TSTP Solution File: SWW616_2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW616_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:27 EDT 2022
% Result : Theorem 5.18s 3.55s
% Output : Proof 5.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW616_2 : TPTP v8.1.0. Released v6.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 20:28:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 5.18/3.55 % SZS status Theorem
% 5.18/3.55 % SZS output start Proof
% 5.18/3.55 tff(tptp_fun_Lqt_16_type, type, (
% 5.18/3.55 tptp_fun_Lqt_16: $int)).
% 5.18/3.55 tff(div_type, type, (
% 5.18/3.55 div: ( $int * $int ) > $int)).
% 5.18/3.55 tff(tptp_fun_H_5_type, type, (
% 5.18/3.55 tptp_fun_H_5: $int)).
% 5.18/3.55 tff(tptp_fun_L_6_type, type, (
% 5.18/3.55 tptp_fun_L_6: $int)).
% 5.18/3.55 tff(tptp_fun_Hqt_15_type, type, (
% 5.18/3.55 tptp_fun_Hqt_15: $int)).
% 5.18/3.55 tff(sum_type, type, (
% 5.18/3.55 sum: ( map_int_int * $int * $int ) > $int)).
% 5.18/3.55 tff(tptp_fun_A1_7_type, type, (
% 5.18/3.55 tptp_fun_A1_7: map_int_int)).
% 5.18/3.55 tff(tptp_fun_Ms_12_type, type, (
% 5.18/3.55 tptp_fun_Ms_12: $int)).
% 5.18/3.55 tff(tptp_fun_S_13_type, type, (
% 5.18/3.55 tptp_fun_S_13: $int)).
% 5.18/3.55 tff(tptp_fun_Hi_10_type, type, (
% 5.18/3.55 tptp_fun_Hi_10: $int)).
% 5.18/3.55 tff(tptp_fun_Lo1_11_type, type, (
% 5.18/3.55 tptp_fun_Lo1_11: $int)).
% 5.18/3.55 tff(tptp_fun_S1_14_type, type, (
% 5.18/3.55 tptp_fun_S1_14: $int)).
% 5.18/3.55 tff(tptp_fun_Lo_9_type, type, (
% 5.18/3.55 tptp_fun_Lo_9: $int)).
% 5.18/3.55 tff(tptp_fun_A_8_type, type, (
% 5.18/3.55 tptp_fun_A_8: $int)).
% 5.18/3.55 tff(tb2t_type, type, (
% 5.18/3.55 tb2t: uni > $int)).
% 5.18/3.55 tff(t2tb_type, type, (
% 5.18/3.55 t2tb: $int > uni)).
% 5.18/3.55 tff(1,plain,
% 5.18/3.55 ((($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $greatereq($sum(A!8, $product(-1, H!5)), 0)) & (~($sum(L!6, $product(-1, H!5)) = 0)) & (($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0) & $greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))) <=> ($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $greatereq($sum(A!8, $product(-1, H!5)), 0) & (~($sum(L!6, $product(-1, H!5)) = 0)) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0) & $greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))),
% 5.18/3.55 inference(rewrite,[status(thm)],[])).
% 5.18/3.55 tff(2,plain,
% 5.18/3.55 ((($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0) & ($greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))) <=> (($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0) & $greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))),
% 5.18/3.55 inference(rewrite,[status(thm)],[])).
% 5.18/3.55 tff(3,plain,
% 5.18/3.55 (($greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))) <=> ($greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))),
% 5.18/3.55 inference(rewrite,[status(thm)],[])).
% 5.18/3.55 tff(4,plain,
% 5.18/3.55 ((![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ((~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0)) & ($lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))) <=> (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))),
% 5.18/3.55 inference(rewrite,[status(thm)],[])).
% 5.18/3.55 tff(5,plain,
% 5.18/3.55 (($greatereq($sum(Lo1!11, $product(-1, L!6)), 0) & $lesseq($sum(Lo1!11, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & ($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))) = 0)) <=> ($lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))),
% 5.18/3.55 inference(rewrite,[status(thm)],[])).
% 5.18/3.55 tff(6,plain,
% 5.18/3.55 (((~((~($greatereq($sum(Lqt!16, $product(-1, L!6)), 0) & $lesseq($sum(Lqt!16, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $greatereq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $lesseq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, Ms!12)), 0))) & (~(~$greatereq($sum(H!5, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 1))) & (~(~($sum(Ms!12, $product(-1, S1!14)) = 0)))) <=> ((~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0))),
% 5.18/3.56 inference(rewrite,[status(thm)],[])).
% 5.18/3.56 tff(7,plain,
% 5.18/3.56 (^[Lqt: $int] : rewrite(((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) <=> ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)))),
% 5.18/3.56 inference(bind,[status(th)],[])).
% 5.18/3.56 tff(8,plain,
% 5.18/3.56 (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) <=> ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0))),
% 5.18/3.56 inference(quant_intro,[status(thm)],[7])).
% 5.18/3.56 tff(9,plain,
% 5.18/3.56 ((![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ((~((~($greatereq($sum(Lqt!16, $product(-1, L!6)), 0) & $lesseq($sum(Lqt!16, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $greatereq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $lesseq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, Ms!12)), 0))) & (~(~$greatereq($sum(H!5, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 1))) & (~(~($sum(Ms!12, $product(-1, S1!14)) = 0)))) & ($greatereq($sum(Lo1!11, $product(-1, L!6)), 0) & $lesseq($sum(Lo1!11, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & ($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))) = 0))) <=> (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ((~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0)) & ($lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0)))),
% 5.18/3.56 inference(monotonicity,[status(thm)],[8, 6, 5])).
% 5.18/3.56 tff(10,plain,
% 5.18/3.56 ((![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ((~((~($greatereq($sum(Lqt!16, $product(-1, L!6)), 0) & $lesseq($sum(Lqt!16, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $greatereq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $lesseq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, Ms!12)), 0))) & (~(~$greatereq($sum(H!5, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 1))) & (~(~($sum(Ms!12, $product(-1, S1!14)) = 0)))) & ($greatereq($sum(Lo1!11, $product(-1, L!6)), 0) & $lesseq($sum(Lo1!11, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & ($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))) = 0))) <=> (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))),
% 5.18/3.56 inference(transitivity,[status(thm)],[9, 4])).
% 5.18/3.56 tff(11,plain,
% 5.18/3.56 ((~(~($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0))) <=> ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0)),
% 5.18/3.56 inference(rewrite,[status(thm)],[])).
% 5.18/3.56 tff(12,plain,
% 5.18/3.56 ((~($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0)) <=> (~($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0))),
% 5.18/3.56 inference(rewrite,[status(thm)],[])).
% 5.18/3.56 tff(13,plain,
% 5.18/3.56 ((~(~($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0))) <=> (~(~($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0)))),
% 5.18/3.56 inference(monotonicity,[status(thm)],[12])).
% 5.18/3.56 tff(14,plain,
% 5.18/3.56 ((~(~($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0))) <=> ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0)),
% 5.18/3.56 inference(transitivity,[status(thm)],[13, 11])).
% 5.18/3.56 tff(15,plain,
% 5.18/3.56 ((~(~$greatereq(div($sum($product(-1, L!6), H!5), 2), 1))) <=> $greatereq(div($sum($product(-1, L!6), H!5), 2), 1)),
% 5.18/3.56 inference(rewrite,[status(thm)],[])).
% 5.18/3.56 tff(16,plain,
% 5.18/3.56 ((~$greatereq(div($sum(H!5, $product(-1, L!6)), 2), 1)) <=> (~$greatereq(div($sum($product(-1, L!6), H!5), 2), 1))),
% 5.18/3.56 inference(rewrite,[status(thm)],[])).
