TSTP Solution File: SWW575_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW575_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 20:59:19 EDT 2022
% Result : Theorem 1.62s 1.28s
% Output : Proof 1.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW575_2 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 20:11:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.62/1.28 % SZS status Theorem
% 1.62/1.28 % SZS output start Proof
% 1.62/1.28 tff(get3_type, type, (
% 1.62/1.28 get3: ( map_int_int * $int ) > $int)).
% 1.62/1.28 tff(tptp_fun_R_22_type, type, (
% 1.62/1.28 tptp_fun_R_22: $int)).
% 1.62/1.28 tff(tptp_fun_A3_20_type, type, (
% 1.62/1.28 tptp_fun_A3_20: map_int_int)).
% 1.62/1.28 tff(tptp_fun_N_13_type, type, (
% 1.62/1.28 tptp_fun_N_13: $int)).
% 1.62/1.28 tff(tptp_fun_I_18_type, type, (
% 1.62/1.28 tptp_fun_I_18: $int)).
% 1.62/1.28 tff(tptp_fun_A2_17_type, type, (
% 1.62/1.28 tptp_fun_A2_17: map_int_int)).
% 1.62/1.28 tff(tptp_fun_J_19_type, type, (
% 1.62/1.28 tptp_fun_J_19: $int)).
% 1.62/1.28 tff(tptp_fun_M_14_type, type, (
% 1.62/1.28 tptp_fun_M_14: $int)).
% 1.62/1.28 tff(tptp_fun_K_12_type, type, (
% 1.62/1.28 tptp_fun_K_12: $int)).
% 1.62/1.28 tff(tptp_fun_S_21_type, type, (
% 1.62/1.28 tptp_fun_S_21: $int > $int)).
% 1.62/1.28 tff(permut_sub3_type, type, (
% 1.62/1.28 permut_sub3: ( array_int * array_int * $int * $int ) > $o)).
% 1.62/1.28 tff(mk_array3_type, type, (
% 1.62/1.28 mk_array3: ( $int * map_int_int ) > array_int)).
% 1.62/1.28 tff(tptp_fun_A_16_type, type, (
% 1.62/1.28 tptp_fun_A_16: $int)).
% 1.62/1.28 tff(tptp_fun_A1_15_type, type, (
% 1.62/1.28 tptp_fun_A1_15: map_int_int)).
% 1.62/1.28 tff(1,plain,
% 1.62/1.28 (((~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & ($greatereq(M!14, 0) & (~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))) & ($greatereq(A!16, 0) & $greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, N!13)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))) & ($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0)) & $greatereq(A!16, 0) & $lesseq($sum(M!14, $product(-1, J!19)), 0) & (~$lesseq($sum(I!18, $product(-1, J!19)), 0)) & $greatereq($sum(N!13, $product(-1, I!18)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)) & (~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))) <=> ((~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & $greatereq(M!14, 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0)) & $greatereq(A!16, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, N!13)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0)) & $lesseq($sum(M!14, $product(-1, J!19)), 0) & (~$lesseq($sum(I!18, $product(-1, J!19)), 0)) & $greatereq($sum(N!13, $product(-1, I!18)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)) & (~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(2,plain,
% 1.62/1.28 ((($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0))) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & ($greatereq(A!16, 0) & $lesseq($sum(M!14, $product(-1, J!19)), 0) & (~$lesseq($sum(I!18, $product(-1, J!19)), 0)) & $greatereq($sum(N!13, $product(-1, I!18)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42))) & ((~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & $greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))) <=> ($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0)) & $greatereq(A!16, 0) & $lesseq($sum(M!14, $product(-1, J!19)), 0) & (~$lesseq($sum(I!18, $product(-1, J!19)), 0)) & $greatereq($sum(N!13, $product(-1, I!18)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)) & (~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(3,plain,
% 1.62/1.28 (((~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & ($greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0))) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & ($lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))) <=> ((~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & $greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(4,plain,
% 1.62/1.28 ((($lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0)) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)))) <=> ($lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(5,plain,
% 1.62/1.28 ((![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))) <=> (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(6,plain,
% 1.62/1.28 ((~$greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0)) <=> (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(7,plain,
% 1.62/1.28 ((![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))) <=> (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)))),
% 1.62/1.28 inference(monotonicity,[status(thm)],[6])).
% 1.62/1.28 tff(8,plain,
% 1.62/1.28 ((![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))) <=> (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)))),
% 1.62/1.28 inference(transitivity,[status(thm)],[7, 5])).
% 1.62/1.28 tff(9,plain,
% 1.62/1.28 ((~(~($lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0)))) <=> ($lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(10,plain,
% 1.62/1.28 ((~($greatereq($sum(R!22, $product(-1, I!18)), 0) & $lesseq($sum(R!22, $product(-1, N!13)), 0))) <=> (~($lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0)))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(11,plain,
% 1.62/1.28 ((~(~($greatereq($sum(R!22, $product(-1, I!18)), 0) & $lesseq($sum(R!22, $product(-1, N!13)), 0)))) <=> (~(~($lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0))))),
% 1.62/1.28 inference(monotonicity,[status(thm)],[10])).
% 1.62/1.28 tff(12,plain,
% 1.62/1.28 ((~(~($greatereq($sum(R!22, $product(-1, I!18)), 0) & $lesseq($sum(R!22, $product(-1, N!13)), 0)))) <=> ($lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0))),
% 1.62/1.28 inference(transitivity,[status(thm)],[11, 9])).
% 1.62/1.28 tff(13,plain,
% 1.62/1.28 (((~(~($greatereq($sum(R!22, $product(-1, I!18)), 0) & $lesseq($sum(R!22, $product(-1, N!13)), 0)))) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0)))) <=> (($lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0)) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))),
% 1.62/1.28 inference(monotonicity,[status(thm)],[12, 8])).
% 1.62/1.28 tff(14,plain,
% 1.62/1.28 (((~(~($greatereq($sum(R!22, $product(-1, I!18)), 0) & $lesseq($sum(R!22, $product(-1, N!13)), 0)))) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0)))) <=> ($lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))),
% 1.62/1.28 inference(transitivity,[status(thm)],[13, 4])).
% 1.62/1.28 tff(15,plain,
% 1.62/1.28 (^[R: $int] : rewrite(((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | (($greatereq($sum(tptp_fun_S_21(R), $product(-1, M!14)), 0) & $lesseq($sum(tptp_fun_S_21(R), $product(-1, J!19)), 0) & ($sum(get3(A2!17, tptp_fun_S_21(R)), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) <=> ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))))),
% 1.62/1.28 inference(bind,[status(th)],[])).
% 1.62/1.28 tff(16,plain,
% 1.62/1.28 (![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | (($greatereq($sum(tptp_fun_S_21(R), $product(-1, M!14)), 0) & $lesseq($sum(tptp_fun_S_21(R), $product(-1, J!19)), 0) & ($sum(get3(A2!17, tptp_fun_S_21(R)), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) <=> ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))),
% 1.62/1.28 inference(quant_intro,[status(thm)],[15])).
% 1.62/1.28 tff(17,plain,
% 1.62/1.28 (($greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0))) <=> ($greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(18,plain,
% 1.62/1.28 ((~(~permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) <=> permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(19,plain,
% 1.62/1.28 ((~(~permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) <=> permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(20,plain,
% 1.62/1.28 ((~$lesseq($sum(I!18, $product(-1, K!12)), 0)) <=> (~$greatereq($sum(K!12, $product(-1, I!18)), 0))),
% 1.62/1.28 inference(rewrite,[status(thm)],[])).
% 1.62/1.28 tff(21,plain,
% 1.62/1.28 (((~$lesseq($sum(I!18, $product(-1, K!12)), 0)) & (~(~permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & (~(~permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & ($greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0))) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | (($greatereq($sum(tptp_fun_S_21(R), $product(-1, M!14)), 0) & $lesseq($sum(tptp_fun_S_21(R), $product(-1, J!19)), 0) & ($sum(get3(A2!17, tptp_fun_S_21(R)), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & ((~(~($greatereq($sum(R!22, $product(-1, I!18)), 0) & $lesseq($sum(R!22, $product(-1, N!13)), 0)))) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))))) <=> ((~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & ($greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0))) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & ($lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)))))),
% 1.62/1.28 inference(monotonicity,[status(thm)],[20, 19, 18, 17, 16, 14])).
% 1.62/1.28 tff(22,plain,
% 1.62/1.28 (((~$lesseq($sum(I!18, $product(-1, K!12)), 0)) & (~(~permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & (~(~permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & ($greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0))) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | (($greatereq($sum(tptp_fun_S_21(R), $product(-1, M!14)), 0) & $lesseq($sum(tptp_fun_S_21(R), $product(-1, J!19)), 0) & ($sum(get3(A2!17, tptp_fun_S_21(R)), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & ((~(~($greatereq($sum(R!22, $product(-1, I!18)), 0) & $lesseq($sum(R!22, $product(-1, N!13)), 0)))) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))))) <=> ((~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & $greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))),
% 1.62/1.29 inference(transitivity,[status(thm)],[21, 3])).
% 1.62/1.29 tff(23,plain,
% 1.62/1.29 (($greatereq(A!16, 0) & $greatereq($sum(J!19, $product(-1, M!14)), 0) & (~$greatereq($sum(J!19, $product(-1, I!18)), 0)) & $lesseq($sum(I!18, $product(-1, N!13)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$lesseq($sum(I!18, $product(-1, R)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I!18, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42))) <=> ($greatereq(A!16, 0) & $lesseq($sum(M!14, $product(-1, J!19)), 0) & (~$lesseq($sum(I!18, $product(-1, J!19)), 0)) & $greatereq($sum(N!13, $product(-1, I!18)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)))),
% 1.62/1.29 inference(rewrite,[status(thm)],[])).
% 1.62/1.29 tff(24,plain,
% 1.62/1.29 ((~(~$lesseq($sum(K!12, $product(-1, J!19)), 0))) <=> $lesseq($sum(K!12, $product(-1, J!19)), 0)),
% 1.62/1.29 inference(rewrite,[status(thm)],[])).
% 1.62/1.29 tff(25,plain,
% 1.62/1.29 ((~$greatereq($sum(J!19, $product(-1, K!12)), 0)) <=> (~$lesseq($sum(K!12, $product(-1, J!19)), 0))),
% 1.62/1.29 inference(rewrite,[status(thm)],[])).
% 1.62/1.29 tff(26,plain,
% 1.62/1.29 ((~(~$greatereq($sum(J!19, $product(-1, K!12)), 0))) <=> (~(~$lesseq($sum(K!12, $product(-1, J!19)), 0)))),
% 1.62/1.29 inference(monotonicity,[status(thm)],[25])).
% 1.62/1.29 tff(27,plain,
% 1.62/1.29 ((~(~$greatereq($sum(J!19, $product(-1, K!12)), 0))) <=> $lesseq($sum(K!12, $product(-1, J!19)), 0)),
% 1.62/1.29 inference(transitivity,[status(thm)],[26, 24])).
% 1.62/1.29 tff(28,plain,
% 1.62/1.29 ((~(~($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0))))) <=> ($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0)))),
% 1.62/1.29 inference(rewrite,[status(thm)],[])).
% 1.62/1.29 tff(29,plain,
% 1.62/1.29 ((~($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $greatereq($sum(J!19, $product(-1, K!12)), 0) & (~$greatereq($sum(J!19, $product(-1, A!16)), 0)))) <=> (~($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0))))),
% 1.62/1.29 inference(rewrite,[status(thm)],[])).
% 1.62/1.29 tff(30,plain,
% 1.62/1.29 ((~(~($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $greatereq($sum(J!19, $product(-1, K!12)), 0) & (~$greatereq($sum(J!19, $product(-1, A!16)), 0))))) <=> (~(~($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0)))))),
% 1.62/1.29 inference(monotonicity,[status(thm)],[29])).
% 1.62/1.29 tff(31,plain,
% 1.62/1.29 ((~(~($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $greatereq($sum(J!19, $product(-1, K!12)), 0) & (~$greatereq($sum(J!19, $product(-1, A!16)), 0))))) <=> ($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0)))),
% 1.62/1.29 inference(transitivity,[status(thm)],[30, 28])).
