) & (~$lesseq(J, I)) & $lesseq(J, U))) | $lesseq(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), tptp_fun__select__Array_Int_Int__Int__Int_(A, J))))),
% 9.55/6.38 inference(rewrite,[status(thm)],[])).
% 9.55/6.38 tff(475,plain,
% 9.55/6.38 (^[A: 'Array[Int,Int]', L: $int, U: $int] : rewrite((sorted(A, L, U) <=> ![I: $int, J: $int] : ((($lesseq(L, I) & $less(I, J)) & $lesseq(J, U)) => $lesseq(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), tptp_fun__select__Array_Int_Int__Int__Int_(A, J)))) <=> (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq(L, I) & (~$lesseq(J, I)) & $lesseq(J, U))) | $lesseq(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), tptp_fun__select__Array_Int_Int__Int__Int_(A, J)))))),
% 9.55/6.38 inference(bind,[status(th)],[])).
% 9.55/6.38 tff(476,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((($lesseq(L, I) & $less(I, J)) & $lesseq(J, U)) => $lesseq(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), tptp_fun__select__Array_Int_Int__Int__Int_(A, J)))) <=> ![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq(L, I) & (~$lesseq(J, I)) & $lesseq(J, U))) | $lesseq(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), tptp_fun__select__Array_Int_Int__Int__Int_(A, J))))),
% 9.55/6.38 inference(quant_intro,[status(thm)],[475])).
% 9.55/6.38 tff(477,axiom,(![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((($lesseq(L, I) & $less(I, J)) & $lesseq(J, U)) => $lesseq(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), tptp_fun__select__Array_Int_Int__Int__Int_(A, J))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','formula_006')).
% 9.55/6.38 tff(478,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq(L, I) & (~$lesseq(J, I)) & $lesseq(J, U))) | $lesseq(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), tptp_fun__select__Array_Int_Int__Int__Int_(A, J))))),
% 9.55/6.38 inference(modus_ponens,[status(thm)],[477, 476])).
% 9.55/6.38 tff(479,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq(L, I) & (~$lesseq(J, I)) & $lesseq(J, U))) | $lesseq(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), tptp_fun__select__Array_Int_Int__Int__Int_(A, J))))),
% 9.55/6.38 inference(modus_ponens,[status(thm)],[478, 474])).
% 9.55/6.38 tff(480,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, I), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, J))), 0)))),
% 9.55/6.38 inference(modus_ponens,[status(thm)],[479, 473])).
% 9.55/6.38 tff(481,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (sorted(A, L, U) <=> ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0)))),
% 9.55/6.38 inference(modus_ponens,[status(thm)],[480, 471])).
% 9.55/6.38 tff(482,plain,(
% 9.55/6.38 ![A: 'Array[Int,Int]', L: $int, U: $int] : (((~sorted(A, L, U)) | ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0))) & (sorted(A, L, U) | (~((~($greatereq($sum(tptp_fun_I_2(U, L, A), $product(-1, L)), 0) & (~$greatereq($sum(tptp_fun_I_2(U, L, A), $product(-1, tptp_fun_J_1(U, L, A))), 0)) & $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0)))))),
% 9.55/6.38 inference(skolemize,[status(sab)],[481])).
% 9.55/6.38 tff(483,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (((~sorted(A, L, U)) | ![I: $int, J: $int] : ((~($greatereq($sum(I, $product(-1, L)), 0) & (~$greatereq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(J, $product(-1, U)), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0))) & (sorted(A, L, U) | (~((~($lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0) & (~$lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0)) & $greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0))) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0)))))),
% 9.55/6.38 inference(modus_ponens,[status(thm)],[482, 469])).
% 9.55/6.38 tff(484,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))),
% 9.55/6.38 inference(modus_ponens,[status(thm)],[483, 467])).
% 9.55/6.38 tff(485,plain,
% 9.55/6.38 (![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))),
% 9.55/6.38 inference(modus_ponens,[status(thm)],[484, 465])).
% 9.55/6.38 tff(486,plain,
% 9.55/6.38 (((~![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))) | (~((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum(length(A!4), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 1)) | (~$greatereq(tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4), 0))))))))) <=> ((~![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))) | (~((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum(length(A!4), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 1)) | (~$greatereq(tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4), 0)))))))))),
% 9.55/6.38 inference(rewrite,[status(thm)],[])).
% 9.55/6.38 tff(487,plain,
% 9.55/6.38 ((~((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq($sum(I, $product(-1, 0)), 0)) | (~$lesseq($sum(J, $product(-1, $sum(-1, length(A!4)))), 0))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum($sum(-1, length(A!4)), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 0)) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0)))))))) <=> (~((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum(length(A!4), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 1)) | (~$greatereq(tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4), 0))))))))),
% 9.55/6.38 inference(rewrite,[status(thm)],[])).