% 5.18/3.56 tff(17,plain,
% 5.18/3.56 ((~(~$greatereq(div($sum(H!5, $product(-1, L!6)), 2), 1))) <=> (~(~$greatereq(div($sum($product(-1, L!6), H!5), 2), 1)))),
% 5.18/3.56 inference(monotonicity,[status(thm)],[16])).
% 5.18/3.56 tff(18,plain,
% 5.18/3.56 ((~(~$greatereq(div($sum(H!5, $product(-1, L!6)), 2), 1))) <=> $greatereq(div($sum($product(-1, L!6), H!5), 2), 1)),
% 5.18/3.56 inference(transitivity,[status(thm)],[17, 15])).
% 5.18/3.56 tff(19,plain,
% 5.18/3.56 (((~(~$greatereq(div($sum(H!5, $product(-1, L!6)), 2), 1))) & (~(~($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0))) & (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ((~((~($greatereq($sum(Lqt!16, $product(-1, L!6)), 0) & $lesseq($sum(Lqt!16, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $greatereq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $lesseq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, Ms!12)), 0))) & (~(~$greatereq($sum(H!5, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 1))) & (~(~($sum(Ms!12, $product(-1, S1!14)) = 0)))) & ($greatereq($sum(Lo1!11, $product(-1, L!6)), 0) & $lesseq($sum(Lo1!11, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & ($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))) = 0)))) <=> ($greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0)))),
% 5.18/3.56 inference(monotonicity,[status(thm)],[18, 14, 10])).
% 5.18/3.56 tff(20,plain,
% 5.18/3.56 (((~(~$greatereq(div($sum(H!5, $product(-1, L!6)), 2), 1))) & (~(~($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0))) & (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ((~((~($greatereq($sum(Lqt!16, $product(-1, L!6)), 0) & $lesseq($sum(Lqt!16, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $greatereq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $lesseq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, Ms!12)), 0))) & (~(~$greatereq($sum(H!5, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 1))) & (~(~($sum(Ms!12, $product(-1, S1!14)) = 0)))) & ($greatereq($sum(Lo1!11, $product(-1, L!6)), 0) & $lesseq($sum(Lo1!11, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & ($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))) = 0)))) <=> ($greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))),
% 5.18/3.56 inference(transitivity,[status(thm)],[19, 3])).
% 5.18/3.56 tff(21,plain,
% 5.18/3.56 ((~(~($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0))) <=> ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0)),
% 5.18/3.56 inference(rewrite,[status(thm)],[])).
% 5.18/3.56 tff(22,plain,
% 5.18/3.56 ((~($sum(L!6, $sum($product(-1, Lo!9), div($sum($product(-1, L!6), H!5), 2))) = 0)) <=> (~($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0))),
% 5.18/3.56 inference(rewrite,[status(thm)],[])).
% 5.18/3.56 tff(23,plain,
% 5.18/3.56 ((~(~($sum(L!6, $sum($product(-1, Lo!9), div($sum($product(-1, L!6), H!5), 2))) = 0))) <=> (~(~($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0)))),
% 5.18/3.56 inference(monotonicity,[status(thm)],[22])).
% 5.18/3.56 tff(24,plain,
% 5.18/3.56 ((~(~($sum(L!6, $sum($product(-1, Lo!9), div($sum($product(-1, L!6), H!5), 2))) = 0))) <=> ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0)),
% 5.18/3.56 inference(transitivity,[status(thm)],[23, 21])).
% 5.18/3.56 tff(25,plain,
% 5.18/3.56 (((~(~($sum(L!6, $sum($product(-1, Lo!9), div($sum($product(-1, L!6), H!5), 2))) = 0))) & ((~(~$greatereq(div($sum(H!5, $product(-1, L!6)), 2), 1))) & (~(~($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0))) & (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ((~((~($greatereq($sum(Lqt!16, $product(-1, L!6)), 0) & $lesseq($sum(Lqt!16, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $greatereq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $lesseq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, Ms!12)), 0))) & (~(~$greatereq($sum(H!5, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 1))) & (~(~($sum(Ms!12, $product(-1, S1!14)) = 0)))) & ($greatereq($sum(Lo1!11, $product(-1, L!6)), 0) & $lesseq($sum(Lo1!11, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & ($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))) = 0))))) <=> (($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0) & ($greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0)))),
% 5.18/3.56 inference(monotonicity,[status(thm)],[24, 20])).
% 5.18/3.56 tff(26,plain,
% 5.18/3.56 (((~(~($sum(L!6, $sum($product(-1, Lo!9), div($sum($product(-1, L!6), H!5), 2))) = 0))) & ((~(~$greatereq(div($sum(H!5, $product(-1, L!6)), 2), 1))) & (~(~($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0))) & (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ((~((~($greatereq($sum(Lqt!16, $product(-1, L!6)), 0) & $lesseq($sum(Lqt!16, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $greatereq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $lesseq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, Ms!12)), 0))) & (~(~$greatereq($sum(H!5, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 1))) & (~(~($sum(Ms!12, $product(-1, S1!14)) = 0)))) & ($greatereq($sum(Lo1!11, $product(-1, L!6)), 0) & $lesseq($sum(Lo1!11, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & ($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))) = 0))))) <=> (($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0) & $greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))),
% 5.18/3.56 inference(transitivity,[status(thm)],[25, 2])).
% 5.18/3.56 tff(27,plain,
% 5.18/3.56 ((~(~($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $greatereq($sum(A!8, $product(-1, H!5)), 0)))) <=> ($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $greatereq($sum(A!8, $product(-1, H!5)), 0))),
% 5.18/3.56 inference(rewrite,[status(thm)],[])).
% 5.18/3.56 tff(28,plain,
% 5.18/3.56 ((~($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $lesseq($sum(H!5, $product(-1, A!8)), 0))) <=> (~($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $greatereq($sum(A!8, $product(-1, H!5)), 0)))),
% 5.18/3.56 inference(rewrite,[status(thm)],[])).
% 5.18/3.56 tff(29,plain,
% 5.18/3.56 ((~(~($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $lesseq($sum(H!5, $product(-1, A!8)), 0)))) <=> (~(~($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $greatereq($sum(A!8, $product(-1, H!5)), 0))))),
% 5.18/3.56 inference(monotonicity,[status(thm)],[28])).
% 5.18/3.56 tff(30,plain,
% 5.18/3.56 ((~(~($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $lesseq($sum(H!5, $product(-1, A!8)), 0)))) <=> ($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $greatereq($sum(A!8, $product(-1, H!5)), 0))),
% 5.18/3.56 inference(transitivity,[status(thm)],[29, 27])).
% 5.18/3.56 tff(31,plain,
% 5.18/3.56 (((~(~($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $lesseq($sum(H!5, $product(-1, A!8)), 0)))) & (~($sum(L!6, $product(-1, H!5)) = 0)) & ((~(~($sum(L!6, $sum($product(-1, Lo!9), div($sum($product(-1, L!6), H!5), 2))) = 0))) & ((~(~$greatereq(div($sum(H!5, $product(-1, L!6)), 2), 1))) & (~(~($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0))) & (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ((~((~($greatereq($sum(Lqt!16, $product(-1, L!6)), 0) & $lesseq($sum(Lqt!16, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $greatereq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $lesseq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, Ms!12)), 0))) & (~(~$greatereq($sum(H!5, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 1))) & (~(~($sum(Ms!12, $product(-1, S1!14)) = 0)))) & ($greatereq($sum(Lo1!11, $product(-1, L!6)), 0) & $lesseq($sum(Lo1!11, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & ($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))) = 0)))))) <=> (($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $greatereq($sum(A!8, $product(-1, H!5)), 0)) & (~($sum(L!6, $product(-1, H!5)) = 0)) & (($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0) & $greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0)))),
% 5.18/3.57 inference(monotonicity,[status(thm)],[30, 26])).