% 1.62/1.29 tff(32,plain,
% 1.62/1.29 (((~(~($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $greatereq($sum(J!19, $product(-1, K!12)), 0) & (~$greatereq($sum(J!19, $product(-1, A!16)), 0))))) & (~(~$greatereq($sum(J!19, $product(-1, K!12)), 0))) & ($greatereq(A!16, 0) & $greatereq($sum(J!19, $product(-1, M!14)), 0) & (~$greatereq($sum(J!19, $product(-1, I!18)), 0)) & $lesseq($sum(I!18, $product(-1, N!13)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$lesseq($sum(I!18, $product(-1, R)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I!18, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42))) & ((~$lesseq($sum(I!18, $product(-1, K!12)), 0)) & (~(~permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & (~(~permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & ($greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0))) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | (($greatereq($sum(tptp_fun_S_21(R), $product(-1, M!14)), 0) & $lesseq($sum(tptp_fun_S_21(R), $product(-1, J!19)), 0) & ($sum(get3(A2!17, tptp_fun_S_21(R)), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & ((~(~($greatereq($sum(R!22, $product(-1, I!18)), 0) & $lesseq($sum(R!22, $product(-1, N!13)), 0)))) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0)))))) <=> (($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0))) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & ($greatereq(A!16, 0) & $lesseq($sum(M!14, $product(-1, J!19)), 0) & (~$lesseq($sum(I!18, $product(-1, J!19)), 0)) & $greatereq($sum(N!13, $product(-1, I!18)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42))) & ((~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & $greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)))))),
% 1.62/1.29 inference(monotonicity,[status(thm)],[31, 27, 23, 22])).
% 1.62/1.29 tff(33,plain,
% 1.62/1.29 (((~(~($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $greatereq($sum(J!19, $product(-1, K!12)), 0) & (~$greatereq($sum(J!19, $product(-1, A!16)), 0))))) & (~(~$greatereq($sum(J!19, $product(-1, K!12)), 0))) & ($greatereq(A!16, 0) & $greatereq($sum(J!19, $product(-1, M!14)), 0) & (~$greatereq($sum(J!19, $product(-1, I!18)), 0)) & $lesseq($sum(I!18, $product(-1, N!13)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$lesseq($sum(I!18, $product(-1, R)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I!18, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42))) & ((~$lesseq($sum(I!18, $product(-1, K!12)), 0)) & (~(~permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & (~(~permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & ($greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0))) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | (($greatereq($sum(tptp_fun_S_21(R), $product(-1, M!14)), 0) & $lesseq($sum(tptp_fun_S_21(R), $product(-1, J!19)), 0) & ($sum(get3(A2!17, tptp_fun_S_21(R)), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & ((~(~($greatereq($sum(R!22, $product(-1, I!18)), 0) & $lesseq($sum(R!22, $product(-1, N!13)), 0)))) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0)))))) <=> ($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0)) & $greatereq(A!16, 0) & $lesseq($sum(M!14, $product(-1, J!19)), 0) & (~$lesseq($sum(I!18, $product(-1, J!19)), 0)) & $greatereq($sum(N!13, $product(-1, I!18)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)) & (~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))),
% 1.62/1.29 inference(transitivity,[status(thm)],[32, 2])).
% 1.62/1.29 tff(34,plain,
% 1.62/1.29 ((~(~($greatereq(A!16, 0) & $greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, N!13)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))) <=> ($greatereq(A!16, 0) & $greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, N!13)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0)))),
% 1.62/1.29 inference(rewrite,[status(thm)],[])).
% 1.62/1.29 tff(35,plain,
% 1.62/1.29 ((~($greatereq(A!16, 0) & $greatereq(M!14, 0) & $lesseq($sum(M!14, $product(-1, K!12)), 0) & $greatereq($sum(N!13, $product(-1, K!12)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0)))) <=> (~($greatereq(A!16, 0) & $greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, N!13)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))),
% 1.62/1.29 inference(rewrite,[status(thm)],[])).
% 1.62/1.29 tff(36,plain,
% 1.62/1.29 ((~(~($greatereq(A!16, 0) & $greatereq(M!14, 0) & $lesseq($sum(M!14, $product(-1, K!12)), 0) & $greatereq($sum(N!13, $product(-1, K!12)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))) <=> (~(~($greatereq(A!16, 0) & $greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, N!13)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0)))))),
% 1.62/1.29 inference(monotonicity,[status(thm)],[35])).
% 1.62/1.29 tff(37,plain,
% 1.62/1.29 ((~(~($greatereq(A!16, 0) & $greatereq(M!14, 0) & $lesseq($sum(M!14, $product(-1, K!12)), 0) & $greatereq($sum(N!13, $product(-1, K!12)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))) <=> ($greatereq(A!16, 0) & $greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, N!13)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0)))),
% 1.62/1.29 inference(transitivity,[status(thm)],[36, 34])).
% 1.62/1.29 tff(38,plain,
% 1.62/1.29 ((~(~($greatereq(M!14, 0) & (~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))) <=> ($greatereq(M!14, 0) & (~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0)))),
% 1.62/1.29 inference(rewrite,[status(thm)],[])).
% 1.62/1.29 tff(39,plain,
% 1.62/1.29 ((~($greatereq(M!14, 0) & (~$greatereq($sum(M!14, $product(-1, N!13)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0)))) <=> (~($greatereq(M!14, 0) & (~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))),
% 1.62/1.29 inference(rewrite,[status(thm)],[])).
% 1.62/1.29 tff(40,plain,
% 1.62/1.29 ((~(~($greatereq(M!14, 0) & (~$greatereq($sum(M!14, $product(-1, N!13)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))) <=> (~(~($greatereq(M!14, 0) & (~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0)))))),
% 1.62/1.29 inference(monotonicity,[status(thm)],[39])).
% 1.62/1.29 tff(41,plain,
% 1.62/1.29 ((~(~($greatereq(M!14, 0) & (~$greatereq($sum(M!14, $product(-1, N!13)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))) <=> ($greatereq(M!14, 0) & (~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0)))),
% 1.62/1.29 inference(transitivity,[status(thm)],[40, 38])).
% 1.62/1.29 tff(42,plain,
% 1.62/1.29 ((~$greatereq($sum(M!14, $product(-1, N!13)), 0)) <=> (~$lesseq($sum(N!13, $product(-1, M!14)), 0))),
% 1.62/1.29 inference(rewrite,[status(thm)],[])).
% 1.62/1.29 tff(43,plain,
% 1.62/1.29 (((~$greatereq($sum(M!14, $product(-1, N!13)), 0)) & (~(~($greatereq(M!14, 0) & (~$greatereq($sum(M!14, $product(-1, N!13)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))) & (~(~($greatereq(A!16, 0) & $greatereq(M!14, 0) & $lesseq($sum(M!14, $product(-1, K!12)), 0) & $greatereq($sum(N!13, $product(-1, K!12)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))) & ((~(~($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $greatereq($sum(J!19, $product(-1, K!12)), 0) & (~$greatereq($sum(J!19, $product(-1, A!16)), 0))))) & (~(~$greatereq($sum(J!19, $product(-1, K!12)), 0))) & ($greatereq(A!16, 0) & $greatereq($sum(J!19, $product(-1, M!14)), 0) & (~$greatereq($sum(J!19, $product(-1, I!18)), 0)) & $lesseq($sum(I!18, $product(-1, N!13)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$lesseq($sum(I!18, $product(-1, R)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I!18, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42))) & ((~$lesseq($sum(I!18, $product(-1, K!12)), 0)) & (~(~permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & (~(~permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & ($greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0))) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | (($greatereq($sum(tptp_fun_S_21(R), $product(-1, M!14)), 0) & $lesseq($sum(tptp_fun_S_21(R), $product(-1, J!19)), 0) & ($sum(get3(A2!17, tptp_fun_S_21(R)), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & ((~(~($greatereq($sum(R!22, $product(-1, I!18)), 0) & $lesseq($sum(R!22, $product(-1, N!13)), 0)))) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))))))) <=> ((~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & ($greatereq(M!14, 0) & (~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))) & ($greatereq(A!16, 0) & $greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, N!13)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))) & ($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0)) & $greatereq(A!16, 0) & $lesseq($sum(M!14, $product(-1, J!19)), 0) & (~$lesseq($sum(I!18, $product(-1, J!19)), 0)) & $greatereq($sum(N!13, $product(-1, I!18)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)) & (~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)))))),
% 1.62/1.29 inference(monotonicity,[status(thm)],[42, 41, 37, 33])).
% 1.62/1.29 tff(44,plain,
% 1.62/1.29 (((~$greatereq($sum(M!14, $product(-1, N!13)), 0)) & (~(~($greatereq(M!14, 0) & (~$greatereq($sum(M!14, $product(-1, N!13)), 0)) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))) & (~(~($greatereq(A!16, 0) & $greatereq(M!14, 0) & $lesseq($sum(M!14, $product(-1, K!12)), 0) & $greatereq($sum(N!13, $product(-1, K!12)), 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0))))) & ((~(~($greatereq(M!14, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $greatereq($sum(J!19, $product(-1, K!12)), 0) & (~$greatereq($sum(J!19, $product(-1, A!16)), 0))))) & (~(~$greatereq($sum(J!19, $product(-1, K!12)), 0))) & ($greatereq(A!16, 0) & $greatereq($sum(J!19, $product(-1, M!14)), 0) & (~$greatereq($sum(J!19, $product(-1, I!18)), 0)) & $lesseq($sum(I!18, $product(-1, N!13)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$lesseq($sum(I!18, $product(-1, R)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I!18, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42))) & ((~$lesseq($sum(I!18, $product(-1, K!12)), 0)) & (~(~permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & (~(~permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)))) & ($greatereq(A!16, 0) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0))) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | (($greatereq($sum(tptp_fun_S_21(R), $product(-1, M!14)), 0) & $lesseq($sum(tptp_fun_S_21(R), $product(-1, J!19)), 0) & ($sum(get3(A2!17, tptp_fun_S_21(R)), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & ((~(~($greatereq($sum(R!22, $product(-1, I!18)), 0) & $lesseq($sum(R!22, $product(-1, N!13)), 0)))) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))))))) <=> ((~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & $greatereq(M!14, 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0)) & $greatereq(A!16, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, N!13)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0)) & $lesseq($sum(M!14, $product(-1, J!19)), 0) & (~$lesseq($sum(I!18, $product(-1, J!19)), 0)) & $greatereq($sum(N!13, $product(-1, I!18)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)) & (~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))))),
% 1.62/1.29 inference(transitivity,[status(thm)],[43, 1])).
% 1.62/1.29 tff(45,plain,
% 1.62/1.29 ((~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $greatereq($sum(N, $product(-1, K)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : ((~($greatereq(M, 0) & $greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~$greatereq($sum(J, $product(-1, K)), 0)) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42)))) | ![A3: map_int_int] : ($lesseq($sum(I, $product(-1, K)), 0) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, K)), 0))) | $lesseq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $greatereq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)))) | (~![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, M)), 0) & $lesseq($sum(S, $product(-1, J)), 0) & ($sum(get3(A2, S), $product(-1, get3(A3, R))) = 0)) & $lesseq($sum(get3(A3, R), $product(-1, get3(A3, $sum(1, J)))), 0)))) | (~![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & $lesseq($sum(R, $product(-1, N)), 0))) | ($sum(get3(A2, R), $product(-1, get3(A3, R))) = 0))) | ![R: $int] : ((~($greatereq($sum(R, $product(-1, I)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, I)), 0) & $lesseq($sum(S, $product(-1, N)), 0) & ($sum(get3(A3, S), $product(-1, get3(A3, R))) = 0)) & $greatereq($sum(get3(A3, R), $product(-1, get3(A3, $sum(-1, I)))), 0))))))) <=> (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $greatereq($sum(N, $product(-1, K)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : ((~($greatereq(M, 0) & $greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~$greatereq($sum(J, $product(-1, K)), 0)) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42)))) | ![A3: map_int_int] : ($lesseq($sum(I, $product(-1, K)), 0) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, K)), 0))) | $lesseq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $greatereq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)))) | (~![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, M)), 0) & $lesseq($sum(S, $product(-1, J)), 0) & ($sum(get3(A2, S), $product(-1, get3(A3, R))) = 0)) & $lesseq($sum(get3(A3, R), $product(-1, get3(A3, $sum(1, J)))), 0)))) | (~![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & $lesseq($sum(R, $product(-1, N)), 0))) | ($sum(get3(A2, R), $product(-1, get3(A3, R))) = 0))) | ![R: $int] : ((~($greatereq($sum(R, $product(-1, I)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, I)), 0) & $lesseq($sum(S, $product(-1, N)), 0) & ($sum(get3(A3, S), $product(-1, get3(A3, R))) = 0)) & $greatereq($sum(get3(A3, R), $product(-1, get3(A3, $sum(-1, I)))), 0)))))))),
% 1.62/1.29 inference(rewrite,[status(thm)],[])).