% 9.55/6.38 tff(488,plain,
% 9.55/6.38 (((~![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))) | (~((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq($sum(I, $product(-1, 0)), 0)) | (~$lesseq($sum(J, $product(-1, $sum(-1, length(A!4)))), 0))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum($sum(-1, length(A!4)), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 0)) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0))))))))) <=> ((~![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))) | (~((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum(length(A!4), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 1)) | (~$greatereq(tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4), 0)))))))))),
% 9.64/6.38 inference(monotonicity,[status(thm)],[487])).
% 9.64/6.38 tff(489,plain,
% 9.64/6.38 (((~![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))) | (~((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq($sum(I, $product(-1, 0)), 0)) | (~$lesseq($sum(J, $product(-1, $sum(-1, length(A!4)))), 0))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum($sum(-1, length(A!4)), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 0)) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0))))))))) <=> ((~![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))) | (~((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum(length(A!4), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 1)) | (~$greatereq(tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4), 0)))))))))),
% 9.64/6.38 inference(transitivity,[status(thm)],[488, 486])).
% 9.64/6.38 tff(490,plain,
% 9.64/6.38 ((~![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))) | (~((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq($sum(I, $product(-1, 0)), 0)) | (~$lesseq($sum(J, $product(-1, $sum(-1, length(A!4)))), 0))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum($sum(-1, length(A!4)), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 0)) | (~$lesseq($sum(0, $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0))))))))),
% 9.64/6.38 inference(quant_inst,[status(thm)],[])).
% 9.64/6.38 tff(491,plain,
% 9.64/6.38 ((~![A: 'Array[Int,Int]', L: $int, U: $int] : (~((~((~sorted(A, L, U)) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, I))), 0) | (~$greatereq($sum(I, $product(-1, L)), 0)) | (~$lesseq($sum(J, $product(-1, U)), 0))))) | (~(sorted(A, L, U) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_J_1(U, L, A)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A, tptp_fun_I_2(U, L, A)))), 0) | $lesseq($sum(tptp_fun_J_1(U, L, A), $product(-1, tptp_fun_I_2(U, L, A))), 0) | (~$greatereq($sum(U, $product(-1, tptp_fun_J_1(U, L, A))), 0)) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_2(U, L, A))), 0))))))))) | (~((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum(length(A!4), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 1)) | (~$greatereq(tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4), 0))))))))),
% 9.64/6.39 inference(modus_ponens,[status(thm)],[490, 489])).
% 9.64/6.39 tff(492,plain,
% 9.64/6.39 (~((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum(length(A!4), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 1)) | (~$greatereq(tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4), 0)))))))),
% 9.64/6.39 inference(unit_resolution,[status(thm)],[491, 485])).
% 9.64/6.39 tff(493,plain,
% 9.64/6.39 (((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1))))) | (~(sorted(A!4, 0, $sum(-1, length(A!4))) | (~($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4)), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4)))), 0) | $lesseq($sum(tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4), $product(-1, tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4))), 0) | (~$greatereq($sum(length(A!4), $product(-1, tptp_fun_J_1($sum(-1, length(A!4)), 0, A!4))), 1)) | (~$greatereq(tptp_fun_I_2($sum(-1, length(A!4)), 0, A!4), 0))))))) | ((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1))))),
% 9.64/6.39 inference(tautology,[status(thm)],[])).
% 9.64/6.39 tff(494,plain,
% 9.64/6.39 ((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))),
% 9.64/6.39 inference(unit_resolution,[status(thm)],[493, 492])).
% 9.64/6.39 tff(495,plain,
% 9.64/6.39 (sorted(A!4, 0, $sum(-1, length(A!4)))),
% 9.64/6.39 inference(and_elim,[status(thm)],[35])).
% 9.64/6.39 tff(496,plain,
% 9.64/6.39 ((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1))))) | (~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))),
% 9.64/6.39 inference(tautology,[status(thm)],[])).
% 9.64/6.39 tff(497,plain,
% 9.64/6.39 ((~((~sorted(A!4, 0, $sum(-1, length(A!4)))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1))))) | ![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))),
% 9.64/6.39 inference(unit_resolution,[status(thm)],[496, 495])).
% 9.64/6.39 tff(498,plain,
% 9.64/6.39 (![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))),
% 9.64/6.39 inference(unit_resolution,[status(thm)],[497, 494])).
% 9.64/6.39 tff(499,plain,
% 9.64/6.39 (((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | ((~$greatereq($sum(length(A!4), $product(-1, I!12)), 1)) | $lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))) <=> ((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | (~$greatereq($sum(length(A!4), $product(-1, I!12)), 1)) | $lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))),
% 9.64/6.39 inference(rewrite,[status(thm)],[])).