% 5.18/3.57 tff(32,plain,
% 5.18/3.57 (((~(~($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $lesseq($sum(H!5, $product(-1, A!8)), 0)))) & (~($sum(L!6, $product(-1, H!5)) = 0)) & ((~(~($sum(L!6, $sum($product(-1, Lo!9), div($sum($product(-1, L!6), H!5), 2))) = 0))) & ((~(~$greatereq(div($sum(H!5, $product(-1, L!6)), 2), 1))) & (~(~($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0))) & (![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ((~((~($greatereq($sum(Lqt!16, $product(-1, L!6)), 0) & $lesseq($sum(Lqt!16, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $greatereq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & $lesseq($sum(Hqt!15, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, Ms!12)), 0))) & (~(~$greatereq($sum(H!5, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 1))) & (~(~($sum(Ms!12, $product(-1, S1!14)) = 0)))) & ($greatereq($sum(Lo1!11, $product(-1, L!6)), 0) & $lesseq($sum(Lo1!11, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0) & ($sum(Hi!10, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))) = 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum(H!5, $product(-1, L!6)), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum(H!5, $product(-1, L!6)), 2))))) = 0)))))) <=> ($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $greatereq($sum(A!8, $product(-1, H!5)), 0) & (~($sum(L!6, $product(-1, H!5)) = 0)) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0) & $greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0))),
% 5.18/3.57 inference(transitivity,[status(thm)],[31, 1])).
% 5.18/3.57 tff(33,plain,
% 5.18/3.57 ((~![A: $int, A1: map_int_int, L: $int, H: $int] : ((~($greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, H)), 0) & $lesseq($sum(H, $product(-1, A)), 0))) | ($sum(L, $product(-1, H)) = 0) | ![Lo: $int] : ((~($sum(L, $sum($product(-1, Lo), div($sum($product(-1, L), H), 2))) = 0)) | ![Hi: $int] : ((~$greatereq(div($sum(H, $product(-1, L)), 2), 1)) | (~($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![S: $int, Ms: $int, Lo1: $int] : ((~![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0))) | ![S1: $int] : (![Lqt: $int, Hqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $greatereq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $lesseq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, Hqt), $product(-1, Ms)), 0)) | (~$greatereq($sum(H, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 1)) | (~($sum(Ms, $product(-1, S1)) = 0))) | (~($greatereq($sum(Lo1, $product(-1, L)), 0) & $lesseq($sum(Lo1, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & ($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0) & ($sum(Ms, $product(-1, sum(A1, Lo1, Hi))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $greatereq($sum(Ms, $product(-1, sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0)) & ($sum(S, $product(-1, sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))) = 0)))))))) <=> (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((~($greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, H)), 0) & $lesseq($sum(H, $product(-1, A)), 0))) | ($sum(L, $product(-1, H)) = 0) | ![Lo: $int] : ((~($sum(L, $sum($product(-1, Lo), div($sum($product(-1, L), H), 2))) = 0)) | ![Hi: $int] : ((~$greatereq(div($sum(H, $product(-1, L)), 2), 1)) | (~($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![S: $int, Ms: $int, Lo1: $int] : ((~![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0))) | ![S1: $int] : (![Lqt: $int, Hqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $greatereq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $lesseq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, Hqt), $product(-1, Ms)), 0)) | (~$greatereq($sum(H, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 1)) | (~($sum(Ms, $product(-1, S1)) = 0))) | (~($greatereq($sum(Lo1, $product(-1, L)), 0) & $lesseq($sum(Lo1, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & ($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0) & ($sum(Ms, $product(-1, sum(A1, Lo1, Hi))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $greatereq($sum(Ms, $product(-1, sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0)) & ($sum(S, $product(-1, sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))) = 0))))))))),
% 5.18/3.57 inference(rewrite,[status(thm)],[])).
% 5.18/3.57 tff(34,plain,
% 5.18/3.57 ((~![A: $int, A1: map_int_int, L: $int, H: $int] : ((~($greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, H)), 0) & $lesseq($sum(H, $product(-1, A)), 0))) | ($sum(H, $product(-1, L)) = 0) | ![Lo: $int] : ((~($sum(Lo, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![Hi: $int] : ((~$greatereq(div($sum(H, $product(-1, L)), 2), 1)) | (~($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![S: $int, Ms: $int, Lo1: $int] : (![S1: $int] : ((~($sum(S1, $product(-1, Ms)) = 0)) | ![Lqt: $int, Hqt: $int] : ((~($lesseq($sum(L, $product(-1, Lqt)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $lesseq($sum(L, $sum(div($sum(H, $product(-1, L)), 2), $product(-1, Hqt))), 0) & $lesseq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, Hqt), $product(-1, Ms)), 0)) | (~$lesseq($sum(L, $sum(div($sum(H, $product(-1, L)), 2), $product(-1, H))), -1))) | (~![Lqt: $int] : ((~($lesseq($sum(L, $product(-1, Lqt)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0))) | (~($lesseq($sum(L, $product(-1, Lo1)), 0) & $lesseq($sum(Lo1, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & ($sum(L, $sum(div($sum(H, $product(-1, L)), 2), $product(-1, Hi))) = 0) & ($sum(Ms, $product(-1, sum(A1, Lo1, Hi))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, Ms)), 0)) & ($sum(S, $product(-1, sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))) = 0)))))))) <=> (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((~($greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, H)), 0) & $lesseq($sum(H, $product(-1, A)), 0))) | ($sum(L, $product(-1, H)) = 0) | ![Lo: $int] : ((~($sum(L, $sum($product(-1, Lo), div($sum($product(-1, L), H), 2))) = 0)) | ![Hi: $int] : ((~$greatereq(div($sum(H, $product(-1, L)), 2), 1)) | (~($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![S: $int, Ms: $int, Lo1: $int] : ((~![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0))) | ![S1: $int] : (![Lqt: $int, Hqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $greatereq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $lesseq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, Hqt), $product(-1, Ms)), 0)) | (~$greatereq($sum(H, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 1)) | (~($sum(Ms, $product(-1, S1)) = 0))) | (~($greatereq($sum(Lo1, $product(-1, L)), 0) & $lesseq($sum(Lo1, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & ($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0) & ($sum(Ms, $product(-1, sum(A1, Lo1, Hi))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $greatereq($sum(Ms, $product(-1, sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0)) & ($sum(S, $product(-1, sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))) = 0))))))))),
% 5.18/3.57 inference(rewrite,[status(thm)],[])).