% 1.62/1.29 tff(46,plain,
% 1.62/1.29 ((~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($lesseq($sum(N, $product(-1, M)), 0) | (~($greatereq(M, 0) & (~$lesseq($sum(N, $product(-1, M)), 0)) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, N)), 0) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ($lesseq($sum(I, $product(-1, K)), 0) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | (~![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | (?[S: $int] : ($lesseq($sum(M, $product(-1, S)), 0) & $lesseq($sum(S, $product(-1, J)), 0) & ($sum(get3(A3, R), $product(-1, get3(A2, S))) = 0)) & $lesseq($sum(get3(A3, R), $product(-1, get3(A3, $sum(1, J)))), 0)))) | ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | (?[S: $int] : ($lesseq($sum(I, $product(-1, S)), 0) & $lesseq($sum(S, $product(-1, N)), 0) & ($sum(get3(A3, R), $product(-1, get3(A3, S))) = 0)) & $lesseq($sum(get3(A3, $sum(-1, I)), $product(-1, get3(A3, R))), 0))) | (~![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & $lesseq($sum(R, $product(-1, N)), 0))) | ($sum(get3(A3, R), $product(-1, get3(A2, R))) = 0))) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, K)), 0))) | $lesseq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)) & ![R: $int] : ((~($lesseq($sum(K, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq($sum(get3(A3, K), $product(-1, get3(A3, R))), 0))))) | (~$lesseq($sum(K, $product(-1, J)), 0)) | (~($greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, J)), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(A, 0) & $lesseq($sum(M, $product(-1, J)), 0) & (~$lesseq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42))))))) <=> (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $greatereq($sum(N, $product(-1, K)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : ((~($greatereq(M, 0) & $greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~$greatereq($sum(J, $product(-1, K)), 0)) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42)))) | ![A3: map_int_int] : ($lesseq($sum(I, $product(-1, K)), 0) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, K)), 0))) | $lesseq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $greatereq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)))) | (~![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, M)), 0) & $lesseq($sum(S, $product(-1, J)), 0) & ($sum(get3(A2, S), $product(-1, get3(A3, R))) = 0)) & $lesseq($sum(get3(A3, R), $product(-1, get3(A3, $sum(1, J)))), 0)))) | (~![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & $lesseq($sum(R, $product(-1, N)), 0))) | ($sum(get3(A2, R), $product(-1, get3(A3, R))) = 0))) | ![R: $int] : ((~($greatereq($sum(R, $product(-1, I)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, I)), 0) & $lesseq($sum(S, $product(-1, N)), 0) & ($sum(get3(A3, S), $product(-1, get3(A3, R))) = 0)) & $greatereq($sum(get3(A3, R), $product(-1, get3(A3, $sum(-1, I)))), 0)))))))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(47,plain,
% 1.62/1.30 ((~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ($lesseq(I, K) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | (?[S: $int] : ($lesseq(I, S) & $lesseq(S, N) & (get3(A3, R) = get3(A3, S))) & $lesseq(get3(A3, $sum(-1, I)), get3(A3, R)))) | (~![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | (?[S: $int] : ($lesseq(M, S) & $lesseq(S, J) & (get3(A3, R) = get3(A2, S))) & $lesseq(get3(A3, R), get3(A3, $sum(1, J)))))) | (~![R: $int] : ((~((~$lesseq(R, J)) & $lesseq(R, N))) | (get3(A3, R) = get3(A2, R)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, K))) | $lesseq(get3(A3, R), get3(A3, K))) & ![R: $int] : ((~($lesseq(K, R) & $lesseq(R, J))) | $lesseq(get3(A3, K), get3(A3, R)))))) | (~($lesseq(0, M) & $lesseq(M, K) & $lesseq(K, J) & (~$lesseq(A, J)))) | (~$lesseq(K, J)) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, K) & $lesseq(K, N) & (~$lesseq(A, N)))))) <=> (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($lesseq($sum(N, $product(-1, M)), 0) | (~($greatereq(M, 0) & (~$lesseq($sum(N, $product(-1, M)), 0)) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, N)), 0) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ($lesseq($sum(I, $product(-1, K)), 0) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | (~![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | (?[S: $int] : ($lesseq($sum(M, $product(-1, S)), 0) & $lesseq($sum(S, $product(-1, J)), 0) & ($sum(get3(A3, R), $product(-1, get3(A2, S))) = 0)) & $lesseq($sum(get3(A3, R), $product(-1, get3(A3, $sum(1, J)))), 0)))) | ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | (?[S: $int] : ($lesseq($sum(I, $product(-1, S)), 0) & $lesseq($sum(S, $product(-1, N)), 0) & ($sum(get3(A3, R), $product(-1, get3(A3, S))) = 0)) & $lesseq($sum(get3(A3, $sum(-1, I)), $product(-1, get3(A3, R))), 0))) | (~![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & $lesseq($sum(R, $product(-1, N)), 0))) | ($sum(get3(A3, R), $product(-1, get3(A2, R))) = 0))) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, K)), 0))) | $lesseq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)) & ![R: $int] : ((~($lesseq($sum(K, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq($sum(get3(A3, K), $product(-1, get3(A3, R))), 0))))) | (~$lesseq($sum(K, $product(-1, J)), 0)) | (~($greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, J)), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(A, 0) & $lesseq($sum(M, $product(-1, J)), 0) & (~$lesseq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42)))))))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(48,plain,
% 1.62/1.30 ((~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ($lesseq(I, K) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | (?[S: $int] : ($lesseq(I, S) & $lesseq(S, N) & (get3(A3, R) = get3(A3, S))) & $lesseq(get3(A3, $sum(-1, I)), get3(A3, R)))) | (~![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | (?[S: $int] : ($lesseq(M, S) & $lesseq(S, J) & (get3(A3, R) = get3(A2, S))) & $lesseq(get3(A3, R), get3(A3, $sum(1, J)))))) | (~![R: $int] : ((~((~$lesseq(R, J)) & $lesseq(R, N))) | (get3(A3, R) = get3(A2, R)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, K))) | $lesseq(get3(A3, R), get3(A3, K))) & ![R: $int] : ((~($lesseq(K, R) & $lesseq(R, J))) | $lesseq(get3(A3, K), get3(A3, R)))))) | (~($lesseq(0, M) & $lesseq(M, K) & $lesseq(K, J) & (~$lesseq(A, J)))) | (~$lesseq(K, J)) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, K) & $lesseq(K, N) & (~$lesseq(A, N)))))) <=> (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ($lesseq(I, K) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | (?[S: $int] : ($lesseq(I, S) & $lesseq(S, N) & (get3(A3, R) = get3(A3, S))) & $lesseq(get3(A3, $sum(-1, I)), get3(A3, R)))) | (~![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | (?[S: $int] : ($lesseq(M, S) & $lesseq(S, J) & (get3(A3, R) = get3(A2, S))) & $lesseq(get3(A3, R), get3(A3, $sum(1, J)))))) | (~![R: $int] : ((~((~$lesseq(R, J)) & $lesseq(R, N))) | (get3(A3, R) = get3(A2, R)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, K))) | $lesseq(get3(A3, R), get3(A3, K))) & ![R: $int] : ((~($lesseq(K, R) & $lesseq(R, J))) | $lesseq(get3(A3, K), get3(A3, R)))))) | (~($lesseq(0, M) & $lesseq(M, K) & $lesseq(K, J) & (~$lesseq(A, J)))) | (~$lesseq(K, J)) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, K) & $lesseq(K, N) & (~$lesseq(A, N))))))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(49,plain,
% 1.62/1.30 ((~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ((((($lesseq(0, A) & $lesseq(0, M)) & $lesseq(M, K)) & $lesseq(K, N)) & $less(N, A)) => ($less(M, N) => ((($lesseq(0, M) & $less(M, N)) & $less(N, A)) => ![J: $int, I: $int, A2: map_int_int] : (((((((($lesseq(0, A) & $lesseq(M, J)) & $less(J, I)) & $lesseq(I, N)) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(N, 1))) & ![R: $int] : (($lesseq(M, R) & $lesseq(R, J)) => $lesseq(get3(A2, R), 42))) & ![R: $int] : (($less(J, R) & $less(R, I)) => (get3(A2, R) = 42))) & ![R: $int] : (($lesseq(I, R) & $lesseq(R, N)) => $lesseq(42, get3(A2, R)))) => ($lesseq(K, J) => (((($lesseq(0, M) & $lesseq(M, K)) & $lesseq(K, J)) & $less(J, A)) => ![A3: map_int_int] : (((($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(J, 1))) & ![R: $int] : (($lesseq(M, R) & $lesseq(R, K)) => $lesseq(get3(A3, R), get3(A3, K)))) & ![R: $int] : (($lesseq(K, R) & $lesseq(R, J)) => $lesseq(get3(A3, K), get3(A3, R)))) => (permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(N, 1)) => (![R: $int] : (($less(J, R) & $lesseq(R, N)) => (get3(A3, R) = get3(A2, R))) => (![R: $int] : (($lesseq(M, R) & $lesseq(R, J)) => (?[S: $int] : (($lesseq(M, S) & $lesseq(S, J)) & (get3(A3, R) = get3(A2, S))) & $lesseq(get3(A3, R), get3(A3, $sum(J, 1))))) => ((~$lesseq(I, K)) => (permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(N, 1)) => ![R: $int] : (($lesseq(I, R) & $lesseq(R, N)) => (?[S: $int] : (($lesseq(I, S) & $lesseq(S, N)) & (get3(A3, R) = get3(A3, S))) & $lesseq(get3(A3, $difference(I, 1)), get3(A3, R))))))))))))))))) <=> (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ($lesseq(I, K) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | (?[S: $int] : ($lesseq(I, S) & $lesseq(S, N) & (get3(A3, R) = get3(A3, S))) & $lesseq(get3(A3, $sum(-1, I)), get3(A3, R)))) | (~![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | (?[S: $int] : ($lesseq(M, S) & $lesseq(S, J) & (get3(A3, R) = get3(A2, S))) & $lesseq(get3(A3, R), get3(A3, $sum(1, J)))))) | (~![R: $int] : ((~((~$lesseq(R, J)) & $lesseq(R, N))) | (get3(A3, R) = get3(A2, R)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, K))) | $lesseq(get3(A3, R), get3(A3, K))) & ![R: $int] : ((~($lesseq(K, R) & $lesseq(R, J))) | $lesseq(get3(A3, K), get3(A3, R)))))) | (~($lesseq(0, M) & $lesseq(M, K) & $lesseq(K, J) & (~$lesseq(A, J)))) | (~$lesseq(K, J)) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, K) & $lesseq(K, N) & (~$lesseq(A, N))))))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(50,axiom,(~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ((((($lesseq(0, A) & $lesseq(0, M)) & $lesseq(M, K)) & $lesseq(K, N)) & $less(N, A)) => ($less(M, N) => ((($lesseq(0, M) & $less(M, N)) & $less(N, A)) => ![J: $int, I: $int, A2: map_int_int] : (((((((($lesseq(0, A) & $lesseq(M, J)) & $less(J, I)) & $lesseq(I, N)) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(N, 1))) & ![R: $int] : (($lesseq(M, R) & $lesseq(R, J)) => $lesseq(get3(A2, R), 42))) & ![R: $int] : (($less(J, R) & $less(R, I)) => (get3(A2, R) = 42))) & ![R: $int] : (($lesseq(I, R) & $lesseq(R, N)) => $lesseq(42, get3(A2, R)))) => ($lesseq(K, J) => (((($lesseq(0, M) & $lesseq(M, K)) & $lesseq(K, J)) & $less(J, A)) => ![A3: map_int_int] : (((($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(J, 1))) & ![R: $int] : (($lesseq(M, R) & $lesseq(R, K)) => $lesseq(get3(A3, R), get3(A3, K)))) & ![R: $int] : (($lesseq(K, R) & $lesseq(R, J)) => $lesseq(get3(A3, K), get3(A3, R)))) => (permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(N, 1)) => (![R: $int] : (($less(J, R) & $lesseq(R, N)) => (get3(A3, R) = get3(A2, R))) => (![R: $int] : (($lesseq(M, R) & $lesseq(R, J)) => (?[S: $int] : (($lesseq(M, S) & $lesseq(S, J)) & (get3(A3, R) = get3(A2, S))) & $lesseq(get3(A3, R), get3(A3, $sum(J, 1))))) => ((~$lesseq(I, K)) => (permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(N, 1)) => ![R: $int] : (($lesseq(I, R) & $lesseq(R, N)) => (?[S: $int] : (($lesseq(I, S) & $lesseq(S, N)) & (get3(A3, R) = get3(A3, S))) & $lesseq(get3(A3, $difference(I, 1)), get3(A3, R))))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_find')).