% 9.64/6.39 tff(500,plain,
% 9.64/6.39 (($lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | (~$greatereq($sum(length(A!4), $product(-1, I!12)), 1))) <=> ((~$greatereq($sum(length(A!4), $product(-1, I!12)), 1)) | $lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))),
% 9.64/6.39 inference(rewrite,[status(thm)],[])).
% 9.64/6.39 tff(501,plain,
% 9.64/6.39 ((~$lesseq($sum(I!12, $product(-1, length(A!4))), -1)) <=> (~$greatereq($sum(length(A!4), $product(-1, I!12)), 1))),
% 9.64/6.39 inference(rewrite,[status(thm)],[])).
% 9.64/6.39 tff(502,plain,
% 9.64/6.39 ($greatereq($sum($product(-1, I!12), div2($sum(L!6, U!5))), 0) <=> $lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.64/6.39 inference(rewrite,[status(thm)],[])).
% 9.64/6.39 tff(503,plain,
% 9.64/6.39 ($sum(div2($sum(L!6, U!5)), $product(-1, I!12)) = $sum($product(-1, I!12), div2($sum(L!6, U!5)))),
% 9.64/6.39 inference(rewrite,[status(thm)],[])).
% 9.64/6.39 tff(504,plain,
% 9.64/6.39 ($greatereq($sum(div2($sum(L!6, U!5)), $product(-1, I!12)), 0) <=> $greatereq($sum($product(-1, I!12), div2($sum(L!6, U!5))), 0)),
% 9.64/6.39 inference(monotonicity,[status(thm)],[503])).
% 9.64/6.39 tff(505,plain,
% 9.64/6.39 ($greatereq($sum(div2($sum(L!6, U!5)), $product(-1, I!12)), 0) <=> $lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.64/6.39 inference(transitivity,[status(thm)],[504, 502])).
% 9.64/6.39 tff(506,plain,
% 9.64/6.39 (($greatereq($sum(div2($sum(L!6, U!5)), $product(-1, I!12)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | (~$lesseq($sum(I!12, $product(-1, length(A!4))), -1))) <=> ($lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | (~$greatereq($sum(length(A!4), $product(-1, I!12)), 1)))),
% 9.64/6.39 inference(monotonicity,[status(thm)],[505, 501])).
% 9.64/6.39 tff(507,plain,
% 9.64/6.39 (($greatereq($sum(div2($sum(L!6, U!5)), $product(-1, I!12)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | (~$lesseq($sum(I!12, $product(-1, length(A!4))), -1))) <=> ((~$greatereq($sum(length(A!4), $product(-1, I!12)), 1)) | $lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))),
% 9.64/6.39 inference(transitivity,[status(thm)],[506, 500])).
% 9.64/6.39 tff(508,plain,
% 9.64/6.39 (((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | ($greatereq($sum(div2($sum(L!6, U!5)), $product(-1, I!12)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | (~$lesseq($sum(I!12, $product(-1, length(A!4))), -1)))) <=> ((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | ((~$greatereq($sum(length(A!4), $product(-1, I!12)), 1)) | $lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)))),
% 9.64/6.39 inference(monotonicity,[status(thm)],[507])).
% 9.64/6.39 tff(509,plain,
% 9.64/6.39 (((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | ($greatereq($sum(div2($sum(L!6, U!5)), $product(-1, I!12)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | (~$lesseq($sum(I!12, $product(-1, length(A!4))), -1)))) <=> ((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | (~$greatereq($sum(length(A!4), $product(-1, I!12)), 1)) | $lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))),
% 9.64/6.39 inference(transitivity,[status(thm)],[508, 499])).
% 9.64/6.39 tff(510,plain,
% 9.64/6.39 ((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | ($greatereq($sum(div2($sum(L!6, U!5)), $product(-1, I!12)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$greatereq(div2($sum(L!6, U!5)), 0)) | (~$lesseq($sum(I!12, $product(-1, length(A!4))), -1)))),
% 9.64/6.39 inference(quant_inst,[status(thm)],[])).
% 9.64/6.39 tff(511,plain,
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% 9.64/6.39 inference(modus_ponens,[status(thm)],[510, 509])).
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% 9.64/6.39 inference(unit_resolution,[status(thm)],[511, 498, 460, 92])).
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% 9.64/6.39 inference(unit_resolution,[status(thm)],[512, 1])).
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% 9.64/6.39 inference(tautology,[status(thm)],[])).
% 9.64/6.39 tff(515,plain,
% 9.64/6.39 ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0),
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% 9.64/6.39 inference(theory_lemma,[status(thm)],[])).
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% 9.64/6.39 inference(rewrite,[status(thm)],[])).