% 5.18/3.57 tff(35,plain,
% 5.18/3.57 ((~![A: $int, A1: map_int_int, L: $int, H: $int] : ((H = L) | ![Lo: $int] : ((~(Lo = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![Hi: $int] : ((~$lesseq(1, div($sum(H, $product(-1, L)), 2))) | (~(Hi = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![S: $int, Ms: $int, Lo1: $int] : (![S1: $int] : ((~(S1 = Ms)) | ![Lqt: $int, Hqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), Hqt) & $lesseq(Hqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, Hqt), Ms)) | (~$lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), $sum(-1, H)))) | (~![Lqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2)))))) | (~($lesseq(L, Lo1) & $lesseq(Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))) & ($sum(L, div($sum(H, $product(-1, L)), 2)) = Hi) & (Ms = sum(A1, Lo1, Hi)) & ![Lqt: $int] : ((~((~$lesseq(Lqt, $sum(-1, L))) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), Ms)) & (S = sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))))))) | (~($lesseq(0, A) & $lesseq(0, L) & $lesseq(L, H) & $lesseq(H, A))))) <=> (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((~($greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, H)), 0) & $lesseq($sum(H, $product(-1, A)), 0))) | ($sum(H, $product(-1, L)) = 0) | ![Lo: $int] : ((~($sum(Lo, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![Hi: $int] : ((~$greatereq(div($sum(H, $product(-1, L)), 2), 1)) | (~($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![S: $int, Ms: $int, Lo1: $int] : (![S1: $int] : ((~($sum(S1, $product(-1, Ms)) = 0)) | ![Lqt: $int, Hqt: $int] : ((~($lesseq($sum(L, $product(-1, Lqt)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $lesseq($sum(L, $sum(div($sum(H, $product(-1, L)), 2), $product(-1, Hqt))), 0) & $lesseq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, Hqt), $product(-1, Ms)), 0)) | (~$lesseq($sum(L, $sum(div($sum(H, $product(-1, L)), 2), $product(-1, H))), -1))) | (~![Lqt: $int] : ((~($lesseq($sum(L, $product(-1, Lqt)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0))) | (~($lesseq($sum(L, $product(-1, Lo1)), 0) & $lesseq($sum(Lo1, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & ($sum(L, $sum(div($sum(H, $product(-1, L)), 2), $product(-1, Hi))) = 0) & ($sum(Ms, $product(-1, sum(A1, Lo1, Hi))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, Ms)), 0)) & ($sum(S, $product(-1, sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))) = 0))))))))),
% 5.18/3.57 inference(rewrite,[status(thm)],[])).
% 5.18/3.57 tff(36,plain,
% 5.18/3.57 ((~![A: $int, A1: map_int_int, L: $int, H: $int] : ((H = L) | ![Lo: $int] : ((~(Lo = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![Hi: $int] : ((~$lesseq(1, div($sum(H, $product(-1, L)), 2))) | (~(Hi = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![S: $int, Ms: $int, Lo1: $int] : (![S1: $int] : ((~(S1 = Ms)) | ![Lqt: $int, Hqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), Hqt) & $lesseq(Hqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, Hqt), Ms)) | (~$lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), $sum(-1, H)))) | (~![Lqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2)))))) | (~($lesseq(L, Lo1) & $lesseq(Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))) & ($sum(L, div($sum(H, $product(-1, L)), 2)) = Hi) & (Ms = sum(A1, Lo1, Hi)) & ![Lqt: $int] : ((~((~$lesseq(Lqt, $sum(-1, L))) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), Ms)) & (S = sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))))))) | (~($lesseq(0, A) & $lesseq(0, L) & $lesseq(L, H) & $lesseq(H, A))))) <=> (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((H = L) | ![Lo: $int] : ((~(Lo = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![Hi: $int] : ((~$lesseq(1, div($sum(H, $product(-1, L)), 2))) | (~(Hi = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![S: $int, Ms: $int, Lo1: $int] : (![S1: $int] : ((~(S1 = Ms)) | ![Lqt: $int, Hqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), Hqt) & $lesseq(Hqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, Hqt), Ms)) | (~$lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), $sum(-1, H)))) | (~![Lqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2)))))) | (~($lesseq(L, Lo1) & $lesseq(Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))) & ($sum(L, div($sum(H, $product(-1, L)), 2)) = Hi) & (Ms = sum(A1, Lo1, Hi)) & ![Lqt: $int] : ((~((~$lesseq(Lqt, $sum(-1, L))) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), Ms)) & (S = sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))))))) | (~($lesseq(0, A) & $lesseq(0, L) & $lesseq(L, H) & $lesseq(H, A)))))),
% 5.18/3.57 inference(rewrite,[status(thm)],[])).
% 5.18/3.57 tff(37,plain,
% 5.18/3.57 ((~![A: $int, A1: map_int_int, L: $int, H: $int] : (((($lesseq(0, A) & $lesseq(0, L)) & $lesseq(L, H)) & $lesseq(H, A)) => ((~(H = L)) => ![Lo: $int] : ((Lo = $sum(L, div($difference(H, L), 2))) => ![Hi: $int] : ((Hi = $sum(L, div($difference(H, L), 2))) => ($lesseq(L, $difference($sum(L, div($difference(H, L), 2)), 1)) => ![S: $int, Ms: $int, Lo1: $int] : (((((($lesseq(L, Lo1) & $lesseq(Lo1, $sum(L, div($difference(H, L), 2)))) & ($sum(L, div($difference(H, L), 2)) = Hi)) & (Ms = sum(A1, Lo1, Hi))) & ![Lqt: $int] : (($less($difference(L, 1), Lqt) & $lesseq(Lqt, $sum(L, div($difference(H, L), 2)))) => $lesseq(sum(A1, Lqt, $sum(L, div($difference(H, L), 2))), Ms))) & (S = sum(A1, $sum($difference(L, 1), 1), $sum(L, div($difference(H, L), 2))))) => (![Lqt: $int] : (($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($difference(H, L), 2)))) => $lesseq(sum(A1, Lqt, $sum(L, div($difference(H, L), 2))), sum(A1, Lo1, $sum(L, div($difference(H, L), 2))))) => ![S1: $int] : ((S1 = Ms) => ($lesseq($sum(L, div($difference(H, L), 2)), $difference(H, 1)) => ![Lqt: $int, Hqt: $int] : (((($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($difference(H, L), 2)))) & $lesseq($sum(L, div($difference(H, L), 2)), Hqt)) & $lesseq(Hqt, $sum(L, div($difference(H, L), 2)))) => $lesseq(sum(A1, Lqt, Hqt), Ms)))))))))))) <=> (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((H = L) | ![Lo: $int] : ((~(Lo = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![Hi: $int] : ((~$lesseq(1, div($sum(H, $product(-1, L)), 2))) | (~(Hi = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![S: $int, Ms: $int, Lo1: $int] : (![S1: $int] : ((~(S1 = Ms)) | ![Lqt: $int, Hqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), Hqt) & $lesseq(Hqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, Hqt), Ms)) | (~$lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), $sum(-1, H)))) | (~![Lqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2)))))) | (~($lesseq(L, Lo1) & $lesseq(Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))) & ($sum(L, div($sum(H, $product(-1, L)), 2)) = Hi) & (Ms = sum(A1, Lo1, Hi)) & ![Lqt: $int] : ((~((~$lesseq(Lqt, $sum(-1, L))) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), Ms)) & (S = sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))))))) | (~($lesseq(0, A) & $lesseq(0, L) & $lesseq(L, H) & $lesseq(H, A)))))),
% 5.18/3.57 inference(rewrite,[status(thm)],[])).