% 1.62/1.30 tff(51,plain,
% 1.62/1.30 (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ($lesseq(I, K) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | (?[S: $int] : ($lesseq(I, S) & $lesseq(S, N) & (get3(A3, R) = get3(A3, S))) & $lesseq(get3(A3, $sum(-1, I)), get3(A3, R)))) | (~![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | (?[S: $int] : ($lesseq(M, S) & $lesseq(S, J) & (get3(A3, R) = get3(A2, S))) & $lesseq(get3(A3, R), get3(A3, $sum(1, J)))))) | (~![R: $int] : ((~((~$lesseq(R, J)) & $lesseq(R, N))) | (get3(A3, R) = get3(A2, R)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, K))) | $lesseq(get3(A3, R), get3(A3, K))) & ![R: $int] : ((~($lesseq(K, R) & $lesseq(R, J))) | $lesseq(get3(A3, K), get3(A3, R)))))) | (~($lesseq(0, M) & $lesseq(M, K) & $lesseq(K, J) & (~$lesseq(A, J)))) | (~$lesseq(K, J)) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, K) & $lesseq(K, N) & (~$lesseq(A, N)))))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.62/1.30 tff(52,plain,
% 1.62/1.30 (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ($lesseq(I, K) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | (?[S: $int] : ($lesseq(I, S) & $lesseq(S, N) & (get3(A3, R) = get3(A3, S))) & $lesseq(get3(A3, $sum(-1, I)), get3(A3, R)))) | (~![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | (?[S: $int] : ($lesseq(M, S) & $lesseq(S, J) & (get3(A3, R) = get3(A2, S))) & $lesseq(get3(A3, R), get3(A3, $sum(1, J)))))) | (~![R: $int] : ((~((~$lesseq(R, J)) & $lesseq(R, N))) | (get3(A3, R) = get3(A2, R)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, K))) | $lesseq(get3(A3, R), get3(A3, K))) & ![R: $int] : ((~($lesseq(K, R) & $lesseq(R, J))) | $lesseq(get3(A3, K), get3(A3, R)))))) | (~($lesseq(0, M) & $lesseq(M, K) & $lesseq(K, J) & (~$lesseq(A, J)))) | (~$lesseq(K, J)) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, K) & $lesseq(K, N) & (~$lesseq(A, N)))))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[51, 48])).
% 1.62/1.30 tff(53,plain,
% 1.62/1.30 (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ($lesseq(I, K) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | (?[S: $int] : ($lesseq(I, S) & $lesseq(S, N) & (get3(A3, R) = get3(A3, S))) & $lesseq(get3(A3, $sum(-1, I)), get3(A3, R)))) | (~![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | (?[S: $int] : ($lesseq(M, S) & $lesseq(S, J) & (get3(A3, R) = get3(A2, S))) & $lesseq(get3(A3, R), get3(A3, $sum(1, J)))))) | (~![R: $int] : ((~((~$lesseq(R, J)) & $lesseq(R, N))) | (get3(A3, R) = get3(A2, R)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, K))) | $lesseq(get3(A3, R), get3(A3, K))) & ![R: $int] : ((~($lesseq(K, R) & $lesseq(R, J))) | $lesseq(get3(A3, K), get3(A3, R)))))) | (~($lesseq(0, M) & $lesseq(M, K) & $lesseq(K, J) & (~$lesseq(A, J)))) | (~$lesseq(K, J)) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, K) & $lesseq(K, N) & (~$lesseq(A, N)))))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.62/1.30 tff(54,plain,
% 1.62/1.30 (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($lesseq(N, M) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ($lesseq(I, K) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | (?[S: $int] : ($lesseq(I, S) & $lesseq(S, N) & (get3(A3, R) = get3(A3, S))) & $lesseq(get3(A3, $sum(-1, I)), get3(A3, R)))) | (~![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | (?[S: $int] : ($lesseq(M, S) & $lesseq(S, J) & (get3(A3, R) = get3(A2, S))) & $lesseq(get3(A3, R), get3(A3, $sum(1, J)))))) | (~![R: $int] : ((~((~$lesseq(R, J)) & $lesseq(R, N))) | (get3(A3, R) = get3(A2, R)))) | (~($lesseq(0, A) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, K))) | $lesseq(get3(A3, R), get3(A3, K))) & ![R: $int] : ((~($lesseq(K, R) & $lesseq(R, J))) | $lesseq(get3(A3, K), get3(A3, R)))))) | (~($lesseq(0, M) & $lesseq(M, K) & $lesseq(K, J) & (~$lesseq(A, J)))) | (~$lesseq(K, J)) | (~($lesseq(0, A) & $lesseq(M, J) & (~$lesseq(I, J)) & $lesseq(I, N) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq(M, R) & $lesseq(R, J))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq(R, J)) & (~$lesseq(I, R)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq(I, R) & $lesseq(R, N))) | $lesseq(42, get3(A2, R)))))) | (~($lesseq(0, M) & (~$lesseq(N, M)) & (~$lesseq(A, N)))) | (~($lesseq(0, A) & $lesseq(0, M) & $lesseq(M, K) & $lesseq(K, N) & (~$lesseq(A, N)))))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[53, 48])).
% 1.62/1.30 tff(55,plain,
% 1.62/1.30 (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($lesseq($sum(N, $product(-1, M)), 0) | (~($greatereq(M, 0) & (~$lesseq($sum(N, $product(-1, M)), 0)) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, N)), 0) & (~$lesseq($sum(A, $product(-1, N)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : (![A3: map_int_int] : ($lesseq($sum(I, $product(-1, K)), 0) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | (~![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | (?[S: $int] : ($lesseq($sum(M, $product(-1, S)), 0) & $lesseq($sum(S, $product(-1, J)), 0) & ($sum(get3(A3, R), $product(-1, get3(A2, S))) = 0)) & $lesseq($sum(get3(A3, R), $product(-1, get3(A3, $sum(1, J)))), 0)))) | ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | (?[S: $int] : ($lesseq($sum(I, $product(-1, S)), 0) & $lesseq($sum(S, $product(-1, N)), 0) & ($sum(get3(A3, R), $product(-1, get3(A3, S))) = 0)) & $lesseq($sum(get3(A3, $sum(-1, I)), $product(-1, get3(A3, R))), 0))) | (~![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & $lesseq($sum(R, $product(-1, N)), 0))) | ($sum(get3(A3, R), $product(-1, get3(A2, R))) = 0))) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, K)), 0))) | $lesseq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)) & ![R: $int] : ((~($lesseq($sum(K, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq($sum(get3(A3, K), $product(-1, get3(A3, R))), 0))))) | (~$lesseq($sum(K, $product(-1, J)), 0)) | (~($greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, J)), 0) & (~$lesseq($sum(A, $product(-1, J)), 0)))) | (~($greatereq(A, 0) & $lesseq($sum(M, $product(-1, J)), 0) & (~$lesseq($sum(I, $product(-1, J)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42))))))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.62/1.30 tff(56,plain,
% 1.62/1.30 (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $greatereq($sum(N, $product(-1, K)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : ((~($greatereq(M, 0) & $greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~$greatereq($sum(J, $product(-1, K)), 0)) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42)))) | ![A3: map_int_int] : ($lesseq($sum(I, $product(-1, K)), 0) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, K)), 0))) | $lesseq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $greatereq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)))) | (~![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, M)), 0) & $lesseq($sum(S, $product(-1, J)), 0) & ($sum(get3(A2, S), $product(-1, get3(A3, R))) = 0)) & $lesseq($sum(get3(A3, R), $product(-1, get3(A3, $sum(1, J)))), 0)))) | (~![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & $lesseq($sum(R, $product(-1, N)), 0))) | ($sum(get3(A2, R), $product(-1, get3(A3, R))) = 0))) | ![R: $int] : ((~($greatereq($sum(R, $product(-1, I)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, I)), 0) & $lesseq($sum(S, $product(-1, N)), 0) & ($sum(get3(A3, S), $product(-1, get3(A3, R))) = 0)) & $greatereq($sum(get3(A3, R), $product(-1, get3(A3, $sum(-1, I)))), 0))))))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[55, 46])).
% 1.62/1.30 tff(57,plain,
% 1.62/1.30 (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $greatereq($sum(N, $product(-1, K)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : ((~($greatereq(M, 0) & $greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~$greatereq($sum(J, $product(-1, K)), 0)) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42)))) | ![A3: map_int_int] : ($lesseq($sum(I, $product(-1, K)), 0) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, K)), 0))) | $lesseq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $greatereq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)))) | (~![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, M)), 0) & $lesseq($sum(S, $product(-1, J)), 0) & ($sum(get3(A2, S), $product(-1, get3(A3, R))) = 0)) & $lesseq($sum(get3(A3, R), $product(-1, get3(A3, $sum(1, J)))), 0)))) | (~![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & $lesseq($sum(R, $product(-1, N)), 0))) | ($sum(get3(A2, R), $product(-1, get3(A3, R))) = 0))) | ![R: $int] : ((~($greatereq($sum(R, $product(-1, I)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, I)), 0) & $lesseq($sum(S, $product(-1, N)), 0) & ($sum(get3(A3, S), $product(-1, get3(A3, R))) = 0)) & $greatereq($sum(get3(A3, R), $product(-1, get3(A3, $sum(-1, I)))), 0))))))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[56, 45])).
% 1.62/1.30 tff(58,plain,
% 1.62/1.30 (~![A: $int, A1: map_int_int, M: $int, N: $int, K: $int] : ($greatereq($sum(M, $product(-1, N)), 0) | (~($greatereq(M, 0) & (~$greatereq($sum(M, $product(-1, N)), 0)) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | (~($greatereq(A, 0) & $greatereq(M, 0) & $lesseq($sum(M, $product(-1, K)), 0) & $greatereq($sum(N, $product(-1, K)), 0) & (~$greatereq($sum(N, $product(-1, A)), 0)))) | ![J: $int, I: $int, A2: map_int_int] : ((~($greatereq(M, 0) & $greatereq($sum(K, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, K)), 0) & (~$greatereq($sum(J, $product(-1, A)), 0)))) | (~$greatereq($sum(J, $product(-1, K)), 0)) | (~($greatereq(A, 0) & $greatereq($sum(J, $product(-1, M)), 0) & (~$greatereq($sum(J, $product(-1, I)), 0)) & $lesseq($sum(I, $product(-1, N)), 0) & permut_sub3(mk_array3(A, A1), mk_array3(A, A2), M, $sum(1, N)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $lesseq(get3(A2, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & (~$lesseq($sum(I, $product(-1, R)), 0)))) | (get3(A2, R) = 42)) & ![R: $int] : ((~($lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | $greatereq(get3(A2, R), 42)))) | ![A3: map_int_int] : ($lesseq($sum(I, $product(-1, K)), 0) | (~permut_sub3(mk_array3(A, A3), mk_array3(A, A3), M, $sum(1, N))) | (~permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, N))) | (~($greatereq(A, 0) & permut_sub3(mk_array3(A, A2), mk_array3(A, A3), M, $sum(1, J)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, K)), 0))) | $lesseq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | $greatereq($sum(get3(A3, R), $product(-1, get3(A3, K))), 0)))) | (~![R: $int] : ((~($greatereq($sum(R, $product(-1, M)), 0) & $lesseq($sum(R, $product(-1, J)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, M)), 0) & $lesseq($sum(S, $product(-1, J)), 0) & ($sum(get3(A2, S), $product(-1, get3(A3, R))) = 0)) & $lesseq($sum(get3(A3, R), $product(-1, get3(A3, $sum(1, J)))), 0)))) | (~![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J)), 0)) & $lesseq($sum(R, $product(-1, N)), 0))) | ($sum(get3(A2, R), $product(-1, get3(A3, R))) = 0))) | ![R: $int] : ((~($greatereq($sum(R, $product(-1, I)), 0) & $lesseq($sum(R, $product(-1, N)), 0))) | (?[S: $int] : ($greatereq($sum(S, $product(-1, I)), 0) & $lesseq($sum(S, $product(-1, N)), 0) & ($sum(get3(A3, S), $product(-1, get3(A3, R))) = 0)) & $greatereq($sum(get3(A3, R), $product(-1, get3(A3, $sum(-1, I)))), 0))))))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[57, 45])).