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% 9.64/6.39 inference(rewrite,[status(thm)],[])).
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% 9.64/6.39 ((~$lesseq($sum(I!12, $product(-1, U!5)), 0)) <=> (~$greatereq($sum(U!5, $product(-1, I!12)), 0))),
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% 9.64/6.39 inference(monotonicity,[status(thm)],[530, 529])).
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% 9.64/6.39 inference(transitivity,[status(thm)],[531, 528])).
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% 9.64/6.39 inference(monotonicity,[status(thm)],[532])).
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% 9.64/6.39 inference(transitivity,[status(thm)],[533, 527])).
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% 9.64/6.39 inference(quant_inst,[status(thm)],[])).
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% 9.64/6.39 inference(modus_ponens,[status(thm)],[535, 534])).
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% 9.64/6.39 tff(539,plain,
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% 9.64/6.39 inference(unit_resolution,[status(thm)],[538, 515, 455, 525])).
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% 9.64/6.39 inference(unit_resolution,[status(thm)],[205, 540])).
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% 9.64/6.39 inference(unit_resolution,[status(thm)],[182, 542])).
% 9.64/6.39 tff(548,plain,
% 9.64/6.39 ((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))),
% 9.64/6.39 inference(unit_resolution,[status(thm)],[161, 547])).
% 9.64/6.39 tff(549,plain,
% 9.64/6.39 (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))),
% 9.64/6.39 inference(unit_resolution,[status(thm)],[548, 546])).
% 9.64/6.39 tff(550,plain,
% 9.64/6.39 (![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))),
% 9.64/6.39 inference(unit_resolution,[status(thm)],[163, 549])).
% 9.64/6.39 tff(551,assumption,(~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))), introduced(assumption)).
% 9.64/6.39 tff(552,plain,
% 9.64/6.39 (((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))) <=> ((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1))))),
% 9.64/6.39 inference(rewrite,[status(thm)],[])).
% 9.64/6.39 tff(553,plain,
% 9.64/6.39 (($false | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))) <=> ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.39 inference(rewrite,[status(thm)],[])).
% 9.64/6.39 tff(554,plain,
% 9.64/6.39 (^[I: $int] : trans(monotonicity(rewrite((~$lesseq($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)) <=> (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1))), (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1))))), rewrite(((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))), (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))))),
% 9.64/6.39 inference(bind,[status(th)],[])).
% 9.64/6.39 tff(555,plain,
% 9.64/6.39 (![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0))) <=> ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.39 inference(quant_intro,[status(thm)],[554])).
% 9.64/6.39 tff(556,plain,
% 9.64/6.39 ((1 = 1) <=> $true),
% 9.64/6.39 inference(rewrite,[status(thm)],[])).
% 9.64/6.39 tff(557,plain,
% 9.64/6.39 ($sum($sum(1, div2($sum(L!6, U!5))), $product(-1, div2($sum(L!6, U!5)))) = 1),
% 9.64/6.39 inference(rewrite,[status(thm)],[])).
% 9.64/6.39 tff(558,plain,
% 9.64/6.39 ($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))) = $sum(1, div2($sum(L!6, U!5)))),
% 9.64/6.39 inference(rewrite,[status(thm)],[])).
% 9.64/6.39 tff(559,plain,
% 9.64/6.39 ($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = $sum($sum(1, div2($sum(L!6, U!5))), $product(-1, div2($sum(L!6, U!5))))),
% 9.64/6.39 inference(monotonicity,[status(thm)],[558])).
% 9.64/6.39 tff(560,plain,
% 9.64/6.39 ($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 1),
% 9.64/6.39 inference(transitivity,[status(thm)],[559, 557])).
% 9.64/6.39 tff(561,plain,
% 9.64/6.39 (($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 1) <=> (1 = 1)),
% 9.64/6.39 inference(monotonicity,[status(thm)],[560])).
% 9.64/6.39 tff(562,plain,
% 9.64/6.39 (($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 1) <=> $true),
% 9.64/6.39 inference(transitivity,[status(thm)],[561, 556])).
% 9.64/6.39 tff(563,plain,
% 9.64/6.39 ((~($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 1)) <=> (~$true)),
% 9.64/6.39 inference(monotonicity,[status(thm)],[562])).
% 9.64/6.39 tff(564,plain,
% 9.64/6.39 ((~($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 1)) <=> $false),
% 9.64/6.39 inference(transitivity,[status(thm)],[563, 187])).
% 9.64/6.39 tff(565,plain,
% 9.64/6.39 (((~($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)))) <=> ($false | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1))))),
% 9.64/6.39 inference(monotonicity,[status(thm)],[564, 555])).