% 5.18/3.57 tff(38,axiom,(~![A: $int, A1: map_int_int, L: $int, H: $int] : (((($lesseq(0, A) & $lesseq(0, L)) & $lesseq(L, H)) & $lesseq(H, A)) => ((~(H = L)) => ![Lo: $int] : ((Lo = $sum(L, div($difference(H, L), 2))) => ![Hi: $int] : ((Hi = $sum(L, div($difference(H, L), 2))) => ($lesseq(L, $difference($sum(L, div($difference(H, L), 2)), 1)) => ![S: $int, Ms: $int, Lo1: $int] : (((((($lesseq(L, Lo1) & $lesseq(Lo1, $sum(L, div($difference(H, L), 2)))) & ($sum(L, div($difference(H, L), 2)) = Hi)) & (Ms = sum(A1, Lo1, Hi))) & ![Lqt: $int] : (($less($difference(L, 1), Lqt) & $lesseq(Lqt, $sum(L, div($difference(H, L), 2)))) => $lesseq(sum(A1, Lqt, $sum(L, div($difference(H, L), 2))), Ms))) & (S = sum(A1, $sum($difference(L, 1), 1), $sum(L, div($difference(H, L), 2))))) => (![Lqt: $int] : (($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($difference(H, L), 2)))) => $lesseq(sum(A1, Lqt, $sum(L, div($difference(H, L), 2))), sum(A1, Lo1, $sum(L, div($difference(H, L), 2))))) => ![S1: $int] : ((S1 = Ms) => ($lesseq($sum(L, div($difference(H, L), 2)), $difference(H, 1)) => ![Lqt: $int, Hqt: $int] : (((($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($difference(H, L), 2)))) & $lesseq($sum(L, div($difference(H, L), 2)), Hqt)) & $lesseq(Hqt, $sum(L, div($difference(H, L), 2)))) => $lesseq(sum(A1, Lqt, Hqt), Ms)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_maximum_subarray_rec')).
% 5.18/3.57 tff(39,plain,
% 5.18/3.57 (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((H = L) | ![Lo: $int] : ((~(Lo = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![Hi: $int] : ((~$lesseq(1, div($sum(H, $product(-1, L)), 2))) | (~(Hi = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![S: $int, Ms: $int, Lo1: $int] : (![S1: $int] : ((~(S1 = Ms)) | ![Lqt: $int, Hqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), Hqt) & $lesseq(Hqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, Hqt), Ms)) | (~$lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), $sum(-1, H)))) | (~![Lqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2)))))) | (~($lesseq(L, Lo1) & $lesseq(Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))) & ($sum(L, div($sum(H, $product(-1, L)), 2)) = Hi) & (Ms = sum(A1, Lo1, Hi)) & ![Lqt: $int] : ((~((~$lesseq(Lqt, $sum(-1, L))) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), Ms)) & (S = sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))))))) | (~($lesseq(0, A) & $lesseq(0, L) & $lesseq(L, H) & $lesseq(H, A))))),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[38, 37])).
% 5.18/3.57 tff(40,plain,
% 5.18/3.57 (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((H = L) | ![Lo: $int] : ((~(Lo = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![Hi: $int] : ((~$lesseq(1, div($sum(H, $product(-1, L)), 2))) | (~(Hi = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![S: $int, Ms: $int, Lo1: $int] : (![S1: $int] : ((~(S1 = Ms)) | ![Lqt: $int, Hqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), Hqt) & $lesseq(Hqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, Hqt), Ms)) | (~$lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), $sum(-1, H)))) | (~![Lqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2)))))) | (~($lesseq(L, Lo1) & $lesseq(Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))) & ($sum(L, div($sum(H, $product(-1, L)), 2)) = Hi) & (Ms = sum(A1, Lo1, Hi)) & ![Lqt: $int] : ((~((~$lesseq(Lqt, $sum(-1, L))) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), Ms)) & (S = sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))))))) | (~($lesseq(0, A) & $lesseq(0, L) & $lesseq(L, H) & $lesseq(H, A))))),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[39, 36])).
% 5.18/3.57 tff(41,plain,
% 5.18/3.57 (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((H = L) | ![Lo: $int] : ((~(Lo = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![Hi: $int] : ((~$lesseq(1, div($sum(H, $product(-1, L)), 2))) | (~(Hi = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![S: $int, Ms: $int, Lo1: $int] : (![S1: $int] : ((~(S1 = Ms)) | ![Lqt: $int, Hqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), Hqt) & $lesseq(Hqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, Hqt), Ms)) | (~$lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), $sum(-1, H)))) | (~![Lqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2)))))) | (~($lesseq(L, Lo1) & $lesseq(Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))) & ($sum(L, div($sum(H, $product(-1, L)), 2)) = Hi) & (Ms = sum(A1, Lo1, Hi)) & ![Lqt: $int] : ((~((~$lesseq(Lqt, $sum(-1, L))) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), Ms)) & (S = sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))))))) | (~($lesseq(0, A) & $lesseq(0, L) & $lesseq(L, H) & $lesseq(H, A))))),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[40, 36])).
% 5.18/3.57 tff(42,plain,
% 5.18/3.57 (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((H = L) | ![Lo: $int] : ((~(Lo = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![Hi: $int] : ((~$lesseq(1, div($sum(H, $product(-1, L)), 2))) | (~(Hi = $sum(L, div($sum(H, $product(-1, L)), 2)))) | ![S: $int, Ms: $int, Lo1: $int] : (![S1: $int] : ((~(S1 = Ms)) | ![Lqt: $int, Hqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))) & $lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), Hqt) & $lesseq(Hqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, Hqt), Ms)) | (~$lesseq($sum(L, div($sum(H, $product(-1, L)), 2)), $sum(-1, H)))) | (~![Lqt: $int] : ((~($lesseq(L, Lqt) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2)))))) | (~($lesseq(L, Lo1) & $lesseq(Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))) & ($sum(L, div($sum(H, $product(-1, L)), 2)) = Hi) & (Ms = sum(A1, Lo1, Hi)) & ![Lqt: $int] : ((~((~$lesseq(Lqt, $sum(-1, L))) & $lesseq(Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))) | $lesseq(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), Ms)) & (S = sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))))))) | (~($lesseq(0, A) & $lesseq(0, L) & $lesseq(L, H) & $lesseq(H, A))))),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[41, 36])).
% 5.18/3.57 tff(43,plain,
% 5.18/3.57 (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((~($greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, H)), 0) & $lesseq($sum(H, $product(-1, A)), 0))) | ($sum(H, $product(-1, L)) = 0) | ![Lo: $int] : ((~($sum(Lo, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![Hi: $int] : ((~$greatereq(div($sum(H, $product(-1, L)), 2), 1)) | (~($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![S: $int, Ms: $int, Lo1: $int] : (![S1: $int] : ((~($sum(S1, $product(-1, Ms)) = 0)) | ![Lqt: $int, Hqt: $int] : ((~($lesseq($sum(L, $product(-1, Lqt)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $lesseq($sum(L, $sum(div($sum(H, $product(-1, L)), 2), $product(-1, Hqt))), 0) & $lesseq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, Hqt), $product(-1, Ms)), 0)) | (~$lesseq($sum(L, $sum(div($sum(H, $product(-1, L)), 2), $product(-1, H))), -1))) | (~![Lqt: $int] : ((~($lesseq($sum(L, $product(-1, Lqt)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0))) | (~($lesseq($sum(L, $product(-1, Lo1)), 0) & $lesseq($sum(Lo1, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & ($sum(L, $sum(div($sum(H, $product(-1, L)), 2), $product(-1, Hi))) = 0) & ($sum(Ms, $product(-1, sum(A1, Lo1, Hi))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, Ms)), 0)) & ($sum(S, $product(-1, sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))) = 0)))))))),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[42, 35])).