% 1.62/1.30 tff(59,plain,
% 1.62/1.30 ((~$lesseq($sum(N!13, $product(-1, M!14)), 0)) & $greatereq(M!14, 0) & (~$greatereq($sum(N!13, $product(-1, A!16)), 0)) & $greatereq(A!16, 0) & $greatereq($sum(K!12, $product(-1, M!14)), 0) & $lesseq($sum(K!12, $product(-1, N!13)), 0) & $lesseq($sum(K!12, $product(-1, J!19)), 0) & (~$lesseq($sum(A!16, $product(-1, J!19)), 0)) & $lesseq($sum(M!14, $product(-1, J!19)), 0) & (~$lesseq($sum(I!18, $product(-1, J!19)), 0)) & $greatereq($sum(N!13, $product(-1, I!18)), 0) & permut_sub3(mk_array3(A!16, A1!15), mk_array3(A!16, A2!17), M!14, $sum(1, N!13)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)) & (~$greatereq($sum(K!12, $product(-1, I!18)), 0)) & permut_sub3(mk_array3(A!16, A3!20), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, N!13)) & permut_sub3(mk_array3(A!16, A2!17), mk_array3(A!16, A3!20), M!14, $sum(1, J!19)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, K!12)), 0))) | $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, K!12)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $greatereq($sum(get3(A3!20, R), $product(-1, get3(A3!20, K!12))), 0)) & ![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) & ![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) & $lesseq($sum(I!18, $product(-1, R!22)), 0) & $greatereq($sum(N!13, $product(-1, R!22)), 0) & (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[58, 44])).
% 1.62/1.30 tff(60,plain,
% 1.62/1.30 ($greatereq($sum(K!12, $product(-1, M!14)), 0)),
% 1.62/1.30 inference(and_elim,[status(thm)],[59])).
% 1.62/1.30 tff(61,plain,
% 1.62/1.30 (~$lesseq($sum(I!18, $product(-1, J!19)), 0)),
% 1.62/1.30 inference(and_elim,[status(thm)],[59])).
% 1.62/1.30 tff(62,plain,
% 1.62/1.30 ($lesseq($sum(K!12, $product(-1, J!19)), 0)),
% 1.62/1.30 inference(and_elim,[status(thm)],[59])).
% 1.62/1.30 tff(63,plain,
% 1.62/1.30 ($lesseq($sum(M!14, $product(-1, I!18)), -1) | (~$greatereq($sum(K!12, $product(-1, M!14)), 0)) | (~$lesseq($sum(K!12, $product(-1, J!19)), 0)) | $lesseq($sum(I!18, $product(-1, J!19)), 0)),
% 1.62/1.30 inference(theory_lemma,[status(thm)],[])).
% 1.62/1.30 tff(64,plain,
% 1.62/1.30 ($lesseq($sum(M!14, $product(-1, I!18)), -1)),
% 1.62/1.30 inference(unit_resolution,[status(thm)],[63, 62, 61, 60])).
% 1.62/1.30 tff(65,assumption,(~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)), introduced(assumption)).
% 1.62/1.30 tff(66,assumption,(~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0)))), introduced(assumption)).
% 1.62/1.30 tff(67,plain,
% 1.62/1.30 (((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))) | $greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)),
% 1.62/1.30 inference(tautology,[status(thm)],[])).
% 1.62/1.30 tff(68,plain,
% 1.62/1.30 ($greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)),
% 1.62/1.30 inference(unit_resolution,[status(thm)],[67, 66])).
% 1.62/1.30 tff(69,plain,
% 1.62/1.30 (((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))) | $lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)),
% 1.62/1.30 inference(tautology,[status(thm)],[])).
% 1.62/1.30 tff(70,plain,
% 1.62/1.30 ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)),
% 1.62/1.30 inference(unit_resolution,[status(thm)],[69, 66])).
% 1.62/1.30 tff(71,plain,
% 1.62/1.30 (^[R: $int] : refl(($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))) <=> ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))))),
% 1.62/1.30 inference(bind,[status(th)],[])).
% 1.62/1.30 tff(72,plain,
% 1.62/1.30 (![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))) <=> ![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))),
% 1.62/1.30 inference(quant_intro,[status(thm)],[71])).
% 1.62/1.30 tff(73,plain,
% 1.62/1.30 (^[R: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0)) <=> (~((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))))), ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) <=> (~(~((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))))))), rewrite((~(~((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))))) <=> ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))), ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) <=> ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))))), (((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) <=> (((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))) | $lesseq(get3(A2!17, R), 42)))), rewrite((((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))) | $lesseq(get3(A2!17, R), 42)) <=> ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))), (((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) <=> ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))))),
% 1.62/1.30 inference(bind,[status(th)],[])).
% 1.62/1.30 tff(74,plain,
% 1.62/1.30 (![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42)) <=> ![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))),
% 1.62/1.30 inference(quant_intro,[status(thm)],[73])).
% 1.62/1.30 tff(75,plain,
% 1.62/1.30 (![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | $lesseq(get3(A2!17, R), 42))),
% 1.62/1.30 inference(and_elim,[status(thm)],[59])).
% 1.62/1.30 tff(76,plain,
% 1.62/1.30 (![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.62/1.30 tff(77,plain,
% 1.62/1.30 (![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[76, 72])).
% 1.62/1.30 tff(78,plain,
% 1.62/1.30 (((~![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))) | ((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | $lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42))) <=> ((~![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))) | (~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | $lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(79,plain,
% 1.62/1.30 (($lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0))) <=> ((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | $lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(80,plain,
% 1.62/1.30 ((~$greatereq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, M!14)), 0)) <=> (~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(81,plain,
% 1.62/1.30 ((~$lesseq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, J!19)), 0)) <=> (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(82,plain,
% 1.62/1.30 (($lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42) | (~$lesseq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, J!19)), 0)) | (~$greatereq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, M!14)), 0))) <=> ($lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)))),
% 1.62/1.30 inference(monotonicity,[status(thm)],[81, 80])).
% 1.62/1.30 tff(83,plain,
% 1.62/1.30 (($lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42) | (~$lesseq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, J!19)), 0)) | (~$greatereq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, M!14)), 0))) <=> ((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | $lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42))),
% 1.62/1.30 inference(transitivity,[status(thm)],[82, 79])).
% 1.62/1.30 tff(84,plain,
% 1.62/1.30 (((~![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))) | ($lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42) | (~$lesseq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, J!19)), 0)) | (~$greatereq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, M!14)), 0)))) <=> ((~![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))) | ((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | $lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42)))),
% 1.62/1.30 inference(monotonicity,[status(thm)],[83])).
% 1.62/1.30 tff(85,plain,
% 1.62/1.30 (((~![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))) | ($lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42) | (~$lesseq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, J!19)), 0)) | (~$greatereq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, M!14)), 0)))) <=> ((~![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))) | (~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | $lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42))),
% 1.62/1.30 inference(transitivity,[status(thm)],[84, 78])).
% 1.62/1.30 tff(86,plain,
% 1.62/1.30 ((~![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))) | ($lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42) | (~$lesseq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, J!19)), 0)) | (~$greatereq($sum(tptp_fun_S_21($sum(-1, I!18)), $product(-1, M!14)), 0)))),
% 1.62/1.30 inference(quant_inst,[status(thm)],[])).
% 1.62/1.30 tff(87,plain,
% 1.62/1.30 ((~![R: $int] : ($lesseq(get3(A2!17, R), 42) | (~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))) | (~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | $lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42)),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.62/1.30 tff(88,plain,
% 1.62/1.30 ($lesseq(get3(A2!17, tptp_fun_S_21($sum(-1, I!18))), 42)),
% 1.62/1.30 inference(unit_resolution,[status(thm)],[87, 77, 70, 68])).
% 1.62/1.30 tff(89,plain,
% 1.62/1.30 ($lesseq($sum(I!18, $product(-1, R!22)), 0)),
% 1.62/1.30 inference(and_elim,[status(thm)],[59])).
% 1.62/1.30 tff(90,plain,
% 1.62/1.30 ((~$greatereq($sum(J!19, $product(-1, R!22)), 0)) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)) | $lesseq($sum(I!18, $product(-1, J!19)), 0)),
% 1.62/1.30 inference(theory_lemma,[status(thm)],[])).
% 1.62/1.30 tff(91,plain,
% 1.62/1.30 (~$greatereq($sum(J!19, $product(-1, R!22)), 0)),
% 1.62/1.30 inference(unit_resolution,[status(thm)],[90, 89, 61])).
% 1.62/1.30 tff(92,plain,
% 1.62/1.30 ($greatereq($sum(N!13, $product(-1, R!22)), 0)),
% 1.62/1.30 inference(and_elim,[status(thm)],[59])).
% 1.62/1.30 tff(93,plain,
% 1.62/1.30 (^[R: $int] : refl(($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0))) <=> ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0))))),
% 1.62/1.30 inference(bind,[status(th)],[])).
% 1.62/1.30 tff(94,plain,
% 1.62/1.30 (![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0))) <=> ![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))),
% 1.62/1.30 inference(quant_intro,[status(thm)],[93])).
% 1.62/1.30 tff(95,plain,
% 1.62/1.30 (^[R: $int] : trans(monotonicity(trans(monotonicity(rewrite(((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0)) <=> (~($lesseq($sum(R, $product(-1, J!19)), 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0))))), ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) <=> (~(~($lesseq($sum(R, $product(-1, J!19)), 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0))))))), rewrite((~(~($lesseq($sum(R, $product(-1, J!19)), 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0))))) <=> ($lesseq($sum(R, $product(-1, J!19)), 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))), ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) <=> ($lesseq($sum(R, $product(-1, J!19)), 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0))))), (((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) <=> (($lesseq($sum(R, $product(-1, J!19)), 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)))), rewrite((($lesseq($sum(R, $product(-1, J!19)), 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) <=> ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))), (((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) <=> ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))))),
% 1.62/1.30 inference(bind,[status(th)],[])).
% 1.62/1.30 tff(96,plain,
% 1.62/1.30 (![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0)) <=> ![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))),
% 1.62/1.30 inference(quant_intro,[status(thm)],[95])).
% 1.62/1.30 tff(97,plain,
% 1.62/1.30 (![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & $lesseq($sum(R, $product(-1, N!13)), 0))) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0))),
% 1.62/1.30 inference(and_elim,[status(thm)],[59])).
% 1.62/1.30 tff(98,plain,
% 1.62/1.30 (![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.62/1.30 tff(99,plain,
% 1.62/1.30 (![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))),
% 1.62/1.30 inference(modus_ponens,[status(thm)],[98, 94])).
% 1.62/1.30 tff(100,plain,
% 1.62/1.30 (((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | (($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0) | $greatereq($sum(J!19, $product(-1, R!22)), 0) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)))) <=> ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0) | $greatereq($sum(J!19, $product(-1, R!22)), 0) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(101,plain,
% 1.62/1.30 (($greatereq($sum(J!19, $product(-1, R!22)), 0) | ($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0))) <=> (($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0) | $greatereq($sum(J!19, $product(-1, R!22)), 0) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(102,plain,
% 1.62/1.30 ((~$lesseq($sum(R!22, $product(-1, N!13)), 0)) <=> (~$greatereq($sum(N!13, $product(-1, R!22)), 0))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(103,plain,
% 1.62/1.30 (($sum($product(-1, get3(A3!20, R!22)), get3(A2!17, R!22)) = 0) <=> ($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0)),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(104,plain,
% 1.62/1.30 ($sum(get3(A2!17, R!22), $product(-1, get3(A3!20, R!22))) = $sum($product(-1, get3(A3!20, R!22)), get3(A2!17, R!22))),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(105,plain,
% 1.62/1.30 (($sum(get3(A2!17, R!22), $product(-1, get3(A3!20, R!22))) = 0) <=> ($sum($product(-1, get3(A3!20, R!22)), get3(A2!17, R!22)) = 0)),
% 1.62/1.30 inference(monotonicity,[status(thm)],[104])).