% 9.64/6.39 tff(566,plain,
% 9.64/6.39 (((~($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0)))) <=> ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.39 inference(transitivity,[status(thm)],[565, 553])).
% 9.64/6.39 tff(567,plain,
% 9.64/6.39 (((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ((~($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0))))) <=> ((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1))))),
% 9.64/6.39 inference(monotonicity,[status(thm)],[566])).
% 9.64/6.39 tff(568,plain,
% 9.64/6.39 (((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ((~($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0))))) <=> ((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1))))),
% 9.64/6.39 inference(transitivity,[status(thm)],[567, 552])).
% 9.64/6.39 tff(569,plain,
% 9.64/6.39 ((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ((~($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum($sum(1, $product(-1, $product(-1, div2($sum(L!6, U!5))))), $product(-1, I)), 0))))),
% 9.64/6.39 inference(quant_inst,[status(thm)],[])).
% 9.64/6.39 tff(570,plain,
% 9.64/6.39 ((~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.39 inference(modus_ponens,[status(thm)],[569, 568])).
% 9.64/6.39 tff(571,plain,
% 9.64/6.39 ($false),
% 9.64/6.39 inference(unit_resolution,[status(thm)],[570, 170, 551])).
% 9.64/6.39 tff(572,plain,(![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1))) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0)))))), inference(lemma,lemma(discharge,[]))).
% 9.64/6.39 tff(573,plain,
% 9.64/6.39 (![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[572, 550])).
% 9.64/6.40 tff(574,plain,
% 9.64/6.40 ($greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1) | $lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.64/6.40 inference(theory_lemma,[status(thm)],[])).
% 9.64/6.40 tff(575,plain,
% 9.64/6.40 ($greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1)),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[574, 1])).
% 9.64/6.40 tff(576,plain,
% 9.64/6.40 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))) | ((~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.40 inference(rewrite,[status(thm)],[])).
% 9.64/6.40 tff(577,plain,
% 9.64/6.40 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1))) <=> ((~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.40 inference(rewrite,[status(thm)],[])).
% 9.64/6.40 tff(578,plain,
% 9.64/6.40 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, U!5)), 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.40 inference(monotonicity,[status(thm)],[529])).
% 9.64/6.40 tff(579,plain,
% 9.64/6.40 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, U!5)), 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1))) <=> ((~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.40 inference(transitivity,[status(thm)],[578, 577])).
% 9.64/6.40 tff(580,plain,
% 9.64/6.40 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, U!5)), 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))) | ((~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1))))),
% 9.64/6.40 inference(monotonicity,[status(thm)],[579])).
% 9.64/6.40 tff(581,plain,
% 9.64/6.40 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, U!5)), 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.40 inference(transitivity,[status(thm)],[580, 576])).
% 9.64/6.40 tff(582,plain,
% 9.64/6.40 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, U!5)), 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.40 inference(quant_inst,[status(thm)],[])).
% 9.64/6.40 tff(583,plain,
% 9.64/6.40 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$greatereq($sum(I, $product(-1, div2($sum(L!6, U!5)))), 1)))) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 1))),
% 9.64/6.40 inference(modus_ponens,[status(thm)],[582, 581])).
% 9.64/6.40 tff(584,plain,
% 9.64/6.40 ($false),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[583, 455, 515, 575, 573])).
% 9.64/6.40 tff(585,plain,($lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)), inference(lemma,lemma(discharge,[]))).
% 9.64/6.40 tff(586,assumption,(~((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)))), introduced(assumption)).
% 9.64/6.40 tff(587,plain,
% 9.64/6.40 ($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[514, 586])).
% 9.64/6.40 tff(588,plain,
% 9.64/6.40 ((($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, I!12)) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))) | (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, I!12)) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0)))))))))) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))),
% 9.64/6.40 inference(tautology,[status(thm)],[])).
% 9.64/6.40 tff(589,plain,
% 9.64/6.40 (($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, I!12)) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))) | (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, I!12)) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0)))))))))),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[588, 587])).
% 9.64/6.40 tff(590,assumption,($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0), introduced(assumption)).
% 9.64/6.40 tff(591,plain,
% 9.64/6.40 ((~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)) | $greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.64/6.40 inference(theory_lemma,[status(thm)],[])).
% 9.64/6.40 tff(592,plain,
% 9.64/6.40 ($greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[591, 590])).
% 9.64/6.40 tff(593,plain,
% 9.64/6.40 ((~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$lesseq($sum(L!6, $product(-1, div2($sum(L!6, U!5)))), 0)) | $lesseq($sum(L!6, $product(-1, I!12)), 0)),
% 9.64/6.40 inference(theory_lemma,[status(thm)],[])).
% 9.64/6.40 tff(594,plain,
% 9.64/6.40 ((~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)) | $lesseq($sum(L!6, $product(-1, I!12)), 0)),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[593, 88])).