% 5.18/3.57 tff(44,plain,
% 5.18/3.57 (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((~($greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, H)), 0) & $lesseq($sum(H, $product(-1, A)), 0))) | ($sum(L, $product(-1, H)) = 0) | ![Lo: $int] : ((~($sum(L, $sum($product(-1, Lo), div($sum($product(-1, L), H), 2))) = 0)) | ![Hi: $int] : ((~$greatereq(div($sum(H, $product(-1, L)), 2), 1)) | (~($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![S: $int, Ms: $int, Lo1: $int] : ((~![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0))) | ![S1: $int] : (![Lqt: $int, Hqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $greatereq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $lesseq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, Hqt), $product(-1, Ms)), 0)) | (~$greatereq($sum(H, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 1)) | (~($sum(Ms, $product(-1, S1)) = 0))) | (~($greatereq($sum(Lo1, $product(-1, L)), 0) & $lesseq($sum(Lo1, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & ($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0) & ($sum(Ms, $product(-1, sum(A1, Lo1, Hi))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $greatereq($sum(Ms, $product(-1, sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0)) & ($sum(S, $product(-1, sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))) = 0)))))))),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[43, 34])).
% 5.18/3.57 tff(45,plain,
% 5.18/3.57 (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((~($greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, H)), 0) & $lesseq($sum(H, $product(-1, A)), 0))) | ($sum(L, $product(-1, H)) = 0) | ![Lo: $int] : ((~($sum(L, $sum($product(-1, Lo), div($sum($product(-1, L), H), 2))) = 0)) | ![Hi: $int] : ((~$greatereq(div($sum(H, $product(-1, L)), 2), 1)) | (~($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![S: $int, Ms: $int, Lo1: $int] : ((~![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0))) | ![S1: $int] : (![Lqt: $int, Hqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $greatereq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $lesseq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, Hqt), $product(-1, Ms)), 0)) | (~$greatereq($sum(H, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 1)) | (~($sum(Ms, $product(-1, S1)) = 0))) | (~($greatereq($sum(Lo1, $product(-1, L)), 0) & $lesseq($sum(Lo1, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & ($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0) & ($sum(Ms, $product(-1, sum(A1, Lo1, Hi))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $greatereq($sum(Ms, $product(-1, sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0)) & ($sum(S, $product(-1, sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))) = 0)))))))),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[44, 33])).
% 5.18/3.57 tff(46,plain,
% 5.18/3.57 (~![A: $int, A1: map_int_int, L: $int, H: $int] : ((~($greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, H)), 0) & $lesseq($sum(H, $product(-1, A)), 0))) | ($sum(L, $product(-1, H)) = 0) | ![Lo: $int] : ((~($sum(L, $sum($product(-1, Lo), div($sum($product(-1, L), H), 2))) = 0)) | ![Hi: $int] : ((~$greatereq(div($sum(H, $product(-1, L)), 2), 1)) | (~($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0)) | ![S: $int, Ms: $int, Lo1: $int] : ((~![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))), $product(-1, sum(A1, Lo1, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0))) | ![S1: $int] : (![Lqt: $int, Hqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $greatereq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & $lesseq($sum(Hqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $lesseq($sum(sum(A1, Lqt, Hqt), $product(-1, Ms)), 0)) | (~$greatereq($sum(H, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 1)) | (~($sum(Ms, $product(-1, S1)) = 0))) | (~($greatereq($sum(Lo1, $product(-1, L)), 0) & $lesseq($sum(Lo1, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0) & ($sum(Hi, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))) = 0) & ($sum(Ms, $product(-1, sum(A1, Lo1, Hi))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L), $product(-1, div($sum(H, $product(-1, L)), 2)))), 0))) | $greatereq($sum(Ms, $product(-1, sum(A1, Lqt, $sum(L, div($sum(H, $product(-1, L)), 2))))), 0)) & ($sum(S, $product(-1, sum(A1, L, $sum(L, div($sum(H, $product(-1, L)), 2))))) = 0)))))))),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[45, 33])).
% 5.18/3.57 tff(47,plain,
% 5.18/3.57 ($greatereq(A!8, 0) & $greatereq(L!6, 0) & $lesseq($sum(L!6, $product(-1, H!5)), 0) & $greatereq($sum(A!8, $product(-1, H!5)), 0) & (~($sum(L!6, $product(-1, H!5)) = 0)) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo!9))) = 0) & $greatereq(div($sum($product(-1, L!6), H!5), 2), 1) & ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0) & ![Lqt: $int] : ((~($greatereq($sum(Lqt, $product(-1, L!6)), 0) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $lesseq($sum(sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))), $product(-1, sum(A1!7, Lo1!11, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))) & $lesseq($sum(L!6, $sum($product(-1, H!5), div($sum($product(-1, L!6), H!5), 2))), -1) & ($sum(Ms!12, $product(-1, S1!14)) = 0) & $lesseq($sum(L!6, $product(-1, Lo1!11)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lo1!11))), 0) & ($sum(Ms!12, $product(-1, sum(A1!7, Lo1!11, Hi!10))) = 0) & ![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) & ($sum(S!13, $product(-1, sum(A1!7, L!6, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) = 0)),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[46, 32])).
% 5.18/3.57 tff(48,plain,
% 5.18/3.57 (~((~($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0))),
% 5.18/3.57 inference(and_elim,[status(thm)],[47])).
% 5.18/3.57 tff(49,plain,
% 5.18/3.57 ($lesseq($sum(L!6, $product(-1, Lqt!16)), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0) & $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0) & $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0)),
% 5.18/3.57 inference(or_elim,[status(thm)],[48])).
% 5.18/3.57 tff(50,plain,
% 5.18/3.57 ($greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Lqt!16))), 0)),
% 5.18/3.57 inference(and_elim,[status(thm)],[49])).
% 5.18/3.57 tff(51,plain,
% 5.18/3.57 (^[I: $int] : refl(($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0))),
% 5.18/3.57 inference(bind,[status(th)],[])).
% 5.18/3.57 tff(52,plain,
% 5.18/3.57 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 5.18/3.57 inference(quant_intro,[status(thm)],[51])).
% 5.18/3.57 tff(53,plain,
% 5.18/3.57 (^[I: $int] : trans(monotonicity(rewrite($sum(tb2t(t2tb(I)), $product(-1, I)) = $sum($product(-1, I), tb2t(t2tb(I)))), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum($product(-1, I), tb2t(t2tb(I))) = 0))), rewrite(($sum($product(-1, I), tb2t(t2tb(I))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)))),
% 5.18/3.57 inference(bind,[status(th)],[])).
% 5.18/3.57 tff(54,plain,
% 5.18/3.57 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 5.18/3.57 inference(quant_intro,[status(thm)],[53])).
% 5.18/3.57 tff(55,plain,
% 5.18/3.57 (^[I: $int] : rewrite((tb2t(t2tb(I)) = I) <=> ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0))),
% 5.18/3.57 inference(bind,[status(th)],[])).
% 5.18/3.57 tff(56,plain,
% 5.18/3.57 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 5.18/3.57 inference(quant_intro,[status(thm)],[55])).
% 5.18/3.57 tff(57,plain,
% 5.18/3.57 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : (tb2t(t2tb(I)) = I)),
% 5.18/3.57 inference(rewrite,[status(thm)],[])).
% 5.18/3.57 tff(58,axiom,(![I: $int] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeL')).
% 5.18/3.57 tff(59,plain,
% 5.18/3.57 (![I: $int] : (tb2t(t2tb(I)) = I)),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[58, 57])).
% 5.18/3.57 tff(60,plain,
% 5.18/3.57 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[59, 56])).
% 5.18/3.57 tff(61,plain,
% 5.18/3.57 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[60, 54])).
% 5.18/3.57 tff(62,plain,(
% 5.18/3.57 ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 5.18/3.57 inference(skolemize,[status(sab)],[61])).
% 5.18/3.57 tff(63,plain,
% 5.18/3.57 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[62, 52])).
% 5.18/3.57 tff(64,plain,
% 5.18/3.57 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(Lqt!16, $product(-1, tb2t(t2tb(Lqt!16)))) = 0)),
% 5.18/3.57 inference(quant_inst,[status(thm)],[])).