% 1.62/1.30 tff(106,plain,
% 1.62/1.30 (($sum(get3(A2!17, R!22), $product(-1, get3(A3!20, R!22))) = 0) <=> ($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0)),
% 1.62/1.30 inference(transitivity,[status(thm)],[105, 103])).
% 1.62/1.30 tff(107,plain,
% 1.62/1.30 ($lesseq($sum($product(-1, J!19), R!22), 0) <=> $greatereq($sum(J!19, $product(-1, R!22)), 0)),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(108,plain,
% 1.62/1.30 ($sum(R!22, $product(-1, J!19)) = $sum($product(-1, J!19), R!22)),
% 1.62/1.30 inference(rewrite,[status(thm)],[])).
% 1.62/1.30 tff(109,plain,
% 1.62/1.30 ($lesseq($sum(R!22, $product(-1, J!19)), 0) <=> $lesseq($sum($product(-1, J!19), R!22), 0)),
% 1.62/1.30 inference(monotonicity,[status(thm)],[108])).
% 1.62/1.30 tff(110,plain,
% 1.62/1.30 ($lesseq($sum(R!22, $product(-1, J!19)), 0) <=> $greatereq($sum(J!19, $product(-1, R!22)), 0)),
% 1.62/1.30 inference(transitivity,[status(thm)],[109, 107])).
% 1.62/1.30 tff(111,plain,
% 1.62/1.30 (($lesseq($sum(R!22, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R!22), $product(-1, get3(A3!20, R!22))) = 0) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0))) <=> ($greatereq($sum(J!19, $product(-1, R!22)), 0) | ($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)))),
% 1.62/1.31 inference(monotonicity,[status(thm)],[110, 106, 102])).
% 1.62/1.31 tff(112,plain,
% 1.62/1.31 (($lesseq($sum(R!22, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R!22), $product(-1, get3(A3!20, R!22))) = 0) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0))) <=> (($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0) | $greatereq($sum(J!19, $product(-1, R!22)), 0) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)))),
% 1.62/1.31 inference(transitivity,[status(thm)],[111, 101])).
% 1.62/1.31 tff(113,plain,
% 1.62/1.31 (((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($lesseq($sum(R!22, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R!22), $product(-1, get3(A3!20, R!22))) = 0) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0)))) <=> ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | (($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0) | $greatereq($sum(J!19, $product(-1, R!22)), 0) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0))))),
% 1.62/1.31 inference(monotonicity,[status(thm)],[112])).
% 1.62/1.31 tff(114,plain,
% 1.62/1.31 (((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($lesseq($sum(R!22, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R!22), $product(-1, get3(A3!20, R!22))) = 0) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0)))) <=> ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0) | $greatereq($sum(J!19, $product(-1, R!22)), 0) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)))),
% 1.62/1.31 inference(transitivity,[status(thm)],[113, 100])).
% 1.62/1.31 tff(115,plain,
% 1.62/1.31 ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($lesseq($sum(R!22, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R!22), $product(-1, get3(A3!20, R!22))) = 0) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0)))),
% 1.62/1.31 inference(quant_inst,[status(thm)],[])).
% 1.62/1.31 tff(116,plain,
% 1.62/1.31 ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0) | $greatereq($sum(J!19, $product(-1, R!22)), 0) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0))),
% 1.62/1.31 inference(modus_ponens,[status(thm)],[115, 114])).
% 1.62/1.31 tff(117,plain,
% 1.62/1.31 (($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0) | $greatereq($sum(J!19, $product(-1, R!22)), 0)),
% 1.62/1.31 inference(unit_resolution,[status(thm)],[116, 99, 92])).
% 1.62/1.31 tff(118,plain,
% 1.62/1.31 ($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0),
% 1.62/1.31 inference(unit_resolution,[status(thm)],[117, 91])).
% 1.62/1.31 tff(119,plain,
% 1.62/1.31 ((~($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))) = 0)) | $greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))), 0)),
% 1.62/1.31 inference(theory_lemma,[status(thm)],[])).
% 1.62/1.31 tff(120,plain,
% 1.62/1.31 ($greatereq($sum(get3(A3!20, R!22), $product(-1, get3(A2!17, R!22))), 0)),
% 1.62/1.31 inference(unit_resolution,[status(thm)],[119, 118])).
% 1.62/1.31 tff(121,plain,
% 1.62/1.31 (^[R: $int] : refl(($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0))) <=> ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0))))),
% 1.62/1.31 inference(bind,[status(th)],[])).
% 1.62/1.31 tff(122,plain,
% 1.62/1.31 (![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0))) <=> ![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))),
% 1.62/1.31 inference(quant_intro,[status(thm)],[121])).
% 1.62/1.31 tff(123,plain,
% 1.62/1.31 (^[R: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0)) <=> (~((~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0))))), ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) <=> (~(~((~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0))))))), rewrite((~(~((~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0))))) <=> ((~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))), ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) <=> ((~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0))))), (((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)) <=> (((~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)))), rewrite((((~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)) <=> ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))), (((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)) <=> ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))))),
% 1.62/1.31 inference(bind,[status(th)],[])).
% 1.62/1.31 tff(124,plain,
% 1.62/1.31 (![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42)) <=> ![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))),
% 1.62/1.31 inference(quant_intro,[status(thm)],[123])).
% 1.62/1.31 tff(125,plain,
% 1.62/1.31 (![R: $int] : ((~($greatereq($sum(R, $product(-1, I!18)), 0) & $lesseq($sum(R, $product(-1, N!13)), 0))) | $greatereq(get3(A2!17, R), 42))),
% 1.62/1.31 inference(and_elim,[status(thm)],[59])).
% 1.62/1.31 tff(126,plain,
% 1.62/1.31 (![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))),
% 1.62/1.31 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.62/1.31 tff(127,plain,
% 1.62/1.31 (![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))),
% 1.62/1.31 inference(modus_ponens,[status(thm)],[126, 122])).
% 1.62/1.31 tff(128,plain,
% 1.62/1.31 (((~![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ((~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | $greatereq(get3(A2!17, R!22), 42) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)))) <=> ((~![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | $greatereq(get3(A2!17, R!22), 42) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)))),
% 1.62/1.31 inference(rewrite,[status(thm)],[])).
% 1.62/1.31 tff(129,plain,
% 1.62/1.31 (($greatereq(get3(A2!17, R!22), 42) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0))) <=> ((~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | $greatereq(get3(A2!17, R!22), 42) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)))),
% 1.62/1.31 inference(rewrite,[status(thm)],[])).
% 1.62/1.31 tff(130,plain,
% 1.62/1.31 ((~$greatereq($sum(R!22, $product(-1, I!18)), 0)) <=> (~$lesseq($sum(I!18, $product(-1, R!22)), 0))),
% 1.62/1.31 inference(rewrite,[status(thm)],[])).
% 1.62/1.31 tff(131,plain,
% 1.62/1.31 (($greatereq(get3(A2!17, R!22), 42) | (~$greatereq($sum(R!22, $product(-1, I!18)), 0)) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0))) <=> ($greatereq(get3(A2!17, R!22), 42) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)))),
% 1.62/1.31 inference(monotonicity,[status(thm)],[130, 102])).
% 1.62/1.31 tff(132,plain,
% 1.62/1.31 (($greatereq(get3(A2!17, R!22), 42) | (~$greatereq($sum(R!22, $product(-1, I!18)), 0)) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0))) <=> ((~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | $greatereq(get3(A2!17, R!22), 42) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)))),
% 1.62/1.31 inference(transitivity,[status(thm)],[131, 129])).
% 1.62/1.31 tff(133,plain,
% 1.62/1.31 (((~![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($greatereq(get3(A2!17, R!22), 42) | (~$greatereq($sum(R!22, $product(-1, I!18)), 0)) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0)))) <=> ((~![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ((~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | $greatereq(get3(A2!17, R!22), 42) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0))))),
% 1.62/1.31 inference(monotonicity,[status(thm)],[132])).
% 1.62/1.31 tff(134,plain,
% 1.62/1.31 (((~![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($greatereq(get3(A2!17, R!22), 42) | (~$greatereq($sum(R!22, $product(-1, I!18)), 0)) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0)))) <=> ((~![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | $greatereq(get3(A2!17, R!22), 42) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)))),
% 1.62/1.31 inference(transitivity,[status(thm)],[133, 128])).
% 1.62/1.31 tff(135,plain,
% 1.62/1.31 ((~![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($greatereq(get3(A2!17, R!22), 42) | (~$greatereq($sum(R!22, $product(-1, I!18)), 0)) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0)))),
% 1.62/1.31 inference(quant_inst,[status(thm)],[])).
% 1.62/1.31 tff(136,plain,
% 1.62/1.31 ((~![R: $int] : ($greatereq(get3(A2!17, R), 42) | (~$greatereq($sum(R, $product(-1, I!18)), 0)) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | $greatereq(get3(A2!17, R!22), 42) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0))),
% 1.62/1.31 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.62/1.31 tff(137,plain,
% 1.62/1.31 ($greatereq(get3(A2!17, R!22), 42)),
% 1.62/1.31 inference(unit_resolution,[status(thm)],[136, 127, 89, 92])).
% 1.62/1.31 tff(138,plain,
% 1.62/1.31 (((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))) | ($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)),
% 1.62/1.31 inference(tautology,[status(thm)],[])).
% 1.62/1.31 tff(139,plain,
% 1.62/1.31 ($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0),
% 1.62/1.31 inference(unit_resolution,[status(thm)],[138, 66])).
% 1.62/1.31 tff(140,plain,
% 1.62/1.31 ((~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | $lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))), 0)),
% 1.62/1.31 inference(theory_lemma,[status(thm)],[])).
% 1.62/1.31 tff(141,plain,
% 1.62/1.31 ($lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))), 0)),
% 1.62/1.31 inference(unit_resolution,[status(thm)],[140, 139])).
% 1.62/1.31 tff(142,plain,
% 1.62/1.31 ($false),
% 1.62/1.31 inference(theory_lemma,[status(thm)],[141, 65, 137, 120, 88])).
% 1.62/1.31 tff(143,plain,(((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))) | $lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.31 tff(144,plain,
% 1.62/1.31 ((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))),
% 1.62/1.31 inference(unit_resolution,[status(thm)],[143, 65])).
% 1.62/1.31 tff(145,plain,
% 1.62/1.31 (^[R: $int] : refl(((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))))) <=> ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))))))),
% 1.62/1.31 inference(bind,[status(th)],[])).
% 1.62/1.31 tff(146,plain,
% 1.62/1.31 (![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))))) <=> ![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))),
% 1.62/1.31 inference(quant_intro,[status(thm)],[145])).
% 1.62/1.31 tff(147,plain,
% 1.62/1.31 (^[R: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0)) <=> (~((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))))), ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) <=> (~(~((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))))))), rewrite((~(~((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))))) <=> ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)))), ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) <=> ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))))), rewrite(($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)) <=> (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))))), (((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) <=> (((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))))))), rewrite((((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0))) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))))) <=> ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))), (((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) <=> ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))))),
% 1.62/1.31 inference(bind,[status(th)],[])).
% 1.62/1.31 tff(148,plain,
% 1.62/1.31 (![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))) <=> ![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))),
% 1.62/1.31 inference(quant_intro,[status(thm)],[147])).
% 1.62/1.31 tff(149,plain,
% 1.62/1.31 (![R: $int] : ((~($greatereq($sum(R, $product(-1, M!14)), 0) & $lesseq($sum(R, $product(-1, J!19)), 0))) | ($lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0) & $greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0) & ($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0) & $lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))),
% 1.62/1.31 inference(and_elim,[status(thm)],[59])).
% 1.62/1.31 tff(150,plain,
% 1.62/1.31 (![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))),
% 1.62/1.31 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.62/1.31 tff(151,plain,
% 1.62/1.31 (![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))),
% 1.62/1.31 inference(modus_ponens,[status(thm)],[150, 146])).