% 9.64/6.40 tff(595,plain,
% 9.64/6.40 ($lesseq($sum(L!6, $product(-1, I!12)), 0)),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[594, 592])).
% 9.64/6.40 tff(596,plain,
% 9.64/6.40 ($greatereq($sum(U!5, $product(-1, I!12)), 0)),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[41, 586])).
% 9.64/6.40 tff(597,plain,
% 9.64/6.40 (~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)))),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[538, 587, 596, 595])).
% 9.64/6.40 tff(598,plain,
% 9.64/6.40 (~((~$lesseq($sum(L!6, $product(-1, U!5)), 0)) | (~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))))),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[221, 597])).
% 9.64/6.40 tff(599,plain,
% 9.64/6.40 (![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[205, 598])).
% 9.64/6.40 tff(600,plain,
% 9.64/6.40 (((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | ((~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, I!12)) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))) | (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, I!12)) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))))))))) <=> ((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | (~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, I!12)) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))) | (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, I!12)) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))))))))),
% 9.64/6.40 inference(rewrite,[status(thm)],[])).
% 9.64/6.40 tff(601,plain,
% 9.64/6.40 (((~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(I!12, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(I!12, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)))))))))))) <=> ((~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, I!12)) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))) | (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, I!12)) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))))))))),
% 9.64/6.40 inference(rewrite,[status(thm)],[])).
% 9.64/6.40 tff(602,plain,
% 9.64/6.40 (((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | ((~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(I!12, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(I!12, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) <=> ((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | ((~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, I!12)) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))) | (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, I!12)) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0)))))))))))))),
% 9.64/6.40 inference(monotonicity,[status(thm)],[601])).
% 9.64/6.40 tff(603,plain,
% 9.64/6.40 (((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | ((~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(I!12, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(I!12, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) <=> ((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | (~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, I!12)) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))) | (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, I!12)) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))))))))),
% 9.64/6.40 inference(transitivity,[status(thm)],[602, 600])).
% 9.64/6.40 tff(604,plain,
% 9.64/6.40 ((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | ((~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(I!12, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(I!12, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))),
% 9.64/6.40 inference(quant_inst,[status(thm)],[])).
% 9.64/6.40 tff(605,plain,
% 9.64/6.40 ((~![M_2: $int] : ((~($sum(M_2, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))) = 0) | (~((~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0) | (~![L_4: $int] : ((~($sum(M_2, $product(-1, L_4)) = -1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0))))))) | (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, M_2))), 0)) | (~![U_6: $int] : ((~($sum(M_2, $product(-1, U_6)) = 1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))))))))) | (~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)) | (~(($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0) | (~((~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, I!12)) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))) | (~($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, I!12)) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0)))))))))))),
% 9.64/6.40 inference(modus_ponens,[status(thm)],[604, 603])).
% 9.64/6.40 tff(606,plain,
% 9.64/6.40 ($false),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[605, 599, 590, 589])).
% 9.64/6.40 tff(607,plain,(((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq($sum(U!5, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0))) | (~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0))), inference(lemma,lemma(discharge,[]))).
% 9.64/6.40 tff(608,plain,
% 9.64/6.40 (~($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0)),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[607, 454])).
% 9.64/6.40 tff(609,plain,
% 9.64/6.40 (($sum(I!12, $product(-1, div2($sum(L!6, U!5)))) = 0) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0))),
% 9.64/6.40 inference(theory_lemma,[status(thm)],[])).
% 9.64/6.40 tff(610,plain,
% 9.64/6.40 ((~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)) | (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0))),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[609, 608])).
% 9.64/6.40 tff(611,plain,
% 9.64/6.40 (~$greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[610, 585])).
% 9.64/6.40 tff(612,plain,
% 9.64/6.40 ($greatereq(I!12, 0) | (~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$greatereq(L!6, 0))),
% 9.64/6.40 inference(theory_lemma,[status(thm)],[])).
% 9.64/6.40 tff(613,plain,
% 9.64/6.40 ($greatereq(I!12, 0) | (~$lesseq($sum(L!6, $product(-1, I!12)), 0))),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[612, 89])).
% 9.64/6.40 tff(614,plain,
% 9.64/6.40 ($greatereq(I!12, 0)),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[613, 525])).
% 9.64/6.40 tff(615,assumption,($lesseq($sum(L!6, $product(-1, U!5)), 0)), introduced(assumption)).
% 9.64/6.40 tff(616,assumption,(~$greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1)), introduced(assumption)).
% 9.64/6.40 tff(617,plain,
% 9.64/6.40 ($false),
% 9.64/6.40 inference(theory_lemma,[status(thm)],[250, 616, 456, 615])).