% 5.18/3.57 tff(65,plain,
% 5.18/3.57 ($sum(Lqt!16, $product(-1, tb2t(t2tb(Lqt!16)))) = 0),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[64, 63])).
% 5.18/3.57 tff(66,plain,
% 5.18/3.57 ((~($sum(Lqt!16, $product(-1, tb2t(t2tb(Lqt!16)))) = 0)) | $greatereq($sum(Lqt!16, $product(-1, tb2t(t2tb(Lqt!16)))), 0)),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(67,plain,
% 5.18/3.57 ($greatereq($sum(Lqt!16, $product(-1, tb2t(t2tb(Lqt!16)))), 0)),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[66, 65])).
% 5.18/3.57 tff(68,plain,
% 5.18/3.57 ($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0),
% 5.18/3.57 inference(and_elim,[status(thm)],[47])).
% 5.18/3.57 tff(69,plain,
% 5.18/3.57 ((~($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0)) | $greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))), 0)),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(70,plain,
% 5.18/3.57 ($greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))), 0)),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[69, 68])).
% 5.18/3.57 tff(71,plain,
% 5.18/3.57 ($lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0)),
% 5.18/3.57 inference(and_elim,[status(thm)],[49])).
% 5.18/3.57 tff(72,plain,
% 5.18/3.57 ($lesseq($sum(Hi!10, $product(-1, Hqt!15)), 0) | (~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))), 0)) | (~$lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(73,plain,
% 5.18/3.57 ($lesseq($sum(Hi!10, $product(-1, Hqt!15)), 0)),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[72, 71, 70])).
% 5.18/3.57 tff(74,plain,
% 5.18/3.57 ((~($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))) = 0)) | $lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))), 0)),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(75,plain,
% 5.18/3.57 ($lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))), 0)),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[74, 68])).
% 5.18/3.57 tff(76,plain,
% 5.18/3.57 ($greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0)),
% 5.18/3.57 inference(and_elim,[status(thm)],[49])).
% 5.18/3.57 tff(77,plain,
% 5.18/3.57 ($greatereq($sum(Hi!10, $product(-1, Hqt!15)), 0) | (~$lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))), 0)) | (~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hqt!15))), 0))),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(78,plain,
% 5.18/3.57 ($greatereq($sum(Hi!10, $product(-1, Hqt!15)), 0)),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[77, 76, 75])).
% 5.18/3.57 tff(79,plain,
% 5.18/3.57 ((Hi!10 = Hqt!15) | (~$lesseq($sum(Hi!10, $product(-1, Hqt!15)), 0)) | (~$greatereq($sum(Hi!10, $product(-1, Hqt!15)), 0))),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(80,plain,
% 5.18/3.57 (Hi!10 = Hqt!15),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[79, 78, 73])).
% 5.18/3.57 tff(81,plain,
% 5.18/3.57 ($lesseq($sum(Hi!10, $product(-1, $sum(L!6, div($sum($product(-1, L!6), H!5), 2)))), 0) | (~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))), 0))),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(82,plain,
% 5.18/3.57 ($lesseq($sum(Hi!10, $product(-1, $sum(L!6, div($sum($product(-1, L!6), H!5), 2)))), 0)),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[81, 70])).
% 5.18/3.57 tff(83,plain,
% 5.18/3.57 ($greatereq($sum(Hi!10, $product(-1, $sum(L!6, div($sum($product(-1, L!6), H!5), 2)))), 0) | (~$lesseq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, Hi!10))), 0))),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(84,plain,
% 5.18/3.57 ($greatereq($sum(Hi!10, $product(-1, $sum(L!6, div($sum($product(-1, L!6), H!5), 2)))), 0)),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[83, 75])).
% 5.18/3.57 tff(85,plain,
% 5.18/3.57 ((Hi!10 = $sum(L!6, div($sum($product(-1, L!6), H!5), 2))) | (~$lesseq($sum(Hi!10, $product(-1, $sum(L!6, div($sum($product(-1, L!6), H!5), 2)))), 0)) | (~$greatereq($sum(Hi!10, $product(-1, $sum(L!6, div($sum($product(-1, L!6), H!5), 2)))), 0))),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(86,plain,
% 5.18/3.57 (Hi!10 = $sum(L!6, div($sum($product(-1, L!6), H!5), 2))),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[85, 84, 82])).
% 5.18/3.57 tff(87,plain,
% 5.18/3.57 ($sum(L!6, div($sum($product(-1, L!6), H!5), 2)) = Hi!10),
% 5.18/3.57 inference(symmetry,[status(thm)],[86])).
% 5.18/3.57 tff(88,plain,
% 5.18/3.57 ($sum(L!6, div($sum($product(-1, L!6), H!5), 2)) = Hqt!15),
% 5.18/3.57 inference(transitivity,[status(thm)],[87, 80])).
% 5.18/3.57 tff(89,plain,
% 5.18/3.57 ((~($sum(Lqt!16, $product(-1, tb2t(t2tb(Lqt!16)))) = 0)) | $lesseq($sum(Lqt!16, $product(-1, tb2t(t2tb(Lqt!16)))), 0)),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(90,plain,
% 5.18/3.57 ($lesseq($sum(Lqt!16, $product(-1, tb2t(t2tb(Lqt!16)))), 0)),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[89, 65])).
% 5.18/3.57 tff(91,plain,
% 5.18/3.57 (Lqt!16 = tb2t(t2tb(Lqt!16))),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[67, 90])).
% 5.18/3.57 tff(92,plain,
% 5.18/3.57 (tb2t(t2tb(Lqt!16)) = Lqt!16),
% 5.18/3.57 inference(symmetry,[status(thm)],[91])).
% 5.18/3.57 tff(93,plain,
% 5.18/3.57 (sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))) = sum(A1!7, Lqt!16, Hqt!15)),
% 5.18/3.57 inference(monotonicity,[status(thm)],[92, 88])).
% 5.18/3.57 tff(94,plain,
% 5.18/3.57 (sum(A1!7, Lqt!16, Hqt!15) = sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2)))),
% 5.18/3.57 inference(symmetry,[status(thm)],[93])).
% 5.18/3.57 tff(95,plain,
% 5.18/3.57 ((~(sum(A1!7, Lqt!16, Hqt!15) = sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))) | $lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(96,plain,
% 5.18/3.57 ($lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[95, 94])).
% 5.18/3.57 tff(97,plain,
% 5.18/3.57 (~$greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0)),
% 5.18/3.57 inference(or_elim,[status(thm)],[48])).
% 5.18/3.57 tff(98,plain,
% 5.18/3.57 ((~$greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt!16, Hqt!15))), 0) | (~$lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0))),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[])).
% 5.18/3.57 tff(99,plain,
% 5.18/3.57 ((~$greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) | (~$lesseq($sum(sum(A1!7, Lqt!16, Hqt!15), $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0))),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[98, 97])).
% 5.18/3.57 tff(100,plain,
% 5.18/3.57 (~$greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)),
% 5.18/3.57 inference(unit_resolution,[status(thm)],[99, 96])).
% 5.18/3.57 tff(101,plain,
% 5.18/3.57 ($lesseq($sum(L!6, $product(-1, Lqt!16)), 0)),
% 5.18/3.57 inference(and_elim,[status(thm)],[49])).
% 5.18/3.57 tff(102,assumption,($greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1)), introduced(assumption)).
% 5.18/3.57 tff(103,plain,
% 5.18/3.57 ($false),
% 5.18/3.57 inference(theory_lemma,[status(thm)],[102, 90, 101])).