% 1.62/1.31 tff(152,plain,
% 1.62/1.31 (((~![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))) | ((~$lesseq($sum(I!18, $product(-1, J!19)), 1)) | (~$lesseq($sum(M!14, $product(-1, I!18)), -1)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0)))))) <=> ((~![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))) | (~$lesseq($sum(I!18, $product(-1, J!19)), 1)) | (~$lesseq($sum(M!14, $product(-1, I!18)), -1)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0)))))),
% 1.62/1.31 inference(rewrite,[status(thm)],[])).
% 1.62/1.31 tff(153,plain,
% 1.62/1.31 (((~$lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0)) | (~$greatereq($sum($sum(-1, I!18), $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(1, J!19)))), 0))))) <=> ((~$lesseq($sum(I!18, $product(-1, J!19)), 1)) | (~$lesseq($sum(M!14, $product(-1, I!18)), -1)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0)))))),
% 1.62/1.31 inference(rewrite,[status(thm)],[])).
% 1.62/1.31 tff(154,plain,
% 1.62/1.31 (((~![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))) | ((~$lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0)) | (~$greatereq($sum($sum(-1, I!18), $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))) <=> ((~![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))) | ((~$lesseq($sum(I!18, $product(-1, J!19)), 1)) | (~$lesseq($sum(M!14, $product(-1, I!18)), -1)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))))))),
% 1.62/1.31 inference(monotonicity,[status(thm)],[153])).
% 1.62/1.31 tff(155,plain,
% 1.62/1.31 (((~![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))) | ((~$lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0)) | (~$greatereq($sum($sum(-1, I!18), $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))) <=> ((~![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))) | (~$lesseq($sum(I!18, $product(-1, J!19)), 1)) | (~$lesseq($sum(M!14, $product(-1, I!18)), -1)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0)))))),
% 1.62/1.31 inference(transitivity,[status(thm)],[154, 152])).
% 1.62/1.31 tff(156,plain,
% 1.62/1.31 ((~![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))) | ((~$lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0)) | (~$greatereq($sum($sum(-1, I!18), $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))),
% 1.62/1.31 inference(quant_inst,[status(thm)],[])).
% 1.62/1.31 tff(157,plain,
% 1.62/1.31 ((~![R: $int] : ((~$lesseq($sum(R, $product(-1, J!19)), 0)) | (~$greatereq($sum(R, $product(-1, M!14)), 0)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21(R))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21(R))), 0)) | (~($sum(get3(A3!20, R), $product(-1, get3(A2!17, tptp_fun_S_21(R)))) = 0)) | (~$lesseq($sum(get3(A3!20, R), $product(-1, get3(A3!20, $sum(1, J!19)))), 0)))))) | (~$lesseq($sum(I!18, $product(-1, J!19)), 1)) | (~$lesseq($sum(M!14, $product(-1, I!18)), -1)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))))),
% 1.62/1.31 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.62/1.31 tff(158,plain,
% 1.62/1.31 ((~$lesseq($sum(I!18, $product(-1, J!19)), 1)) | (~$lesseq($sum(M!14, $product(-1, I!18)), -1)) | (~((~$lesseq($sum(M!14, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~$greatereq($sum(J!19, $product(-1, tptp_fun_S_21($sum(-1, I!18)))), 0)) | (~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, tptp_fun_S_21($sum(-1, I!18))))) = 0)) | (~$greatereq($sum(get3(A3!20, $sum(1, J!19)), $product(-1, get3(A3!20, $sum(-1, I!18)))), 0))))),
% 1.62/1.31 inference(unit_resolution,[status(thm)],[157, 151])).
% 1.62/1.31 tff(159,plain,
% 1.62/1.31 (~$lesseq($sum(I!18, $product(-1, J!19)), 1)),
% 1.62/1.31 inference(unit_resolution,[status(thm)],[158, 144, 64])).
% 1.62/1.31 tff(160,plain,
% 1.62/1.31 (^[R: $int] : refl(($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0)) <=> ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0)))),
% 1.62/1.31 inference(bind,[status(th)],[])).
% 1.62/1.31 tff(161,plain,
% 1.62/1.31 (![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0)) <=> ![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))),
% 1.62/1.31 inference(quant_intro,[status(thm)],[160])).
% 1.62/1.31 tff(162,plain,
% 1.62/1.31 (^[R: $int] : trans(monotonicity(trans(monotonicity(rewrite(((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0))) <=> (~($lesseq($sum(R, $product(-1, J!19)), 0) | $greatereq($sum(R, $product(-1, I!18)), 0)))), ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) <=> (~(~($lesseq($sum(R, $product(-1, J!19)), 0) | $greatereq($sum(R, $product(-1, I!18)), 0)))))), rewrite((~(~($lesseq($sum(R, $product(-1, J!19)), 0) | $greatereq($sum(R, $product(-1, I!18)), 0)))) <=> ($lesseq($sum(R, $product(-1, J!19)), 0) | $greatereq($sum(R, $product(-1, I!18)), 0))), ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) <=> ($lesseq($sum(R, $product(-1, J!19)), 0) | $greatereq($sum(R, $product(-1, I!18)), 0)))), (((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) <=> (($lesseq($sum(R, $product(-1, J!19)), 0) | $greatereq($sum(R, $product(-1, I!18)), 0)) | (get3(A2!17, R) = 42)))), rewrite((($lesseq($sum(R, $product(-1, J!19)), 0) | $greatereq($sum(R, $product(-1, I!18)), 0)) | (get3(A2!17, R) = 42)) <=> ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))), (((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) <=> ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))))),
% 1.62/1.31 inference(bind,[status(th)],[])).
% 1.62/1.31 tff(163,plain,
% 1.62/1.31 (![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42)) <=> ![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))),
% 1.62/1.31 inference(quant_intro,[status(thm)],[162])).
% 1.62/1.31 tff(164,plain,
% 1.62/1.31 (![R: $int] : ((~((~$lesseq($sum(R, $product(-1, J!19)), 0)) & (~$greatereq($sum(R, $product(-1, I!18)), 0)))) | (get3(A2!17, R) = 42))),
% 1.62/1.31 inference(and_elim,[status(thm)],[59])).
% 1.62/1.31 tff(165,plain,
% 1.62/1.31 (![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))),
% 1.62/1.31 inference(modus_ponens,[status(thm)],[164, 163])).
% 1.62/1.31 tff(166,plain,
% 1.62/1.31 (![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))),
% 1.62/1.31 inference(modus_ponens,[status(thm)],[165, 161])).
% 1.62/1.31 tff(167,plain,
% 1.62/1.31 (((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))) | ($lesseq($sum(I!18, $product(-1, J!19)), 1) | (get3(A2!17, $sum(-1, I!18)) = 42))) <=> ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))) | $lesseq($sum(I!18, $product(-1, J!19)), 1) | (get3(A2!17, $sum(-1, I!18)) = 42))),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(168,plain,
% 1.62/1.32 (($lesseq($sum(I!18, $product(-1, J!19)), 1) | (get3(A2!17, $sum(-1, I!18)) = 42) | $false) <=> ($lesseq($sum(I!18, $product(-1, J!19)), 1) | (get3(A2!17, $sum(-1, I!18)) = 42))),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(169,plain,
% 1.62/1.32 ($greatereq(-1, 0) <=> $false),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(170,plain,
% 1.62/1.32 ($sum($sum(-1, I!18), $product(-1, I!18)) = -1),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(171,plain,
% 1.62/1.32 ($greatereq($sum($sum(-1, I!18), $product(-1, I!18)), 0) <=> $greatereq(-1, 0)),
% 1.62/1.32 inference(monotonicity,[status(thm)],[170])).
% 1.62/1.32 tff(172,plain,
% 1.62/1.32 ($greatereq($sum($sum(-1, I!18), $product(-1, I!18)), 0) <=> $false),
% 1.62/1.32 inference(transitivity,[status(thm)],[171, 169])).
% 1.62/1.32 tff(173,plain,
% 1.62/1.32 ($lesseq($sum(-1, $sum(I!18, $product(-1, J!19))), 0) <=> $lesseq($sum(I!18, $product(-1, J!19)), 1)),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(174,plain,
% 1.62/1.32 ($sum($sum(-1, I!18), $product(-1, J!19)) = $sum(-1, $sum(I!18, $product(-1, J!19)))),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(175,plain,
% 1.62/1.32 ($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) <=> $lesseq($sum(-1, $sum(I!18, $product(-1, J!19))), 0)),
% 1.62/1.32 inference(monotonicity,[status(thm)],[174])).
% 1.62/1.32 tff(176,plain,
% 1.62/1.32 ($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) <=> $lesseq($sum(I!18, $product(-1, J!19)), 1)),
% 1.62/1.32 inference(transitivity,[status(thm)],[175, 173])).
% 1.62/1.32 tff(177,plain,
% 1.62/1.32 (($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) | (get3(A2!17, $sum(-1, I!18)) = 42) | $greatereq($sum($sum(-1, I!18), $product(-1, I!18)), 0)) <=> ($lesseq($sum(I!18, $product(-1, J!19)), 1) | (get3(A2!17, $sum(-1, I!18)) = 42) | $false)),
% 1.62/1.32 inference(monotonicity,[status(thm)],[176, 172])).
% 1.62/1.32 tff(178,plain,
% 1.62/1.32 (($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) | (get3(A2!17, $sum(-1, I!18)) = 42) | $greatereq($sum($sum(-1, I!18), $product(-1, I!18)), 0)) <=> ($lesseq($sum(I!18, $product(-1, J!19)), 1) | (get3(A2!17, $sum(-1, I!18)) = 42))),
% 1.62/1.32 inference(transitivity,[status(thm)],[177, 168])).
% 1.62/1.32 tff(179,plain,
% 1.62/1.32 (((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))) | ($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) | (get3(A2!17, $sum(-1, I!18)) = 42) | $greatereq($sum($sum(-1, I!18), $product(-1, I!18)), 0))) <=> ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))) | ($lesseq($sum(I!18, $product(-1, J!19)), 1) | (get3(A2!17, $sum(-1, I!18)) = 42)))),
% 1.62/1.32 inference(monotonicity,[status(thm)],[178])).
% 1.62/1.32 tff(180,plain,
% 1.62/1.32 (((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))) | ($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) | (get3(A2!17, $sum(-1, I!18)) = 42) | $greatereq($sum($sum(-1, I!18), $product(-1, I!18)), 0))) <=> ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))) | $lesseq($sum(I!18, $product(-1, J!19)), 1) | (get3(A2!17, $sum(-1, I!18)) = 42))),
% 1.62/1.32 inference(transitivity,[status(thm)],[179, 167])).
% 1.62/1.32 tff(181,plain,
% 1.62/1.32 ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))) | ($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) | (get3(A2!17, $sum(-1, I!18)) = 42) | $greatereq($sum($sum(-1, I!18), $product(-1, I!18)), 0))),
% 1.62/1.32 inference(quant_inst,[status(thm)],[])).
% 1.62/1.32 tff(182,plain,
% 1.62/1.32 ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | (get3(A2!17, R) = 42) | $greatereq($sum(R, $product(-1, I!18)), 0))) | $lesseq($sum(I!18, $product(-1, J!19)), 1) | (get3(A2!17, $sum(-1, I!18)) = 42)),
% 1.62/1.32 inference(modus_ponens,[status(thm)],[181, 180])).
% 1.62/1.32 tff(183,plain,
% 1.62/1.32 (get3(A2!17, $sum(-1, I!18)) = 42),
% 1.62/1.32 inference(unit_resolution,[status(thm)],[182, 166, 159])).
% 1.62/1.32 tff(184,plain,
% 1.62/1.32 ((~(get3(A2!17, $sum(-1, I!18)) = 42)) | $lesseq(get3(A2!17, $sum(-1, I!18)), 42)),
% 1.62/1.32 inference(theory_lemma,[status(thm)],[])).
% 1.62/1.32 tff(185,plain,
% 1.62/1.32 ($lesseq(get3(A2!17, $sum(-1, I!18)), 42)),
% 1.62/1.32 inference(unit_resolution,[status(thm)],[184, 183])).
% 1.62/1.32 tff(186,plain,
% 1.62/1.32 ($greatereq($sum(N!13, $product(-1, I!18)), 0)),
% 1.62/1.32 inference(and_elim,[status(thm)],[59])).
% 1.62/1.32 tff(187,plain,
% 1.62/1.32 ($greatereq($sum(N!13, $product(-1, I!18)), -1) | (~$greatereq($sum(N!13, $product(-1, I!18)), 0))),
% 1.62/1.32 inference(theory_lemma,[status(thm)],[])).