% 9.64/6.40 tff(618,plain,($greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1) | (~$lesseq($sum(L!6, $product(-1, U!5)), 0))), inference(lemma,lemma(discharge,[]))).
% 9.64/6.40 tff(619,plain,
% 9.64/6.40 ($greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1)),
% 9.64/6.40 inference(unit_resolution,[status(thm)],[618, 48])).
% 9.64/6.40 tff(620,plain,
% 9.64/6.40 (((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | ((~$greatereq(I!12, 0)) | $greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1)) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))) <=> ((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | (~$greatereq(I!12, 0)) | $greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1)) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))),
% 9.64/6.40 inference(rewrite,[status(thm)],[])).
% 9.64/6.40 tff(621,plain,
% 9.64/6.40 (($greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$greatereq(I!12, 0)) | (~$greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1))) <=> ((~$greatereq(I!12, 0)) | $greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1)) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))),
% 9.64/6.40 inference(rewrite,[status(thm)],[])).
% 9.64/6.40 tff(622,plain,
% 9.64/6.40 ((~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, length(A!4))), -1)) <=> (~$greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1))),
% 9.64/6.40 inference(rewrite,[status(thm)],[])).
% 9.64/6.40 tff(623,plain,
% 9.64/6.40 ($greatereq($sum($product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12)), tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5)))), 0) <=> $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.64/6.40 inference(rewrite,[status(thm)],[])).
% 9.64/6.40 tff(624,plain,
% 9.64/6.40 ($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = $sum($product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12)), tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))),
% 9.64/6.40 inference(rewrite,[status(thm)],[])).
% 9.64/6.40 tff(625,plain,
% 9.64/6.40 ($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) <=> $greatereq($sum($product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12)), tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5)))), 0)),
% 9.64/6.40 inference(monotonicity,[status(thm)],[624])).
% 9.64/6.40 tff(626,plain,
% 9.64/6.40 ($greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) <=> $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.64/6.40 inference(transitivity,[status(thm)],[625, 623])).
% 9.64/6.40 tff(627,plain,
% 9.64/6.40 (($greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~$greatereq(I!12, 0)) | (~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, length(A!4))), -1))) <=> ($greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$greatereq(I!12, 0)) | (~$greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1)))),
% 9.64/6.40 inference(monotonicity,[status(thm)],[626, 622])).
% 9.64/6.40 tff(628,plain,
% 9.64/6.40 (($greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~$greatereq(I!12, 0)) | (~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, length(A!4))), -1))) <=> ((~$greatereq(I!12, 0)) | $greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1)) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))),
% 9.64/6.40 inference(transitivity,[status(thm)],[627, 621])).
% 9.64/6.40 tff(629,plain,
% 9.64/6.40 (((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | ($greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~$greatereq(I!12, 0)) | (~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, length(A!4))), -1)))) <=> ((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | ((~$greatereq(I!12, 0)) | $greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1)) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)))),
% 9.64/6.40 inference(monotonicity,[status(thm)],[628])).
% 9.64/6.40 tff(630,plain,
% 9.64/6.40 (((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | ($greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~$greatereq(I!12, 0)) | (~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, length(A!4))), -1)))) <=> ((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | (~$greatereq(I!12, 0)) | $greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1)) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))),
% 9.64/6.41 inference(transitivity,[status(thm)],[629, 620])).
% 9.64/6.41 tff(631,plain,
% 9.64/6.41 ((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | ($greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0) | (~$greatereq(I!12, 0)) | (~$lesseq($sum(div2($sum(L!6, U!5)), $product(-1, length(A!4))), -1)))),
% 9.64/6.41 inference(quant_inst,[status(thm)],[])).
% 9.64/6.41 tff(632,plain,
% 9.64/6.41 ((~![I: $int, J: $int] : ($greatereq($sum(I, $product(-1, J)), 0) | $greatereq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, J), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))), 0) | (~$greatereq(I, 0)) | (~$lesseq($sum(J, $product(-1, length(A!4))), -1)))) | (~$greatereq(I!12, 0)) | $greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | (~$greatereq($sum(length(A!4), $product(-1, div2($sum(L!6, U!5)))), 1)) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.64/6.41 inference(modus_ponens,[status(thm)],[631, 630])).
% 9.64/6.41 tff(633,plain,
% 9.64/6.41 ($greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0) | $lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.64/6.41 inference(unit_resolution,[status(thm)],[632, 498, 619, 614])).
% 9.64/6.41 tff(634,plain,
% 9.64/6.41 ($lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.64/6.41 inference(unit_resolution,[status(thm)],[633, 611])).
% 9.64/6.41 tff(635,plain,
% 9.64/6.41 ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | $lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)),
% 9.64/6.41 inference(theory_lemma,[status(thm)],[])).