% 5.18/3.57 tff(104,plain,(~$greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1)), inference(lemma,lemma(discharge,[]))).
% 5.18/3.57 tff(105,assumption,($greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0)), introduced(assumption)).
% 5.18/3.57 tff(106,assumption,(~$greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)), introduced(assumption)).
% 5.18/3.57 tff(107,plain,
% 5.18/3.57 (^[Lqt: $int] : refl(($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) <=> ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))))),
% 5.18/3.57 inference(bind,[status(th)],[])).
% 5.18/3.57 tff(108,plain,
% 5.18/3.57 (![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) <=> ![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))),
% 5.18/3.57 inference(quant_intro,[status(thm)],[107])).
% 5.18/3.57 tff(109,plain,
% 5.18/3.57 (^[Lqt: $int] : trans(monotonicity(trans(monotonicity(rewrite(((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)) <=> (~($lesseq($sum(Lqt, $product(-1, L!6)), -1) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))))), ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) <=> (~(~($lesseq($sum(Lqt, $product(-1, L!6)), -1) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))))))), rewrite((~(~($lesseq($sum(Lqt, $product(-1, L!6)), -1) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))))) <=> ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))), ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) <=> ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))))), (((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) <=> (($lesseq($sum(Lqt, $product(-1, L!6)), -1) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)))), rewrite((($lesseq($sum(Lqt, $product(-1, L!6)), -1) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) <=> ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))), (((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) <=> ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))))),
% 5.18/3.57 inference(bind,[status(th)],[])).
% 5.18/3.57 tff(110,plain,
% 5.18/3.57 (![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0)) <=> ![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))),
% 5.18/3.57 inference(quant_intro,[status(thm)],[109])).
% 5.18/3.57 tff(111,plain,
% 5.18/3.57 (![Lqt: $int] : ((~((~$lesseq($sum(Lqt, $product(-1, L!6)), -1)) & $lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0))),
% 5.18/3.57 inference(and_elim,[status(thm)],[47])).
% 5.18/3.57 tff(112,plain,
% 5.18/3.57 (![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[111, 110])).
% 5.18/3.57 tff(113,plain,
% 5.18/3.57 (![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))),
% 5.18/3.57 inference(modus_ponens,[status(thm)],[112, 108])).
% 5.18/3.57 tff(114,plain,
% 5.18/3.57 (((~![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))) | ((~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0)) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | $greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1))) <=> ((~![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))) | (~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0)) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | $greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1))),
% 5.18/3.58 inference(rewrite,[status(thm)],[])).
% 5.18/3.58 tff(115,plain,
% 5.18/3.58 (($greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0))) <=> ((~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0)) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | $greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1))),
% 5.18/3.58 inference(rewrite,[status(thm)],[])).
% 5.18/3.58 tff(116,plain,
% 5.18/3.58 ((~$lesseq($sum(tb2t(t2tb(Lqt!16)), $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)) <=> (~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0))),
% 5.18/3.58 inference(rewrite,[status(thm)],[])).
% 5.18/3.58 tff(117,plain,
% 5.18/3.58 ($lesseq($sum($product(-1, L!6), tb2t(t2tb(Lqt!16))), -1) <=> $greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1)),
% 5.18/3.58 inference(rewrite,[status(thm)],[])).
% 5.18/3.58 tff(118,plain,
% 5.18/3.58 ($sum(tb2t(t2tb(Lqt!16)), $product(-1, L!6)) = $sum($product(-1, L!6), tb2t(t2tb(Lqt!16)))),
% 5.18/3.58 inference(rewrite,[status(thm)],[])).
% 5.18/3.58 tff(119,plain,
% 5.18/3.58 ($lesseq($sum(tb2t(t2tb(Lqt!16)), $product(-1, L!6)), -1) <=> $lesseq($sum($product(-1, L!6), tb2t(t2tb(Lqt!16))), -1)),
% 5.18/3.58 inference(monotonicity,[status(thm)],[118])).
% 5.18/3.58 tff(120,plain,
% 5.18/3.58 ($lesseq($sum(tb2t(t2tb(Lqt!16)), $product(-1, L!6)), -1) <=> $greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1)),
% 5.18/3.58 inference(transitivity,[status(thm)],[119, 117])).
% 5.18/3.58 tff(121,plain,
% 5.18/3.58 (($lesseq($sum(tb2t(t2tb(Lqt!16)), $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(tb2t(t2tb(Lqt!16)), $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) <=> ($greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0)))),
% 5.18/3.58 inference(monotonicity,[status(thm)],[120, 116])).
% 5.18/3.58 tff(122,plain,
% 5.18/3.58 (($lesseq($sum(tb2t(t2tb(Lqt!16)), $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(tb2t(t2tb(Lqt!16)), $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0))) <=> ((~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0)) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | $greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1))),
% 5.18/3.58 inference(transitivity,[status(thm)],[121, 115])).
% 5.18/3.58 tff(123,plain,
% 5.18/3.58 (((~![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))) | ($lesseq($sum(tb2t(t2tb(Lqt!16)), $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(tb2t(t2tb(Lqt!16)), $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))) <=> ((~![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))) | ((~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0)) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | $greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1)))),
% 5.18/3.58 inference(monotonicity,[status(thm)],[122])).
% 5.18/3.58 tff(124,plain,
% 5.18/3.58 (((~![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))) | ($lesseq($sum(tb2t(t2tb(Lqt!16)), $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(tb2t(t2tb(Lqt!16)), $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))) <=> ((~![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))) | (~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0)) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | $greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1))),
% 5.18/3.58 inference(transitivity,[status(thm)],[123, 114])).
% 5.18/3.58 tff(125,plain,
% 5.18/3.58 ((~![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))) | ($lesseq($sum(tb2t(t2tb(Lqt!16)), $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(tb2t(t2tb(Lqt!16)), $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))),
% 5.18/3.58 inference(quant_inst,[status(thm)],[])).
% 5.18/3.58 tff(126,plain,
% 5.18/3.58 ((~![Lqt: $int] : ($lesseq($sum(Lqt, $product(-1, L!6)), -1) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, Lqt, $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$lesseq($sum(Lqt, $sum($product(-1, L!6), $product(-1, div($sum($product(-1, L!6), H!5), 2)))), 0)))) | (~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0)) | $greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | $greatereq($sum(L!6, $product(-1, tb2t(t2tb(Lqt!16)))), 1)),
% 5.18/3.58 inference(modus_ponens,[status(thm)],[125, 124])).
% 5.18/3.58 tff(127,plain,
% 5.18/3.58 ($false),
% 5.18/3.58 inference(unit_resolution,[status(thm)],[126, 113, 106, 105, 104])).
% 5.18/3.58 tff(128,plain,($greatereq($sum(Ms!12, $product(-1, sum(A1!7, tb2t(t2tb(Lqt!16)), $sum(L!6, div($sum($product(-1, L!6), H!5), 2))))), 0) | (~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0))), inference(lemma,lemma(discharge,[]))).
% 5.18/3.58 tff(129,plain,
% 5.18/3.58 (~$greatereq($sum(L!6, $sum(div($sum($product(-1, L!6), H!5), 2), $product(-1, tb2t(t2tb(Lqt!16))))), 0)),
% 5.18/3.59 inference(unit_resolution,[status(thm)],[128, 100])).
% 5.18/3.59 tff(130,plain,
% 5.18/3.59 ($false),
% 5.18/3.59 inference(theory_lemma,[status(thm)],[129, 67, 50])).
% 5.18/3.59 % SZS output end Proof
%------------------------------------------------------------------------------