% 1.62/1.32 tff(188,plain,
% 1.62/1.32 ($greatereq($sum(N!13, $product(-1, I!18)), -1)),
% 1.62/1.32 inference(unit_resolution,[status(thm)],[187, 186])).
% 1.62/1.32 tff(189,plain,
% 1.62/1.32 (((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | (($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0) | $lesseq($sum(I!18, $product(-1, J!19)), 1) | (~$greatereq($sum(N!13, $product(-1, I!18)), -1)))) <=> ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0) | $lesseq($sum(I!18, $product(-1, J!19)), 1) | (~$greatereq($sum(N!13, $product(-1, I!18)), -1)))),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(190,plain,
% 1.62/1.32 (($lesseq($sum(I!18, $product(-1, J!19)), 1) | ($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0) | (~$greatereq($sum(N!13, $product(-1, I!18)), -1))) <=> (($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0) | $lesseq($sum(I!18, $product(-1, J!19)), 1) | (~$greatereq($sum(N!13, $product(-1, I!18)), -1)))),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(191,plain,
% 1.62/1.32 ((~$lesseq($sum($sum(-1, I!18), $product(-1, N!13)), 0)) <=> (~$greatereq($sum(N!13, $product(-1, I!18)), -1))),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(192,plain,
% 1.62/1.32 (($sum($product(-1, get3(A3!20, $sum(-1, I!18))), get3(A2!17, $sum(-1, I!18))) = 0) <=> ($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0)),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(193,plain,
% 1.62/1.32 ($sum(get3(A2!17, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(-1, I!18)))) = $sum($product(-1, get3(A3!20, $sum(-1, I!18))), get3(A2!17, $sum(-1, I!18)))),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(194,plain,
% 1.62/1.32 (($sum(get3(A2!17, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(-1, I!18)))) = 0) <=> ($sum($product(-1, get3(A3!20, $sum(-1, I!18))), get3(A2!17, $sum(-1, I!18))) = 0)),
% 1.62/1.32 inference(monotonicity,[status(thm)],[193])).
% 1.62/1.32 tff(195,plain,
% 1.62/1.32 (($sum(get3(A2!17, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(-1, I!18)))) = 0) <=> ($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0)),
% 1.62/1.32 inference(transitivity,[status(thm)],[194, 192])).
% 1.62/1.32 tff(196,plain,
% 1.62/1.32 (($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) | ($sum(get3(A2!17, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(-1, I!18)))) = 0) | (~$lesseq($sum($sum(-1, I!18), $product(-1, N!13)), 0))) <=> ($lesseq($sum(I!18, $product(-1, J!19)), 1) | ($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0) | (~$greatereq($sum(N!13, $product(-1, I!18)), -1)))),
% 1.62/1.32 inference(monotonicity,[status(thm)],[176, 195, 191])).
% 1.62/1.32 tff(197,plain,
% 1.62/1.32 (($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) | ($sum(get3(A2!17, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(-1, I!18)))) = 0) | (~$lesseq($sum($sum(-1, I!18), $product(-1, N!13)), 0))) <=> (($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0) | $lesseq($sum(I!18, $product(-1, J!19)), 1) | (~$greatereq($sum(N!13, $product(-1, I!18)), -1)))),
% 1.62/1.32 inference(transitivity,[status(thm)],[196, 190])).
% 1.62/1.32 tff(198,plain,
% 1.62/1.32 (((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) | ($sum(get3(A2!17, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(-1, I!18)))) = 0) | (~$lesseq($sum($sum(-1, I!18), $product(-1, N!13)), 0)))) <=> ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | (($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0) | $lesseq($sum(I!18, $product(-1, J!19)), 1) | (~$greatereq($sum(N!13, $product(-1, I!18)), -1))))),
% 1.62/1.32 inference(monotonicity,[status(thm)],[197])).
% 1.62/1.32 tff(199,plain,
% 1.62/1.32 (((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) | ($sum(get3(A2!17, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(-1, I!18)))) = 0) | (~$lesseq($sum($sum(-1, I!18), $product(-1, N!13)), 0)))) <=> ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0) | $lesseq($sum(I!18, $product(-1, J!19)), 1) | (~$greatereq($sum(N!13, $product(-1, I!18)), -1)))),
% 1.62/1.32 inference(transitivity,[status(thm)],[198, 189])).
% 1.62/1.32 tff(200,plain,
% 1.62/1.32 ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($lesseq($sum($sum(-1, I!18), $product(-1, J!19)), 0) | ($sum(get3(A2!17, $sum(-1, I!18)), $product(-1, get3(A3!20, $sum(-1, I!18)))) = 0) | (~$lesseq($sum($sum(-1, I!18), $product(-1, N!13)), 0)))),
% 1.62/1.32 inference(quant_inst,[status(thm)],[])).
% 1.62/1.32 tff(201,plain,
% 1.62/1.32 ((~![R: $int] : ($lesseq($sum(R, $product(-1, J!19)), 0) | ($sum(get3(A2!17, R), $product(-1, get3(A3!20, R))) = 0) | (~$lesseq($sum(R, $product(-1, N!13)), 0)))) | ($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0) | $lesseq($sum(I!18, $product(-1, J!19)), 1) | (~$greatereq($sum(N!13, $product(-1, I!18)), -1))),
% 1.62/1.32 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.62/1.32 tff(202,plain,
% 1.62/1.32 (($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0) | $lesseq($sum(I!18, $product(-1, J!19)), 1)),
% 1.62/1.32 inference(unit_resolution,[status(thm)],[201, 99, 188])).
% 1.62/1.32 tff(203,plain,
% 1.62/1.32 ($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0),
% 1.62/1.32 inference(unit_resolution,[status(thm)],[202, 159])).
% 1.62/1.32 tff(204,plain,
% 1.62/1.32 ((~($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))) = 0)) | $lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))), 0)),
% 1.62/1.32 inference(theory_lemma,[status(thm)],[])).
% 1.62/1.32 tff(205,plain,
% 1.62/1.32 ($lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A2!17, $sum(-1, I!18)))), 0)),
% 1.62/1.32 inference(unit_resolution,[status(thm)],[204, 203])).
% 1.62/1.32 tff(206,plain,
% 1.62/1.32 ($false),
% 1.62/1.32 inference(theory_lemma,[status(thm)],[205, 65, 137, 120, 185])).
% 1.62/1.32 tff(207,plain,($lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.32 tff(208,plain,
% 1.62/1.32 (((~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)) | ![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))) <=> ((~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)) | ![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))))),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(209,plain,
% 1.62/1.32 ((![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))) <=> ((~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)) | ![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))))),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(210,plain,
% 1.62/1.32 (^[S: $int] : trans(monotonicity(rewrite(($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)) <=> (~((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))))), ((~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) <=> (~(~((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))))))), rewrite((~(~((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))))) <=> ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))), ((~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) <=> ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))))),
% 1.62/1.32 inference(bind,[status(th)],[])).
% 1.62/1.32 tff(211,plain,
% 1.62/1.32 (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) <=> ![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))),
% 1.62/1.32 inference(quant_intro,[status(thm)],[210])).
% 1.62/1.32 tff(212,plain,
% 1.62/1.32 ((![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))) <=> (![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)))),
% 1.62/1.32 inference(monotonicity,[status(thm)],[211])).
% 1.62/1.32 tff(213,plain,
% 1.62/1.32 ((![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))) <=> ((~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)) | ![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))))),
% 1.62/1.32 inference(transitivity,[status(thm)],[212, 209])).
% 1.62/1.32 tff(214,plain,
% 1.62/1.32 (![S: $int] : (~($greatereq($sum(S, $product(-1, I!18)), 0) & $lesseq($sum(S, $product(-1, N!13)), 0) & ($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0))) | (~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0))),
% 1.62/1.32 inference(and_elim,[status(thm)],[59])).
% 1.62/1.32 tff(215,plain,
% 1.62/1.32 ((~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)) | ![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))),
% 1.62/1.32 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.62/1.32 tff(216,plain,
% 1.62/1.32 ((~$lesseq($sum(get3(A3!20, $sum(-1, I!18)), $product(-1, get3(A3!20, R!22))), 0)) | ![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))),
% 1.62/1.32 inference(modus_ponens,[status(thm)],[215, 208])).
% 1.62/1.32 tff(217,plain,
% 1.62/1.32 (![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))),
% 1.62/1.32 inference(unit_resolution,[status(thm)],[216, 207])).
% 1.62/1.32 tff(218,plain,
% 1.62/1.32 (((~![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))) | ((~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)))) <=> ((~![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)))),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(219,plain,
% 1.62/1.32 (((~$lesseq($sum(I!18, $product(-1, R!22)), 0)) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | $false) <=> ((~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)))),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(220,plain,
% 1.62/1.32 ((~$true) <=> $false),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(221,plain,
% 1.62/1.32 ((0 = 0) <=> $true),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(222,plain,
% 1.62/1.32 ($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, R!22))) = 0),
% 1.62/1.32 inference(rewrite,[status(thm)],[])).
% 1.62/1.32 tff(223,plain,
% 1.62/1.32 (($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, R!22))) = 0) <=> (0 = 0)),
% 1.62/1.32 inference(monotonicity,[status(thm)],[222])).
% 1.62/1.32 tff(224,plain,
% 1.62/1.32 (($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, R!22))) = 0) <=> $true),
% 1.62/1.32 inference(transitivity,[status(thm)],[223, 221])).
% 1.62/1.32 tff(225,plain,
% 1.62/1.32 ((~($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, R!22))) = 0)) <=> (~$true)),
% 1.62/1.32 inference(monotonicity,[status(thm)],[224])).
% 1.62/1.32 tff(226,plain,
% 1.62/1.32 ((~($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, R!22))) = 0)) <=> $false),
% 1.62/1.32 inference(transitivity,[status(thm)],[225, 220])).
% 1.62/1.32 tff(227,plain,
% 1.62/1.32 (((~$greatereq($sum(R!22, $product(-1, I!18)), 0)) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, R!22))) = 0))) <=> ((~$lesseq($sum(I!18, $product(-1, R!22)), 0)) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | $false)),
% 1.62/1.32 inference(monotonicity,[status(thm)],[130, 102, 226])).
% 1.62/1.32 tff(228,plain,
% 1.62/1.32 (((~$greatereq($sum(R!22, $product(-1, I!18)), 0)) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, R!22))) = 0))) <=> ((~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)))),
% 1.62/1.32 inference(transitivity,[status(thm)],[227, 219])).
% 1.62/1.32 tff(229,plain,
% 1.62/1.32 (((~![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))) | ((~$greatereq($sum(R!22, $product(-1, I!18)), 0)) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, R!22))) = 0)))) <=> ((~![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))) | ((~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0))))),
% 1.62/1.32 inference(monotonicity,[status(thm)],[228])).
% 1.62/1.32 tff(230,plain,
% 1.62/1.32 (((~![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))) | ((~$greatereq($sum(R!22, $product(-1, I!18)), 0)) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, R!22))) = 0)))) <=> ((~![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0)))),
% 1.62/1.33 inference(transitivity,[status(thm)],[229, 218])).
% 1.62/1.33 tff(231,plain,
% 1.62/1.33 ((~![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))) | ((~$greatereq($sum(R!22, $product(-1, I!18)), 0)) | (~$lesseq($sum(R!22, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, R!22), $product(-1, get3(A3!20, R!22))) = 0)))),
% 1.62/1.33 inference(quant_inst,[status(thm)],[])).
% 1.62/1.33 tff(232,plain,
% 1.62/1.33 ((~![S: $int] : ((~$greatereq($sum(S, $product(-1, I!18)), 0)) | (~$lesseq($sum(S, $product(-1, N!13)), 0)) | (~($sum(get3(A3!20, S), $product(-1, get3(A3!20, R!22))) = 0)))) | (~$greatereq($sum(N!13, $product(-1, R!22)), 0)) | (~$lesseq($sum(I!18, $product(-1, R!22)), 0))),
% 1.62/1.33 inference(modus_ponens,[status(thm)],[231, 230])).
% 1.62/1.33 tff(233,plain,
% 1.62/1.33 ($false),
% 1.62/1.33 inference(unit_resolution,[status(thm)],[232, 89, 92, 217])).
% 1.62/1.33 % SZS output end Proof
%------------------------------------------------------------------------------