% 9.64/6.41 tff(636,plain,
% 9.64/6.41 ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)),
% 9.64/6.41 inference(unit_resolution,[status(thm)],[635, 515])).
% 9.64/6.41 tff(637,plain,
% 9.64/6.41 ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))), 0)) | (~$lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))),
% 9.64/6.41 inference(theory_lemma,[status(thm)],[])).
% 9.64/6.41 tff(638,plain,
% 9.64/6.41 ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~$lesseq($sum(tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12), $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0))),
% 9.64/6.41 inference(unit_resolution,[status(thm)],[637, 636])).
% 9.64/6.41 tff(639,plain,
% 9.64/6.41 ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)),
% 9.64/6.41 inference(unit_resolution,[status(thm)],[638, 634])).
% 9.64/6.41 tff(640,plain,
% 9.64/6.41 ($lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0) | (~![L_4: $int] : ((~($sum(L_4, $product(-1, div2($sum(L!6, U!5)))) = 1)) | ![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$lesseq($sum(I, $product(-1, U!5)), 0)) | (~$lesseq($sum(L_4, $product(-1, I)), 0)))))),
% 9.64/6.41 inference(unit_resolution,[status(thm)],[246, 639])).
% 9.64/6.41 tff(641,plain,
% 9.64/6.41 (~((~$lesseq($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, div2($sum(L!6, U!5))))), 0)) | (~![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))))),
% 9.64/6.41 inference(unit_resolution,[status(thm)],[548, 640])).
% 9.64/6.41 tff(642,plain,
% 9.64/6.41 (![U_6: $int] : ((~($sum(U_6, $product(-1, div2($sum(L!6, U!5)))) = -1)) | ![I: $int] : ((~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$greatereq($sum(U_6, $product(-1, I)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0))))),
% 9.64/6.41 inference(unit_resolution,[status(thm)],[404, 641])).
% 9.64/6.41 tff(643,plain,
% 9.64/6.41 (![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.64/6.41 inference(unit_resolution,[status(thm)],[428, 642])).
% 9.64/6.41 tff(644,plain,
% 9.64/6.41 ($lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1) | $greatereq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), 0)),
% 9.64/6.41 inference(theory_lemma,[status(thm)],[])).
% 9.64/6.41 tff(645,plain,
% 9.64/6.41 ($lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1)),
% 9.64/6.41 inference(unit_resolution,[status(thm)],[644, 611])).
% 9.64/6.41 tff(646,plain,
% 9.64/6.41 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | ((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | (~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.64/6.41 inference(rewrite,[status(thm)],[])).
% 9.64/6.41 tff(647,plain,
% 9.64/6.41 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1))) <=> ((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.64/6.41 inference(rewrite,[status(thm)],[])).
% 9.64/6.41 tff(648,plain,
% 9.64/6.41 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1))) <=> ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.64/6.41 inference(monotonicity,[status(thm)],[530])).
% 9.64/6.41 tff(649,plain,
% 9.64/6.41 (((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1))) <=> ((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.64/6.41 inference(transitivity,[status(thm)],[648, 647])).
% 9.64/6.41 tff(650,plain,
% 9.64/6.41 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | ((~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1))))),
% 9.64/6.41 inference(monotonicity,[status(thm)],[649])).
% 9.64/6.41 tff(651,plain,
% 9.64/6.41 (((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1)))) <=> ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | (~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.64/6.41 inference(transitivity,[status(thm)],[650, 646])).
% 9.64/6.41 tff(652,plain,
% 9.64/6.41 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$greatereq($sum(I!12, $product(-1, L!6)), 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1)))),
% 9.64/6.41 inference(quant_inst,[status(thm)],[])).
% 9.64/6.41 tff(653,plain,
% 9.64/6.41 ((~![I: $int] : ((~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I))) = 0)) | (~$greatereq($sum(I, $product(-1, L!6)), 0)) | (~$lesseq($sum(I, $product(-1, div2($sum(L!6, U!5)))), -1)))) | (~$lesseq($sum(L!6, $product(-1, I!12)), 0)) | (~($sum(E!3, $product(-1, tptp_fun__select__Array_Int_Int__Int__Int_(A!4, I!12))) = 0)) | (~$lesseq($sum(I!12, $product(-1, div2($sum(L!6, U!5)))), -1))),
% 9.64/6.41 inference(modus_ponens,[status(thm)],[652, 651])).
% 9.64/6.41 tff(654,plain,
% 9.64/6.41 ($false),
% 9.64/6.41 inference(unit_resolution,[status(thm)],[653, 525, 515, 645, 643])).
% 9.64/6.41 % SZS output end Proof
%------------------------------------------------------------------------------